
Time bar (total: 16.3s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 0 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 1 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 2 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 3 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 4 |
| 0% | 0% | 19% | 49.4% | 0% | 31.6% | 0% | 5 |
| 0% | 0% | 15.8% | 49.4% | 0% | 34.8% | 0% | 6 |
| 0% | 0% | 11.1% | 49.4% | 0% | 39.5% | 0% | 7 |
| 0% | 0% | 8.7% | 49.4% | 0% | 41.9% | 0% | 8 |
| 0% | 0% | 5.9% | 49.4% | 0% | 44.6% | 0% | 9 |
| 0% | 0% | 4.5% | 49.4% | 0% | 46% | 0% | 10 |
| 0% | 0% | 3.1% | 49.4% | 0% | 47.5% | 0% | 11 |
| 0% | 0% | 2.7% | 49.4% | 0% | 47.9% | 0% | 12 |
Compiled 27 to 19 computations (29.6% saved)
| 4.2s | 26 142× | 0 | invalid |
| 1.2s | 2 806× | 1 | valid |
| 940.0ms | 5 450× | 0 | valid |
ival-tan: 1.1s (22.3% of total)const: 954.0ms (19.8% of total)ival-add: 936.0ms (19.4% of total)ival-<=: 531.0ms (11% of total)ival-mult: 387.0ms (8% of total)ival-<: 271.0ms (5.6% of total)ival-fabs: 220.0ms (4.6% of total)ival-sub: 197.0ms (4.1% of total)ival-and: 109.0ms (2.3% of total)adjust: 78.0ms (1.6% of total)exact: 49.0ms (1% of total)ival-assert: 12.0ms (0.2% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 230 | 3 | (-2.0889617513847496e-164 1.3356537702641282e-166) | 3 | (9.631292575085681e-45 1.0816492021419804e-46) | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 1 | 0 | - | 0 | - | (tan.f64 (+.f64 x eps)) |
| 0 | 0 | - | 0 | - | eps |
| 0 | 0 | - | 0 | - | (+.f64 x eps) |
| 0 | 0 | - | 0 | - | (tan.f64 x) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) | cancellation | 230 | 6 |
tan.f64 | (tan.f64 (+.f64 x eps)) | sensitivity | 1 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 227 | 3 |
| - | 3 | 23 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 227 | 3 | 0 |
| - | 3 | 3 | 20 |
| number | freq |
|---|---|
| 0 | 26 |
| 1 | 229 |
| 2 | 1 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 49.0ms | 192× | 1 | valid |
| 16.0ms | 318× | 0 | valid |
| 3.0ms | 2× | 2 | valid |
Compiled 65 to 28 computations (56.9% saved)
ival-tan: 34.0ms (65.9% of total)ival-add: 9.0ms (17.5% of total)adjust: 4.0ms (7.8% of total)ival-sub: 3.0ms (5.8% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 39 |
| 1 | 38 | 35 |
| 2 | 86 | 35 |
| 3 | 169 | 35 |
| 4 | 312 | 35 |
| 5 | 383 | 35 |
| 6 | 469 | 35 |
| 7 | 509 | 35 |
| 8 | 521 | 35 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 13 | 7 |
| 2 | 18 | 7 |
| 3 | 24 | 7 |
| 4 | 32 | 7 |
| 5 | 47 | 7 |
| 6 | 80 | 7 |
| 7 | 110 | 7 |
| 8 | 159 | 7 |
| 9 | 175 | 7 |
| 10 | 183 | 7 |
| 0 | 183 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Outputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 60.8% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (tan.f64 x) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (tan.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 0 | 10 | 18 |
| 1 | 13 | 18 |
| 2 | 18 | 18 |
| 3 | 24 | 18 |
| 4 | 32 | 18 |
| 5 | 47 | 18 |
| 6 | 80 | 18 |
| 7 | 110 | 18 |
| 8 | 159 | 18 |
| 9 | 175 | 18 |
| 10 | 183 | 18 |
| 0 | 183 | 18 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(tan.f64 x) |
| Outputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) |
(tan.f64 (+.f64 x eps)) |
(tan.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
(tan.f64 x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0 | (+.f64 x eps) | |
| accuracy | 0.0 | (tan.f64 x) | |
| accuracy | 0.059303802495346905 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 25.002841220992565 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 32.0ms | 159× | 0 | valid |
| 10.0ms | 96× | 1 | valid |
| 1.0ms | 1× | 2 | valid |
Compiled 38 to 14 computations (63.2% saved)
ival-tan: 6.0ms (54% of total)adjust: 2.0ms (18% of total)ival-add: 2.0ms (18% of total)ival-sub: 2.0ms (18% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(tan.f64 x) |
| Outputs |
|---|
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
eps |
(+ eps x) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(* x (+ 1 (/ eps x))) |
(/ (sin x) (cos x)) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(* eps (+ 1 (/ x eps))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | eps | @ | 0 | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 2.0ms | x | @ | 0 | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 2.0ms | eps | @ | inf | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 1.0ms | x | @ | inf | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 1.0ms | eps | @ | -inf | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 157 | 950 |
| 1 | 464 | 884 |
| 2 | 1539 | 873 |
| 3 | 6077 | 710 |
| 0 | 8335 | 686 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
eps |
(+ eps x) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(* x (+ 1 (/ eps x))) |
(/ (sin x) (cos x)) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(* eps (+ 1 (/ x eps))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
| Outputs |
|---|
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(fma.f64 (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (/.f64 x (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal -1/3 binary64))) #s(literal 1/2 binary64))) x (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps)) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (*.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 4 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (*.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) #s(literal -1/3 binary64))) x) x (*.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps)) #s(literal 1 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
eps |
(+ eps x) |
(+.f64 eps x) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) eps) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 (fma.f64 (*.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(fma.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) eps (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (*.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps (/.f64 (sin.f64 x) (cos.f64 x))) |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 50 | 16 |
| 2 | 402 | 16 |
| 3 | 6137 | 16 |
| 0 | 8166 | 16 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(tan.f64 x) |
| Outputs |
|---|
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x) (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 (+.f64 (+.f64 eps x) x))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (fma.f64 (tan.f64 x) (-.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64)) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) |
(*.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))))) |
(*.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)))))) |
(*.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)))) |
(*.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))) |
(*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (/.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))) |
(*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (*.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64)))) |
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (/.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))))) |
(*.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) (*.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (pow.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64)))) |
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 (tan.f64 x)) (-.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))))) |
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (pow.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) #s(literal -1 binary64)) |
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x))) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (cos.f64 x)) |
(/.f64 (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (cos.f64 (+.f64 eps x))) (cos.f64 x)) |
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64))) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64))) (pow.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 4 binary64)))) |
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(*.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64))) |
(*.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x))) |
(*.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x))) |
(*.f64 (neg.f64 (+.f64 (tan.f64 eps) (tan.f64 x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))))) |
(*.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x))))) |
(*.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) |
(*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64))) |
(*.f64 (sin.f64 (+.f64 eps x)) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal -1 binary64)) |
(pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 1 binary64)) |
(/.f64 (+.f64 (tan.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (tan.f64 (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (tan.f64 (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64))) (-.f64 (tan.f64 x) (tan.f64 eps))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64))) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(/.f64 (neg.f64 (neg.f64 (+.f64 (tan.f64 eps) (tan.f64 x)))) (neg.f64 (neg.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (sin.f64 (+.f64 eps x)))) (neg.f64 (neg.f64 (cos.f64 (+.f64 eps x))))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))) |
(/.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 1 binary64)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) |
(/.f64 (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 1 binary64)) (cos.f64 (+.f64 eps x))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (-.f64 (tan.f64 x) (tan.f64 eps)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))))) |
(/.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (+.f64 (tan.f64 eps) (tan.f64 x))) (neg.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (neg.f64 (cos.f64 (+.f64 eps x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) |
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(neg.f64 (tan.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))) |
(neg.f64 (tan.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))) |
(neg.f64 (tan.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))) |
(neg.f64 (tan.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))) |
(neg.f64 (/.f64 (neg.f64 (+.f64 (tan.f64 eps) (tan.f64 x))) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)))) |
(neg.f64 (/.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (cos.f64 (+.f64 eps x)))) |
(neg.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))))) |
(neg.f64 (/.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 (+.f64 eps x))))) |
(tan.f64 (+.f64 eps x)) |
(exp.f64 (*.f64 (log.f64 (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 (+.f64 eps x)))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x))) |
(*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (-.f64 eps x) eps))) |
(*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (*.f64 (-.f64 eps x) eps) (-.f64 (*.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) |
(*.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x)) |
(*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x))) |
(*.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (*.f64 (-.f64 x eps) (+.f64 eps x))) |
(*.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) |
(*.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps)))) |
(*.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))) |
(*.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (/.f64 (+.f64 eps x) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (*.f64 (+.f64 eps x) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)))) |
(*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (+.f64 eps x)) |
(*.f64 (+.f64 eps x) (/.f64 (-.f64 x eps) (-.f64 x eps))) |
(*.f64 (+.f64 eps x) (*.f64 (-.f64 x eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x)) #s(literal -1 binary64)) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 eps eps (*.f64 x x))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) |
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64)))) |
(/.f64 (*.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal 1 binary64)) (-.f64 x eps)) |
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 x (/.f64 x (-.f64 x eps)))) (*.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 3 binary64))) (fma.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 x (/.f64 x (-.f64 x eps))) (fma.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))) (*.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x))) |
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (neg.f64 (neg.f64 (-.f64 x eps)))) |
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 eps eps (*.f64 x x)) (-.f64 x eps))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x eps)) (*.f64 (-.f64 x eps) (*.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (-.f64 x eps) (fma.f64 eps eps (*.f64 x x)))) |
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x)) |
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (-.f64 x eps) (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x)))) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps)) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps x))) |
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps))) |
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps)))) |
(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))) |
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x))) |
(-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps)))) |
(+.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(+.f64 eps x) |
(+.f64 x eps) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (sin.f64 x)) |
(*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))) |
(*.f64 #s(literal 1 binary64) (tan.f64 x)) |
(*.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal -1 binary64))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 1 binary64)) |
(/.f64 (neg.f64 (neg.f64 (sin.f64 x))) (neg.f64 (neg.f64 (cos.f64 x)))) |
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(neg.f64 (neg.f64 (tan.f64 x))) |
(tan.f64 x) |
(exp.f64 (*.f64 (log.f64 (tan.f64 x)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (neg.f64 (log.f64 (tan.f64 x))) #s(literal -1 binary64))) |
Compiled 7 565 to 1 005 computations (86.7% saved)
22 alts after pruning (21 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 255 | 21 | 276 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 255 | 22 | 277 |
| Status | Accuracy | Program |
|---|---|---|
| 61.0% | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) | |
| ▶ | 61.0% | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
| 60.8% | (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) | |
| 60.8% | (fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x))) | |
| 60.9% | (/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| 59.8% | (/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (neg.f64 (sin.f64 x)))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x))) | |
| 59.9% | (/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| 60.9% | (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| 60.9% | (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) | |
| ▶ | 60.8% | (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
| 60.5% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) | |
| 59.9% | (-.f64 (tan.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x)) | |
| ✓ | 60.8% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 60.4% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))) | |
| 60.2% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))) | |
| 60.9% | (*.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 x (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))) | |
| ▶ | 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
| ▶ | 98.4% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) | |
| ▶ | 100.0% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) |
| 99.7% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) eps)) |
Compiled 1 187 to 612 computations (48.4% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (tan.f64 eps) | |
| cost-diff | 0 | (+.f64 (tan.f64 eps) (tan.f64 x)) | |
| cost-diff | 0 | (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) | |
| cost-diff | 0 | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) | |
| cost-diff | 0 | (pow.f64 (sin.f64 x) #s(literal 2 binary64)) | |
| cost-diff | 0 | (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) | |
| cost-diff | 0 | (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) | |
| cost-diff | 0 | (+.f64 eps x) | |
| cost-diff | 0 | (sin.f64 (+.f64 eps x)) | |
| cost-diff | 0 | (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) | |
| cost-diff | 0 | (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) | |
| cost-diff | 0 | (cos.f64 eps) | |
| cost-diff | 0 | (sin.f64 eps) | |
| cost-diff | 0 | (/.f64 (sin.f64 eps) (cos.f64 eps)) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) | |
| cost-diff | 1 | (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) | |
| cost-diff | 1 | (*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps) | |
| cost-diff | 14 | (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) | |
| cost-diff | 15 | (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 58 | 1147 |
| 0 | 111 | 1147 |
| 1 | 194 | 1147 |
| 2 | 467 | 1147 |
| 3 | 1631 | 1110 |
| 4 | 6301 | 936 |
| 0 | 8240 | 915 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) |
(*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps) |
(fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) |
(neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) |
(fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) |
(sin.f64 x) |
x |
(fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) |
(/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) |
(fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) |
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
#s(literal 2 binary64) |
#s(literal 1 binary64) |
#s(literal -1/3 binary64) |
(/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
#s(literal 4 binary64) |
(neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
eps |
(*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) |
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) |
(/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) |
(*.f64 (sin.f64 x) eps) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(sin.f64 eps) |
eps |
(cos.f64 eps) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(sin.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
(cos.f64 (+.f64 eps x)) |
(tan.f64 x) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(sin.f64 x) |
x |
#s(literal 2 binary64) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
eps |
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
eps |
(tan.f64 x) |
x |
(-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))) |
#s(literal 1 binary64) |
(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (tan.f64 eps) (tan.f64 x)) |
#s(literal 2 binary64) |
(fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) |
(neg.f64 (tan.f64 x)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (neg.f64 eps) #s(literal -1 binary64)))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64))))) |
(*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (neg.f64 eps) #s(literal -1 binary64)))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)))) |
(fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) |
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (neg.f64 eps) #s(literal -1 binary64)))) (*.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (neg.f64 eps) #s(literal -1 binary64)))) eps) |
(neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) |
(fma.f64 (*.f64 #s(literal 1/3 binary64) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (neg.f64 eps) #s(literal -1 binary64)))) |
(fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(fma.f64 (*.f64 #s(literal -1/3 binary64) eps) (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x)) #s(literal -1 binary64)))) |
(*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) |
(*.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -2/3 binary64) (neg.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (sin.f64 x)) |
(sin.f64 x) |
x |
(fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) |
(fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -2/3 binary64) (neg.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) |
(fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) |
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
#s(literal 2 binary64) |
#s(literal 1 binary64) |
#s(literal -1/3 binary64) |
(/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) |
(/.f64 (-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(-.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal -1/3 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
#s(literal 4 binary64) |
(neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
eps |
(*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) |
(*.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64))) |
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) |
(fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) |
(/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) |
(*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x)) |
(*.f64 (sin.f64 x) eps) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(sin.f64 eps) |
eps |
(cos.f64 eps) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(sin.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
(cos.f64 (+.f64 eps x)) |
(tan.f64 x) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps)) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) |
(fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(sin.f64 x) |
x |
#s(literal 2 binary64) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
eps |
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
(fma.f64 (/.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (tan.f64 x))) |
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
eps |
(tan.f64 x) |
x |
(-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64))) |
#s(literal 1 binary64) |
(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (tan.f64 eps) (tan.f64 x)) |
#s(literal 2 binary64) |
(fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) |
(neg.f64 (tan.f64 x)) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.01171875 | (+.f64 (tan.f64 eps) (tan.f64 x)) | |
| accuracy | 0.015625 | (*.f64 (tan.f64 eps) (tan.f64 x)) | |
| accuracy | 0.1328125 | (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) | |
| accuracy | 24.994935743541635 | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) | |
| accuracy | 0.00390625 | (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) | |
| accuracy | 0.01171875 | (pow.f64 (sin.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.01953125 | (pow.f64 (cos.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.5366878961861644 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) | |
| accuracy | 0.0234375 | (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) | |
| accuracy | 0.025722509768442016 | (sin.f64 (+.f64 eps x)) | |
| accuracy | 0.05424472348973429 | (cos.f64 (+.f64 eps x)) | |
| accuracy | 25.002841220992565 | (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) | |
| accuracy | 0.0 | (/.f64 (sin.f64 eps) (cos.f64 eps)) | |
| accuracy | 0.0 | (sin.f64 eps) | |
| accuracy | 0.0 | (cos.f64 eps) | |
| accuracy | 0.9975955860967971 | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) | |
| accuracy | 0.01953125 | (pow.f64 (cos.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.024101269536884032 | (pow.f64 (sin.f64 x) #s(literal 4 binary64)) | |
| accuracy | 0.31640625 | (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) | |
| accuracy | 0.32421875 | (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) |
| 137.0ms | 100× | 1 | valid |
| 88.0ms | 153× | 0 | valid |
| 7.0ms | 2× | 3 | valid |
| 3.0ms | 1× | 2 | valid |
Compiled 2 232 to 122 computations (94.5% saved)
ival-mult: 54.0ms (31.8% of total)ival-div: 23.0ms (13.5% of total)ival-add: 19.0ms (11.2% of total)ival-tan: 14.0ms (8.2% of total)adjust: 14.0ms (8.2% of total)ival-pow2: 10.0ms (5.9% of total)ival-cos: 7.0ms (4.1% of total)ival-sin: 7.0ms (4.1% of total)ival-neg: 6.0ms (3.5% of total)ival-sub: 5.0ms (2.9% of total)const: 5.0ms (2.9% of total)ival-pow: 5.0ms (2.9% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) |
(fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps) |
(neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(sin.f64 eps) |
(cos.f64 eps) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(sin.f64 (+.f64 eps x)) |
(+.f64 eps x) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
(*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 (+.f64 eps x)) |
(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (tan.f64 eps) (tan.f64 x)) |
| Outputs |
|---|
-2/3 |
(- (* -2 (pow x 2)) 2/3) |
(- (* (pow x 2) (- (* -37/12 (pow x 2)) 2)) 2/3) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -154/45 (pow x 2)) 37/12)) 2)) 2/3) |
-1/3 |
(- (* -2/3 (* eps x)) 1/3) |
(- (* x (+ (* -4/3 x) (* -2/3 eps))) 1/3) |
(- (* x (+ (* -2/3 eps) (* x (- (* -17/9 (* eps x)) 4/3)))) 1/3) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3))))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2))))))))) |
1/3 |
(+ 1/3 (* 2/3 (* eps x))) |
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps)))) |
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps)))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
eps |
(+ eps x) |
(+ eps (* eps (pow x 2))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3)))) |
(+ (* x (+ (* x (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ (* x (- (+ (* x (- (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* -1 (/ (* (pow (sin eps) 2) (+ 1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(+ x (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (/ (* x (pow (sin eps) 3)) (pow (cos eps) 3)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* x (- (* x (- 1/3 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))))) (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps))) |
(* -2/3 x) |
(* x (- (* -17/9 (pow x 2)) 2/3)) |
(* x (- (* (pow x 2) (- (* -124/45 (pow x 2)) 17/9)) 2/3)) |
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2764/945 (pow x 2)) 124/45)) 17/9)) 2/3)) |
(* 1/3 eps) |
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x))))))) |
(pow x 4) |
(* (pow x 4) (+ 1 (* -2/3 (pow x 2)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3)))) |
1 |
(+ 1 (* -1 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2)) |
(* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
(* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
(* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
(/ (* x (sin eps)) (cos eps)) |
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps)))) |
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))) |
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps)))) |
(+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))) |
(+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(* eps (+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(sin (+ eps x)) |
x |
(* x (+ 1 (/ eps x))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(pow (sin x) 2) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) |
(pow (sin x) 4) |
(pow (cos x) 2) |
(cos (+ eps x)) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(sin (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(cos (- eps (* -1 x))) |
(+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(- (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(+ 1 (* -1/2 (pow eps 2))) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(/ (sin x) (cos x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(* eps (+ 1 (+ (* eps (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (- (* 2/3 (/ (sin x) (cos x))) (+ (* -1 (/ (* (pow (sin x) 2) (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (pow (cos x) 2))) (* -2/3 (/ (pow (sin x) 3) (pow (cos x) 3)))))))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (/ (* eps (pow (sin x) 3)) (pow (cos x) 3)))) (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* eps (- (* eps (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x))) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(cos x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) |
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(/ (* eps (sin x)) (cos x)) |
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x)))) |
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x)))) |
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x)))) |
(* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) |
(* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(* -1 (* (pow eps 4) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* eps (- (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* eps (+ 1 (/ x eps))) |
(* -1 (* (pow eps 2) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 2) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* -1 (* eps (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(* -1 (* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(sin (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(cos (- x (* -1 eps))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 56.0ms | x | @ | -inf | ((+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x))) (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (pow (sin x) 4) (pow (cos x) 2) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x))) |
| 22.0ms | x | @ | inf | ((+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x))) (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (pow (sin x) 4) (pow (cos x) 2) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x))) |
| 12.0ms | eps | @ | inf | ((+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x))) (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (pow (sin x) 4) (pow (cos x) 2) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x))) |
| 12.0ms | x | @ | 0 | ((+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x))) (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (pow (sin x) 4) (pow (cos x) 2) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x))) |
| 11.0ms | eps | @ | 0 | ((+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x))) (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (/ (sin (+ eps x)) (cos (+ eps x))) (tan x)) (/ (sin (+ eps x)) (cos (+ eps x))) (sin (+ eps x)) (+ eps x) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (pow (sin x) 2) (+ (* (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (* (tan eps) (tan x)) 1)) (neg (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (pow (* (tan eps) (tan x)) 2))) (+ (tan eps) (tan x)) (tan eps) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (pow (sin x) 4) (pow (cos x) 2) (cos (+ eps x)) (pow (* (tan eps) (tan x)) 2) (* (tan eps) (tan x))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 747 | 5061 |
| 1 | 2418 | 4868 |
| 0 | 8010 | 4589 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
-2/3 |
(- (* -2 (pow x 2)) 2/3) |
(- (* (pow x 2) (- (* -37/12 (pow x 2)) 2)) 2/3) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -154/45 (pow x 2)) 37/12)) 2)) 2/3) |
-1/3 |
(- (* -2/3 (* eps x)) 1/3) |
(- (* x (+ (* -4/3 x) (* -2/3 eps))) 1/3) |
(- (* x (+ (* -2/3 eps) (* x (- (* -17/9 (* eps x)) 4/3)))) 1/3) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3))))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2))))))))) |
1/3 |
(+ 1/3 (* 2/3 (* eps x))) |
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps)))) |
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps)))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
eps |
(+ eps x) |
(+ eps (* eps (pow x 2))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3)))) |
(+ (* x (+ (* x (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ (* x (- (+ (* x (- (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* -1 (/ (* (pow (sin eps) 2) (+ 1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(+ x (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (/ (* x (pow (sin eps) 3)) (pow (cos eps) 3)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* x (- (* x (- 1/3 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))))) (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps))) |
(* -2/3 x) |
(* x (- (* -17/9 (pow x 2)) 2/3)) |
(* x (- (* (pow x 2) (- (* -124/45 (pow x 2)) 17/9)) 2/3)) |
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2764/945 (pow x 2)) 124/45)) 17/9)) 2/3)) |
(* 1/3 eps) |
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x))))))) |
(pow x 4) |
(* (pow x 4) (+ 1 (* -2/3 (pow x 2)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3)))) |
1 |
(+ 1 (* -1 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2)) |
(* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
(* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
(* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
(/ (* x (sin eps)) (cos eps)) |
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps)))) |
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))) |
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps)))) |
(+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))) |
(+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(* eps (+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(sin (+ eps x)) |
x |
(* x (+ 1 (/ eps x))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(pow (sin x) 2) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) |
(pow (sin x) 4) |
(pow (cos x) 2) |
(cos (+ eps x)) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(sin (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(cos (- eps (* -1 x))) |
(+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(- (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(+ 1 (* -1/2 (pow eps 2))) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(/ (sin x) (cos x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(* eps (+ 1 (+ (* eps (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (- (* 2/3 (/ (sin x) (cos x))) (+ (* -1 (/ (* (pow (sin x) 2) (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (pow (cos x) 2))) (* -2/3 (/ (pow (sin x) 3) (pow (cos x) 3)))))))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ eps (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (/ (* eps (pow (sin x) 3)) (pow (cos x) 3)))) (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* eps (- (* eps (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) |
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x))) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(cos x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) |
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(/ (* eps (sin x)) (cos x)) |
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x)))) |
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x)))) |
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x)))) |
(* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) |
(* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(* -1 (* (pow eps 4) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* eps (- (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* eps (+ 1 (/ x eps))) |
(* -1 (* (pow eps 2) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 2) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* -1 (* eps (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(* -1 (* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(sin (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(cos (- x (* -1 eps))) |
| Outputs |
|---|
-2/3 |
#s(literal -2/3 binary64) |
(- (* -2 (pow x 2)) 2/3) |
(fma.f64 (*.f64 x x) #s(literal -2 binary64) #s(literal -2/3 binary64)) |
(- (* (pow x 2) (- (* -37/12 (pow x 2)) 2)) 2/3) |
(fma.f64 (fma.f64 #s(literal -37/12 binary64) (*.f64 x x) #s(literal -2 binary64)) (*.f64 x x) #s(literal -2/3 binary64)) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -154/45 (pow x 2)) 37/12)) 2)) 2/3) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -154/45 binary64) (*.f64 x x) #s(literal -37/12 binary64)) (*.f64 x x) #s(literal -2 binary64)) (*.f64 x x) #s(literal -2/3 binary64)) |
-1/3 |
#s(literal -1/3 binary64) |
(- (* -2/3 (* eps x)) 1/3) |
(fma.f64 (*.f64 #s(literal -2/3 binary64) x) eps #s(literal -1/3 binary64)) |
(- (* x (+ (* -4/3 x) (* -2/3 eps))) 1/3) |
(fma.f64 (fma.f64 #s(literal -4/3 binary64) x (*.f64 #s(literal -2/3 binary64) eps)) x #s(literal -1/3 binary64)) |
(- (* x (+ (* -2/3 eps) (* x (- (* -17/9 (* eps x)) 4/3)))) 1/3) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -17/9 binary64) (*.f64 eps x) #s(literal -4/3 binary64)) x (*.f64 #s(literal -2/3 binary64) eps)) x #s(literal -1/3 binary64)) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) |
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2))))) |
(*.f64 eps (fma.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3))))))) |
(fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 5/6 binary64) eps (*.f64 #s(literal 17/9 binary64) (pow.f64 eps #s(literal 3 binary64))))) x) eps (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 4/3 binary64) eps)) x (*.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
1/3 |
#s(literal 1/3 binary64) |
(+ 1/3 (* 2/3 (* eps x))) |
(fma.f64 (*.f64 eps x) #s(literal 2/3 binary64) #s(literal 1/3 binary64)) |
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps)))) |
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)) |
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps)))) |
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 (fma.f64 #s(literal 17/9 binary64) (*.f64 eps x) #s(literal 4/3 binary64)) x)) x #s(literal 1/3 binary64)) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (/.f64 x (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (/.f64 x (cos.f64 eps)) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (cos eps))) |
(fma.f64 (cos.f64 eps) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) #s(literal -1/2 binary64)) x (cos.f64 eps)) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) x (sin.f64 eps)) |
eps |
(+ eps x) |
(+.f64 eps x) |
(+ eps (* eps (pow x 2))) |
(fma.f64 (*.f64 eps x) x eps) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 eps x) x) #s(literal 2/3 binary64) eps) (*.f64 x x) eps) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 #s(literal 1/3 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 x x) #s(literal 2/45 binary64)) (*.f64 x x) #s(literal -1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x) |
(+ (* x (+ (* x (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (+ (* x (- (+ (* x (- (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* -1 (/ (* (pow (sin eps) 2) (+ 1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (+.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ x (/ (sin eps) (cos eps))) |
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) x) |
(+ (* x (+ 1 (/ (* x (pow (sin eps) 3)) (pow (cos eps) 3)))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (+ 1 (* x (- (* x (- 1/3 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1/3 binary64)) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) x #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(* -2/3 x) |
(*.f64 #s(literal -2/3 binary64) x) |
(* x (- (* -17/9 (pow x 2)) 2/3)) |
(*.f64 (fma.f64 #s(literal -17/9 binary64) (*.f64 x x) #s(literal -2/3 binary64)) x) |
(* x (- (* (pow x 2) (- (* -124/45 (pow x 2)) 17/9)) 2/3)) |
(*.f64 (fma.f64 (fma.f64 #s(literal -124/45 binary64) (*.f64 x x) #s(literal -17/9 binary64)) (*.f64 x x) #s(literal -2/3 binary64)) x) |
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2764/945 (pow x 2)) 124/45)) 17/9)) 2/3)) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -2764/945 binary64) (*.f64 x x) #s(literal -124/45 binary64)) (*.f64 x x) #s(literal -17/9 binary64)) (*.f64 x x) #s(literal -2/3 binary64)) x) |
(* 1/3 eps) |
(*.f64 #s(literal 1/3 binary64) eps) |
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x))) |
(fma.f64 (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64)) x (*.f64 #s(literal 1/3 binary64) eps)) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) eps (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) x (*.f64 #s(literal 1/3 binary64) eps)) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 17/9 binary64) (*.f64 #s(literal 4/3 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal 2/3 binary64))) x (*.f64 #s(literal 1/3 binary64) eps)) |
(pow x 4) |
(pow.f64 x #s(literal 4 binary64)) |
(* (pow x 4) (+ 1 (* -2/3 (pow x 2)))) |
(*.f64 (fma.f64 (*.f64 #s(literal -2/3 binary64) x) x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3)))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/5 binary64) (*.f64 x x) #s(literal -2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -34/945 binary64) (*.f64 x x) #s(literal 1/5 binary64)) (*.f64 x x) #s(literal -2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1 (pow x 2))) |
(-.f64 #s(literal 1 binary64) (*.f64 x x)) |
(+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1))) |
(fma.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal -1 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) #s(literal -1/2 binary64)) x) (sin.f64 eps)) x (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64))) x) (sin.f64 eps)) x (cos.f64 eps)) |
(/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2)) |
(*.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (*.f64 x x)) |
(* (pow x 2) (+ (* 2/3 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
(*.f64 (fma.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 2/3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (*.f64 x x) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (*.f64 x x)) |
(* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
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(* (pow x 2) (+ (* (pow x 2) (+ (* 2/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* (pow x 2) (+ (* 62/315 (/ (* (pow x 2) (pow (sin eps) 2)) (pow (cos eps) 2))) (* 17/45 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 62/315 binary64) (*.f64 x x)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 17/45 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (*.f64 x x) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 2/3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (*.f64 x x) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (*.f64 x x)) |
(/ (* x (sin eps)) (cos eps)) |
(*.f64 (sin.f64 eps) (/.f64 x (cos.f64 eps))) |
(* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps)))) |
(*.f64 (fma.f64 (/.f64 (*.f64 (sin.f64 eps) #s(literal 1/3 binary64)) (cos.f64 eps)) (*.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps))) x) |
(* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 x x)) (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (*.f64 (sin.f64 eps) #s(literal 1/3 binary64)) (cos.f64 eps))) (*.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps))) x) |
(* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps)))) |
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(+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))) |
(-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) |
(+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(fma.f64 (*.f64 (sin.f64 x) eps) (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(* eps (+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(*.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (fma.f64 (*.f64 (sin.f64 x) eps) (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 (fma.f64 (sin.f64 x) (/.f64 eps (cos.f64 x)) #s(literal 1 binary64)) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) eps) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(neg.f64 (fma.f64 (*.f64 (sin.f64 x) eps) (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
x |
(* x (+ 1 (/ eps x))) |
(fma.f64 (/.f64 eps x) x x) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow (sin x) 2) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(- (/ (* (+ 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (/.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 eps)) (/.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 1 binary64)) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64))) (/.f64 (neg.f64 (sin.f64 x)) (cos.f64 x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) |
(/.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))) |
(*.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x)) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) eps) (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps) |
(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(/ (* (pow (sin eps) 2) (pow (sin x) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))) |
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/ (* (sin eps) (sin x)) (* (cos eps) (cos x))) |
(*.f64 (/.f64 (sin.f64 x) (cos.f64 eps)) (/.f64 (sin.f64 eps) (cos.f64 x))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 (/.f64 (neg.f64 eps) x) (neg.f64 x) x) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(* eps (+ 1 (+ (* eps (+ (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) eps) (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
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(- (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) |
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))))) |
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(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 #s(literal -1/6 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
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(+ 1 (* -1/2 (pow eps 2))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
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(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
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(fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
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(sin x) |
(sin.f64 x) |
(+ (sin x) (* eps (cos x))) |
(fma.f64 (cos.f64 x) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps (sin.f64 x)) |
(* eps (+ 1 (+ (* eps (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (+ 1 (+ (* eps (- (+ (* eps (- (+ 1/3 (+ (* 1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (- (* 2/3 (/ (sin x) (cos x))) (+ (* -1 (/ (* (pow (sin x) 2) (- (/ (sin x) (cos x)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (pow (cos x) 2))) (* -2/3 (/ (pow (sin x) 3) (pow (cos x) 3)))))))) (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (-.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal 2/3 binary64)) (cos.f64 x)) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(literal -2/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64) #s(literal 1/3 binary64)))) eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(+ eps (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps) |
(+ (* eps (+ 1 (/ (* eps (pow (sin x) 3)) (pow (cos x) 3)))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* eps (+ 1 (* eps (- (* eps (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x))) |
(+.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(*.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 eps)) |
(* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) eps) (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x)) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps (cos.f64 x)) |
(/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) |
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps eps)) |
(* (pow eps 2) (+ (* 2/3 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* (pow eps 2) (+ (* (pow eps 2) (+ (* 17/45 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* (pow eps 2) (+ (* (pow eps 2) (+ (* 2/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* (pow eps 2) (+ (* 62/315 (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2))) (* 17/45 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(/ (* eps (sin x)) (cos x)) |
(*.f64 (sin.f64 x) (/.f64 eps (cos.f64 x))) |
(* eps (+ (* 1/3 (/ (* (pow eps 2) (sin x)) (cos x))) (/ (sin x) (cos x)))) |
(*.f64 (fma.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal 1/3 binary64)) (cos.f64 x)) (*.f64 eps eps) (/.f64 (sin.f64 x) (cos.f64 x))) eps) |
(* eps (+ (* (pow eps 2) (+ (* 2/15 (/ (* (pow eps 2) (sin x)) (cos x))) (* 1/3 (/ (sin x) (cos x))))) (/ (sin x) (cos x)))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) #s(literal 1/3 binary64)) (cos.f64 x))) (pow.f64 eps #s(literal 3 binary64)) (*.f64 (sin.f64 x) (/.f64 eps (cos.f64 x)))) |
(* eps (+ (* (pow eps 2) (+ (* 1/3 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* 17/315 (/ (* (pow eps 2) (sin x)) (cos x))) (* 2/15 (/ (sin x) (cos x))))))) (/ (sin x) (cos x)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 17/315 binary64) (*.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) #s(literal 2/15 binary64)) (cos.f64 x))) (*.f64 eps eps) (/.f64 (*.f64 (sin.f64 x) #s(literal 1/3 binary64)) (cos.f64 x))) (pow.f64 eps #s(literal 3 binary64)) (*.f64 (sin.f64 x) (/.f64 eps (cos.f64 x)))) |
(* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) |
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(* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(*.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) eps) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))) eps) |
(* -1 (* (pow eps 4) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(*.f64 (*.f64 (neg.f64 (pow.f64 eps #s(literal 4 binary64))) (sin.f64 x)) (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
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(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
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(* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(*.f64 (*.f64 (sin.f64 x) (neg.f64 eps)) (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(* eps (- (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
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(* eps (+ 1 (/ x eps))) |
(fma.f64 (/.f64 x eps) eps eps) |
(* -1 (* (pow eps 2) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(*.f64 (*.f64 (*.f64 eps eps) (neg.f64 (sin.f64 x))) (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(* (pow eps 2) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(*.f64 (*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) eps) eps) |
(* -1 (* eps (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps))))) |
(*.f64 eps (fma.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
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(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps)) eps))) (pow.f64 eps #s(literal 4 binary64))) |
(* -1 (* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(*.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) eps) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))) (neg.f64 eps)) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (/.f64 (neg.f64 x) eps) (neg.f64 eps) eps) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(fma.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (neg.f64 eps) eps) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 57 | 665 |
| 0 | 110 | 649 |
| 1 | 485 | 546 |
| 2 | 4365 | 526 |
| 0 | 8147 | 515 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) |
(fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps) |
(neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(sin.f64 eps) |
(cos.f64 eps) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(sin.f64 (+.f64 eps x)) |
(+.f64 eps x) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(pow.f64 (sin.f64 x) #s(literal 2 binary64)) |
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
(*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 (+.f64 eps x)) |
(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (tan.f64 eps) (tan.f64 x)) |
| Outputs |
|---|
(*.f64 (-.f64 (pow.f64 (/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 (cos.f64 x) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) #s(literal -2 binary64))) (pow.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (cos.f64 x)) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (pow.f64 (/.f64 (cos.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) #s(literal -3 binary64)) #s(literal -1/27 binary64) (pow.f64 (/.f64 (cos.f64 x) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) #s(literal -3 binary64))) (pow.f64 (fma.f64 (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x)) (-.f64 (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x)) (/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (cos.f64 x))) (pow.f64 (/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (cos.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) (cos.f64 x)) (-.f64 (pow.f64 (/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 (cos.f64 x) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) #s(literal -2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x)) (-.f64 (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x)) (/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (cos.f64 x))) (pow.f64 (/.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (cos.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (/.f64 (cos.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) #s(literal -3 binary64)) #s(literal -1/27 binary64) (pow.f64 (/.f64 (cos.f64 x) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) #s(literal -3 binary64)))) #s(literal -1 binary64)) |
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(*.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (cos.f64 eps) #s(literal -1 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (sqrt.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (sin.f64 eps) #s(literal 1 binary64)) (pow.f64 (*.f64 (pow.f64 (cos.f64 eps) #s(literal -1 binary64)) (tan.f64 x)) #s(literal 1 binary64))) |
(*.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (pow.f64 (cos.f64 eps) #s(literal -1 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) (sqrt.f64 (*.f64 (tan.f64 eps) (tan.f64 x)))) |
(*.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 1 binary64)) |
(*.f64 (tan.f64 eps) (pow.f64 (*.f64 (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(*.f64 (tan.f64 eps) (*.f64 (tan.f64 x) #s(literal 1 binary64))) |
(*.f64 (tan.f64 eps) (tan.f64 x)) |
(*.f64 (tan.f64 x) (pow.f64 (*.f64 (tan.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(*.f64 (tan.f64 x) (*.f64 (tan.f64 eps) #s(literal 1 binary64))) |
(*.f64 (tan.f64 x) (tan.f64 eps)) |
(*.f64 (sin.f64 eps) (*.f64 (pow.f64 (cos.f64 eps) #s(literal -1 binary64)) (tan.f64 x))) |
(*.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x))) |
(pow.f64 (sqrt.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 1 binary64)) |
(/.f64 (*.f64 (neg.f64 (sin.f64 eps)) (tan.f64 x)) (neg.f64 (cos.f64 eps))) |
(/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps)) |
(/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x)) |
(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)) |
(/.f64 (*.f64 (tan.f64 x) (neg.f64 (sin.f64 eps))) (neg.f64 (cos.f64 eps))) |
(/.f64 (*.f64 (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (tan.f64 eps) #s(literal -1 binary64))) |
(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)) |
(/.f64 (*.f64 #s(literal 1 binary64) (tan.f64 x)) (pow.f64 (tan.f64 eps) #s(literal -1 binary64))) |
(/.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 eps)) (cos.f64 x))) |
(/.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 x) (neg.f64 (cos.f64 eps)))) |
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (pow.f64 (tan.f64 eps) #s(literal -1 binary64)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (pow.f64 (tan.f64 eps) #s(literal -1 binary64)) (cos.f64 x))) |
(/.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(/.f64 (tan.f64 x) (pow.f64 (tan.f64 eps) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 eps) (tan.f64 x))) #s(literal 1 binary64))) |
Compiled 81 153 to 6 140 computations (92.4% saved)
26 alts after pruning (23 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 023 | 16 | 1 039 |
| Fresh | 9 | 7 | 16 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 035 | 26 | 1 061 |
| Status | Accuracy | Program |
|---|---|---|
| 61.0% | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) | |
| ✓ | 61.0% | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
| ▶ | 60.8% | (fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x))) |
| 35.0% | (/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (tan.f64 x))) | |
| 60.9% | (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) | |
| ✓ | 60.8% | (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
| 60.5% | (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x)))) (tan.f64 x)) | |
| 60.5% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) | |
| ✓ | 60.8% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 60.4% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))) | |
| ▶ | 60.2% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))) |
| 99.7% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) | |
| 98.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) eps eps)) | |
| 99.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) | |
| 99.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) | |
| 98.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) | |
| ▶ | 98.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 #s(approx (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) (*.f64 #s(literal -2/3 binary64) x)) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) | |
| ▶ | 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) |
| 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) #s(literal 1/3 binary64)) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) | |
| ▶ | 100.0% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
| 99.7% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) eps)) | |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) | |
| 24.1% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps)) eps))) (pow.f64 eps #s(literal 4 binary64))))) |
Compiled 3 144 to 1 332 computations (57.6% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) | |
| cost-diff | 0 | (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) | |
| cost-diff | 1 | (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) | |
| cost-diff | 0 | (sin.f64 (+.f64 eps x)) | |
| cost-diff | 0 | (neg.f64 (sin.f64 (+.f64 eps x))) | |
| cost-diff | 1 | (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) | |
| cost-diff | 3 | (fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x))) | |
| cost-diff | 0 | #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (tan.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) | |
| cost-diff | 0 | (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) | |
| cost-diff | 1 | (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) | |
| cost-diff | 1 | (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) | |
| cost-diff | 2 | (neg.f64 (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) | |
| cost-diff | 16 | (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 96 | 1465 |
| 0 | 172 | 1455 |
| 1 | 319 | 1442 |
| 2 | 851 | 1421 |
| 3 | 3610 | 1298 |
| 0 | 8200 | 1265 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
(*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps) |
(fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) |
(*.f64 eps eps) |
eps |
(neg.f64 (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
(fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) |
(*.f64 eps (sin.f64 x)) |
(sin.f64 x) |
x |
(fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) |
#s(literal -1/3 binary64) |
(/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) |
(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) |
(tan.f64 x) |
#s(literal 1 binary64) |
(cos.f64 x) |
(/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x)) |
(fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) |
(neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) |
(pow.f64 (cos.f64 x) #s(literal -2 binary64)) |
#s(literal -2 binary64) |
(fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 (sin.f64 x) (tan.f64 x)) |
#s(literal 2 binary64) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) |
(fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) |
(*.f64 x x) |
x |
eps |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x) |
(pow.f64 x #s(literal 3 binary64)) |
#s(literal 3 binary64) |
#s(literal 1/3 binary64) |
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x))) |
(neg.f64 (sin.f64 (+.f64 eps x))) |
(sin.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
(/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) |
#s(literal 1 binary64) |
(neg.f64 (cos.f64 (+.f64 eps x))) |
(cos.f64 (+.f64 eps x)) |
(neg.f64 (tan.f64 x)) |
(tan.f64 x) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) |
(*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps) |
(fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) |
(*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) |
#s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) |
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)) |
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) |
#s(literal 2/3 binary64) |
eps |
(*.f64 #s(literal 4/3 binary64) x) |
#s(literal 4/3 binary64) |
x |
#s(literal 1/3 binary64) |
(*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) |
(fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) |
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(sin.f64 x) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
#s(literal 2 binary64) |
#s(literal 1 binary64) |
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) |
(/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) |
(*.f64 (sin.f64 x) eps) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
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(*.f64 eps eps) |
eps |
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(*.f64 eps (sin.f64 x)) |
(*.f64 (sin.f64 x) eps) |
(sin.f64 x) |
x |
(fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) |
(fma.f64 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (-.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) |
#s(literal -1/3 binary64) |
(/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) |
(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) |
(tan.f64 x) |
#s(literal 1 binary64) |
(cos.f64 x) |
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(neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) |
(pow.f64 (cos.f64 x) #s(literal -2 binary64)) |
#s(literal -2 binary64) |
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(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) |
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(pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 2 binary64)) |
(*.f64 (sin.f64 x) (tan.f64 x)) |
(*.f64 (tan.f64 x) (sin.f64 x)) |
#s(literal 2 binary64) |
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(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
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(*.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) |
(fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) |
(fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) |
(*.f64 x x) |
x |
eps |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))) |
(-.f64 (tan.f64 (+.f64 eps x)) #s(approx (tan x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))) |
(tan.f64 (+.f64 x eps)) |
(tan.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
#s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)) |
#s(approx (tan x) (fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x) |
(fma.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) |
(pow.f64 x #s(literal 3 binary64)) |
#s(literal 3 binary64) |
#s(literal 1/3 binary64) |
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(neg.f64 (sin.f64 (+.f64 eps x))) |
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(+.f64 eps x) |
eps |
x |
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#s(literal 1 binary64) |
(neg.f64 (cos.f64 (+.f64 eps x))) |
(cos.f64 (+.f64 eps x)) |
(neg.f64 (tan.f64 x)) |
(tan.f64 x) |
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(fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) |
(fma.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) |
(*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) |
#s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) |
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)) |
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) |
#s(literal 2/3 binary64) |
eps |
(*.f64 #s(literal 4/3 binary64) x) |
#s(literal 4/3 binary64) |
x |
#s(literal 1/3 binary64) |
(*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) |
(*.f64 (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64))) |
(fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) |
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(sin.f64 x) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
#s(literal 2 binary64) |
#s(literal 1 binary64) |
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) |
(fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64)) |
(/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) |
(*.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x)) |
(*.f64 (sin.f64 x) eps) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.23046875 | (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) | |
| accuracy | 0.3125 | (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) | |
| accuracy | 0.3203125 | (*.f64 #s(literal 4/3 binary64) x) | |
| accuracy | 0.6014202425464805 | #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) | |
| accuracy | 0.0 | (neg.f64 (cos.f64 (+.f64 eps x))) | |
| accuracy | 0.021816259768442016 | (sin.f64 (+.f64 eps x)) | |
| accuracy | 0.05424472348973429 | (cos.f64 (+.f64 eps x)) | |
| accuracy | 24.95173741332391 | (fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x))) | |
| accuracy | 0.0 | (+.f64 x eps) | |
| accuracy | 0.055397552495346905 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 0.5297447882557296 | #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)) | |
| accuracy | 24.964996493222515 | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))) | |
| accuracy | 0.0 | (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) | |
| accuracy | 0.0 | (*.f64 x x) | |
| accuracy | 0.5366878961861644 | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) | |
| accuracy | 0.9785646236900496 | #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) | |
| accuracy | 0.015625 | (*.f64 (sin.f64 x) (tan.f64 x)) | |
| accuracy | 0.01953125 | (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) | |
| accuracy | 0.0234375 | (pow.f64 (tan.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.15300751953688402 | (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
| 178.0ms | 101× | 1 | valid |
| 101.0ms | 151× | 0 | valid |
| 9.0ms | 3× | 5 | exit |
| 4.0ms | 1× | 3 | valid |
Compiled 2 728 to 195 computations (92.9% saved)
ival-mult: 59.0ms (26.2% of total)ival-div: 33.0ms (14.7% of total)ival-add: 32.0ms (14.2% of total)adjust: 23.0ms (10.2% of total)const: 18.0ms (8% of total)ival-pow2: 15.0ms (6.7% of total)ival-pow: 13.0ms (5.8% of total)ival-neg: 10.0ms (4.4% of total)ival-tan: 8.0ms (3.6% of total)ival-cos: 5.0ms (2.2% of total)ival-sin: 5.0ms (2.2% of total)ival-sub: 2.0ms (0.9% of total)exact: 1.0ms (0.4% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) |
(neg.f64 (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
(fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) |
(fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) |
(*.f64 x x) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
#s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)) |
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) |
(neg.f64 (sin.f64 (+.f64 eps x))) |
(sin.f64 (+.f64 eps x)) |
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) |
(*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps) |
(fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(*.f64 (sin.f64 x) (tan.f64 x)) |
(cos.f64 (+.f64 eps x)) |
(neg.f64 (cos.f64 (+.f64 eps x))) |
#s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) |
(*.f64 #s(literal 4/3 binary64) x) |
(*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) |
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) |
| Outputs |
|---|
-1/3 |
(- (* -2/3 (* eps x)) 1/3) |
(- (* x (+ (* -4/3 x) (* -2/3 eps))) 1/3) |
(- (* x (+ (* -2/3 eps) (* x (- (* -17/9 (* eps x)) 4/3)))) 1/3) |
1/3 |
(+ 1/3 (* 2/3 (* eps x))) |
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps)))) |
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps)))) |
(- (* -4/3 (pow x 2)) 1/3) |
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
eps |
(+ eps (* eps (pow x 2))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ eps x) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(/ -1 (cos eps)) |
(- (* -1 (/ (* x (sin eps)) (pow (cos eps) 2))) (/ 1 (cos eps))) |
(- (* x (- (* -1 (* x (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps))) |
(- (* x (- (* x (- (* -1 (* x (+ (* -1/6 (/ (sin eps) (pow (cos eps) 2))) (+ (* 1/2 (/ (sin eps) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3)))) (cos eps)))))) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps))) |
(* -1 (sin eps)) |
(- (* -1 (* x (cos eps))) (sin eps)) |
(- (* x (- (* 1/2 (* x (sin eps))) (cos eps))) (sin eps)) |
(- (* x (- (* x (- (* 1/6 (* x (cos eps))) (* -1/2 (sin eps)))) (cos eps))) (sin eps)) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
1 |
(+ 1 (* eps x)) |
(+ 1 (* x (+ eps (* (pow x 2) (- (* -1/6 eps) (* -1/2 eps)))))) |
(+ 1 (* x (+ eps (* (pow x 2) (- (+ (* -1/6 eps) (* (pow x 2) (- (* 1/120 eps) (+ (* -1/2 (- (* -1/6 eps) (* -1/2 eps))) (* 1/24 eps))))) (* -1/2 eps)))))) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3))))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2))))))))) |
(+ 1 (* 1/3 (pow eps 2))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 2/3 (pow eps 3)))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2))))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps))))))))))) |
(pow x 4) |
(* (pow x 4) (+ 1 (* 1/3 (pow x 2)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* 1/5 (pow x 2)))))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/5 (* 92/945 (pow x 2)))))))) |
(* (pow x 2) (+ 1 (* 1/6 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* 31/360 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 31/360 (* 173/5040 (pow x 2)))))))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(* -1 (cos eps)) |
(- (* x (sin eps)) (cos eps)) |
(- (* x (+ (sin eps) (* 1/2 (* x (cos eps))))) (cos eps)) |
(- (* x (+ (sin eps) (* x (- (* -1/6 (* x (sin eps))) (* -1/2 (cos eps)))))) (cos eps)) |
(* 4/3 x) |
(* 1/3 eps) |
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x))))))) |
(* 2/3 eps) |
(+ (* 2/3 eps) (* 4/3 x)) |
(- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))) 1/3) |
(- 1/3 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))))) |
(- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(* x (+ 1 (/ eps x))) |
(/ (sin x) (cos x)) |
(/ -1 (cos (+ eps x))) |
(* -1 (sin (+ eps x))) |
(sin (+ eps x)) |
(+ 1 (/ (* eps (sin x)) (cos x))) |
(* eps (+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 2) (cos x)) |
(cos (+ eps x)) |
(* -1 (cos (+ eps x))) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) |
(* x (+ 4/3 (* 2/3 (/ eps x)))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(/ -1 (cos (- eps (* -1 x)))) |
(* -1 (sin (- eps (* -1 x)))) |
(sin (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(* -1 (cos (- eps (* -1 x)))) |
(* -1 (* x (- (* -2/3 (/ eps x)) 4/3))) |
(- 1/3 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (* -1 (* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(/ -1 (cos x)) |
(- (* -1 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x))) |
(- (* eps (- (* -1 (* eps (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos x))) |
(- (* eps (- (* eps (- (* -1 (* eps (+ (* -1/6 (/ (sin x) (pow (cos x) 2))) (+ (* 1/2 (/ (sin x) (pow (cos x) 2))) (/ (* (sin x) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3)))) (cos x)))))) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos x))) |
(* -1 (sin x)) |
(- (* -1 (* eps (cos x))) (sin x)) |
(- (* eps (- (* 1/2 (* eps (sin x))) (cos x))) (sin x)) |
(- (* eps (- (* eps (- (* 1/6 (* eps (cos x))) (* -1/2 (sin x)))) (cos x))) (sin x)) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(cos x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(* -1 (cos x)) |
(- (* eps (sin x)) (cos x)) |
(- (* eps (+ (sin x) (* 1/2 (* eps (cos x))))) (cos x)) |
(- (* eps (+ (sin x) (* eps (- (* -1/6 (* eps (sin x))) (* -1/2 (cos x)))))) (cos x)) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(- (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))) |
(* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))) (* 1/3 (/ 1 eps)))) |
(* -1 (* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))) |
(* eps (- (* 1/3 (/ 1 eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))))) |
(* eps (+ 1 (/ x eps))) |
(/ (* eps (sin x)) (cos x)) |
(* eps (+ (/ 1 eps) (/ (sin x) (cos x)))) |
(* -1 (* (pow eps 4) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(* -1 (* (pow eps 3) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* eps (- (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* -1 (* (pow eps 2) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 2) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* eps (+ 2/3 (* 4/3 (/ x eps)))) |
(* -1 (* eps (+ (* -1 (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))) (* -1 (/ (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) eps))))) |
(* -1 (* eps (- (* -1 (/ (- 1/3 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (* -1 (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(/ -1 (cos (- x (* -1 eps)))) |
(* -1 (sin (- x (* -1 eps)))) |
(sin (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps)))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(cos (- x (* -1 eps))) |
(* -1 (cos (- x (* -1 eps)))) |
(* -1 (* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(* -1 (* eps (- (* -4/3 (/ x eps)) 2/3))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 26.0ms | eps | @ | inf | ((+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (+ (* (neg (sin (+ eps x))) (/ 1 (neg (cos (+ eps x))))) (neg (tan x))) (/ 1 (neg (cos (+ eps x)))) (neg (sin (+ eps x))) (sin (+ eps x)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (pow (* (sin x) (tan x)) 2) (pow (tan x) 2) (* (sin x) (tan x)) (cos (+ eps x)) (neg (cos (+ eps x))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (* 4/3 x) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (+ (* 2/3 eps) (* 4/3 x))) |
| 16.0ms | x | @ | -inf | ((+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (+ (* (neg (sin (+ eps x))) (/ 1 (neg (cos (+ eps x))))) (neg (tan x))) (/ 1 (neg (cos (+ eps x)))) (neg (sin (+ eps x))) (sin (+ eps x)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (pow (* (sin x) (tan x)) 2) (pow (tan x) 2) (* (sin x) (tan x)) (cos (+ eps x)) (neg (cos (+ eps x))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (* 4/3 x) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (+ (* 2/3 eps) (* 4/3 x))) |
| 13.0ms | x | @ | inf | ((+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (+ (* (neg (sin (+ eps x))) (/ 1 (neg (cos (+ eps x))))) (neg (tan x))) (/ 1 (neg (cos (+ eps x)))) (neg (sin (+ eps x))) (sin (+ eps x)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (pow (* (sin x) (tan x)) 2) (pow (tan x) 2) (* (sin x) (tan x)) (cos (+ eps x)) (neg (cos (+ eps x))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (* 4/3 x) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (+ (* 2/3 eps) (* 4/3 x))) |
| 9.0ms | eps | @ | 0 | ((+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (+ (* (neg (sin (+ eps x))) (/ 1 (neg (cos (+ eps x))))) (neg (tan x))) (/ 1 (neg (cos (+ eps x)))) (neg (sin (+ eps x))) (sin (+ eps x)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (pow (* (sin x) (tan x)) 2) (pow (tan x) 2) (* (sin x) (tan x)) (cos (+ eps x)) (neg (cos (+ eps x))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (* 4/3 x) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (+ (* 2/3 eps) (* 4/3 x))) |
| 8.0ms | x | @ | 0 | ((+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3))) (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2)) (- (tan (+ x eps)) (tan x)) (+ (* (/ (pow (sin x) 2) (pow (cos x) 2)) eps) eps) (/ (pow (sin x) 2) (pow (cos x) 2)) (* x x) (- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x) (+ (* (neg (sin (+ eps x))) (/ 1 (neg (cos (+ eps x))))) (neg (tan x))) (/ 1 (neg (cos (+ eps x)))) (neg (sin (+ eps x))) (sin (+ eps x)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (pow (* (sin x) (tan x)) 2) (pow (tan x) 2) (* (sin x) (tan x)) (cos (+ eps x)) (neg (cos (+ eps x))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (* 4/3 x) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (+ (* 2/3 eps) (* 4/3 x))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 726 | 5927 |
| 1 | 2368 | 5709 |
| 2 | 7941 | 5650 |
| 0 | 8117 | 5392 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
-1/3 |
(- (* -2/3 (* eps x)) 1/3) |
(- (* x (+ (* -4/3 x) (* -2/3 eps))) 1/3) |
(- (* x (+ (* -2/3 eps) (* x (- (* -17/9 (* eps x)) 4/3)))) 1/3) |
1/3 |
(+ 1/3 (* 2/3 (* eps x))) |
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps)))) |
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps)))) |
(- (* -4/3 (pow x 2)) 1/3) |
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
eps |
(+ eps (* eps (pow x 2))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ eps x) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(/ -1 (cos eps)) |
(- (* -1 (/ (* x (sin eps)) (pow (cos eps) 2))) (/ 1 (cos eps))) |
(- (* x (- (* -1 (* x (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps))) |
(- (* x (- (* x (- (* -1 (* x (+ (* -1/6 (/ (sin eps) (pow (cos eps) 2))) (+ (* 1/2 (/ (sin eps) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3)))) (cos eps)))))) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps))) |
(* -1 (sin eps)) |
(- (* -1 (* x (cos eps))) (sin eps)) |
(- (* x (- (* 1/2 (* x (sin eps))) (cos eps))) (sin eps)) |
(- (* x (- (* x (- (* 1/6 (* x (cos eps))) (* -1/2 (sin eps)))) (cos eps))) (sin eps)) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
1 |
(+ 1 (* eps x)) |
(+ 1 (* x (+ eps (* (pow x 2) (- (* -1/6 eps) (* -1/2 eps)))))) |
(+ 1 (* x (+ eps (* (pow x 2) (- (+ (* -1/6 eps) (* (pow x 2) (- (* 1/120 eps) (+ (* -1/2 (- (* -1/6 eps) (* -1/2 eps))) (* 1/24 eps))))) (* -1/2 eps)))))) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3))))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2))))))))) |
(+ 1 (* 1/3 (pow eps 2))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 2/3 (pow eps 3)))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2))))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps))))))))))) |
(pow x 4) |
(* (pow x 4) (+ 1 (* 1/3 (pow x 2)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* 1/5 (pow x 2)))))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/5 (* 92/945 (pow x 2)))))))) |
(* (pow x 2) (+ 1 (* 1/6 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* 31/360 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 31/360 (* 173/5040 (pow x 2)))))))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(* -1 (cos eps)) |
(- (* x (sin eps)) (cos eps)) |
(- (* x (+ (sin eps) (* 1/2 (* x (cos eps))))) (cos eps)) |
(- (* x (+ (sin eps) (* x (- (* -1/6 (* x (sin eps))) (* -1/2 (cos eps)))))) (cos eps)) |
(* 4/3 x) |
(* 1/3 eps) |
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x))))))) |
(* 2/3 eps) |
(+ (* 2/3 eps) (* 4/3 x)) |
(- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))) 1/3) |
(- 1/3 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))))) |
(- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) |
(+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(+ eps (/ (* eps (pow (sin x) 2)) (pow (cos x) 2))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(* x (+ 1 (/ eps x))) |
(/ (sin x) (cos x)) |
(/ -1 (cos (+ eps x))) |
(* -1 (sin (+ eps x))) |
(sin (+ eps x)) |
(+ 1 (/ (* eps (sin x)) (cos x))) |
(* eps (+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ (pow (sin x) 4) (pow (cos x) 2)) |
(/ (pow (sin x) 2) (cos x)) |
(cos (+ eps x)) |
(* -1 (cos (+ eps x))) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) |
(* x (+ 4/3 (* 2/3 (/ eps x)))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(/ -1 (cos (- eps (* -1 x)))) |
(* -1 (sin (- eps (* -1 x)))) |
(sin (- eps (* -1 x))) |
(cos (- eps (* -1 x))) |
(* -1 (cos (- eps (* -1 x)))) |
(* -1 (* x (- (* -2/3 (/ eps x)) 4/3))) |
(- 1/3 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(- (+ 1/3 (* -1 (* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(/ -1 (cos x)) |
(- (* -1 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x))) |
(- (* eps (- (* -1 (* eps (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos x))) |
(- (* eps (- (* eps (- (* -1 (* eps (+ (* -1/6 (/ (sin x) (pow (cos x) 2))) (+ (* 1/2 (/ (sin x) (pow (cos x) 2))) (/ (* (sin x) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3)))) (cos x)))))) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos x))) |
(* -1 (sin x)) |
(- (* -1 (* eps (cos x))) (sin x)) |
(- (* eps (- (* 1/2 (* eps (sin x))) (cos x))) (sin x)) |
(- (* eps (- (* eps (- (* 1/6 (* eps (cos x))) (* -1/2 (sin x)))) (cos x))) (sin x)) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(cos x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(* -1 (cos x)) |
(- (* eps (sin x)) (cos x)) |
(- (* eps (+ (sin x) (* 1/2 (* eps (cos x))))) (cos x)) |
(- (* eps (+ (sin x) (* eps (- (* -1/6 (* eps (sin x))) (* -1/2 (cos x)))))) (cos x)) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(- (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))) |
(* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))) (* 1/3 (/ 1 eps)))) |
(* -1 (* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))) |
(* eps (- (* 1/3 (/ 1 eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))))) |
(* eps (+ 1 (/ x eps))) |
(/ (* eps (sin x)) (cos x)) |
(* eps (+ (/ 1 eps) (/ (sin x) (cos x)))) |
(* -1 (* (pow eps 4) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(* -1 (* (pow eps 3) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* eps (- (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* -1 (* (pow eps 2) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 2) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* eps (+ 2/3 (* 4/3 (/ x eps)))) |
(* -1 (* eps (+ (* -1 (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))) (* -1 (/ (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) eps))))) |
(* -1 (* eps (- (* -1 (/ (- 1/3 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (* -1 (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(/ -1 (cos (- x (* -1 eps)))) |
(* -1 (sin (- x (* -1 eps)))) |
(sin (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps)))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(cos (- x (* -1 eps))) |
(* -1 (cos (- x (* -1 eps)))) |
(* -1 (* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(* -1 (* eps (- (* -4/3 (/ x eps)) 2/3))) |
| Outputs |
|---|
-1/3 |
#s(literal -1/3 binary64) |
(- (* -2/3 (* eps x)) 1/3) |
(fma.f64 (*.f64 #s(literal -2/3 binary64) eps) x #s(literal -1/3 binary64)) |
(- (* x (+ (* -4/3 x) (* -2/3 eps))) 1/3) |
(fma.f64 (fma.f64 #s(literal -4/3 binary64) x (*.f64 #s(literal -2/3 binary64) eps)) x #s(literal -1/3 binary64)) |
(- (* x (+ (* -2/3 eps) (* x (- (* -17/9 (* eps x)) 4/3)))) 1/3) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -17/9 binary64) (*.f64 x eps) #s(literal -4/3 binary64)) x (*.f64 #s(literal -2/3 binary64) eps)) x #s(literal -1/3 binary64)) |
1/3 |
#s(literal 1/3 binary64) |
(+ 1/3 (* 2/3 (* eps x))) |
(fma.f64 #s(literal 2/3 binary64) (*.f64 x eps) #s(literal 1/3 binary64)) |
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps)))) |
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)) |
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps)))) |
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 (fma.f64 #s(literal 17/9 binary64) (*.f64 x eps) #s(literal 4/3 binary64)) x)) x #s(literal 1/3 binary64)) |
(- (* -4/3 (pow x 2)) 1/3) |
(fma.f64 (*.f64 x x) #s(literal -4/3 binary64) #s(literal -1/3 binary64)) |
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -17/9 binary64) #s(literal -4/3 binary64)) (*.f64 x x) #s(literal -1/3 binary64)) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -248/135 binary64) (*.f64 x x) #s(literal -17/9 binary64)) (*.f64 x x) #s(literal -4/3 binary64)) (*.f64 x x) #s(literal -1/3 binary64)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 2/3 binary64) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (/.f64 x (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
eps |
(+ eps (* eps (pow x 2))) |
(fma.f64 (*.f64 x x) eps eps) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (* -1/3 eps) (* -1 eps)))))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (- (+ (* -1/3 eps) (* (pow x 2) (- (* 2/45 eps) (+ (* -1 (- (* -1/3 eps) (* -1 eps))) (* 1/3 eps))))) (* -1 eps)))))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 2/45 binary64) eps (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 #s(literal 1/3 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (/.f64 x (cos.f64 eps)) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ eps x) |
(+.f64 x eps) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) x) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x) |
(/ -1 (cos eps)) |
(/.f64 #s(literal -1 binary64) (cos.f64 eps)) |
(- (* -1 (/ (* x (sin eps)) (pow (cos eps) 2))) (/ 1 (cos eps))) |
(neg.f64 (fma.f64 (sin.f64 eps) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 eps)))) |
(- (* x (- (* -1 (* x (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps))) |
(fma.f64 (neg.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (cos.f64 eps))) x (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) x (/.f64 #s(literal -1 binary64) (cos.f64 eps))) |
(- (* x (- (* x (- (* -1 (* x (+ (* -1/6 (/ (sin eps) (pow (cos eps) 2))) (+ (* 1/2 (/ (sin eps) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3)))) (cos eps)))))) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps))) |
(fma.f64 (fma.f64 (neg.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1/3 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (cos.f64 eps)) (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (cos.f64 eps))) x (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (cos.f64 eps))))) x (/.f64 (neg.f64 (sin.f64 eps)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 #s(literal -1 binary64) (cos.f64 eps))) |
(* -1 (sin eps)) |
(neg.f64 (sin.f64 eps)) |
(- (* -1 (* x (cos eps))) (sin eps)) |
(neg.f64 (fma.f64 (cos.f64 eps) x (sin.f64 eps))) |
(- (* x (- (* 1/2 (* x (sin eps))) (cos eps))) (sin eps)) |
(-.f64 (*.f64 (-.f64 (*.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/2 binary64)) (cos.f64 eps)) x) (sin.f64 eps)) |
(- (* x (- (* x (- (* 1/6 (* x (cos eps))) (* -1/2 (sin eps)))) (cos eps))) (sin eps)) |
(-.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 eps) (*.f64 (*.f64 (cos.f64 eps) x) #s(literal 1/6 binary64))) x) (cos.f64 eps)) x) (sin.f64 eps)) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (cos eps))) |
(fma.f64 (cos.f64 eps) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) x (cos.f64 eps)) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (cos.f64 eps)) x (sin.f64 eps)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* eps x)) |
(fma.f64 x eps #s(literal 1 binary64)) |
(+ 1 (* x (+ eps (* (pow x 2) (- (* -1/6 eps) (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/3 binary64)) eps eps) x #s(literal 1 binary64)) |
(+ 1 (* x (+ eps (* (pow x 2) (- (+ (* -1/6 eps) (* (pow x 2) (- (* 1/120 eps) (+ (* -1/2 (- (* -1/6 eps) (* -1/2 eps))) (* 1/24 eps))))) (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) eps) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal -1/6 binary64) eps))) (*.f64 x x) (*.f64 #s(literal 1/3 binary64) eps)) (*.f64 x x) eps) x #s(literal 1 binary64)) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) |
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2))))) |
(*.f64 eps (fma.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3))))))) |
(fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (+.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 17/9 binary64) (*.f64 #s(literal 1/3 binary64) eps)) eps) x) eps (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 4/3 binary64) eps)) x (*.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(+ 1 (* 1/3 (pow eps 2))) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 2/3 (pow eps 3)))))) |
(fma.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps))))))))))) |
(fma.f64 (fma.f64 (fma.f64 (+.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 17/9 binary64) (*.f64 #s(literal 1/3 binary64) eps)) eps) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(pow x 4) |
(pow.f64 x #s(literal 4 binary64)) |
(* (pow x 4) (+ 1 (* 1/3 (pow x 2)))) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* 1/5 (pow x 2)))))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/5 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/5 (* 92/945 (pow x 2)))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 92/945 binary64) (*.f64 x x) #s(literal 1/5 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 2) (+ 1 (* 1/6 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* 31/360 (pow x 2)))))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 31/360 binary64) (*.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 31/360 (* 173/5040 (pow x 2)))))))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 173/5040 binary64) (*.f64 x x) #s(literal 31/360 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x) |
(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/2 binary64)) (sin.f64 eps)) x (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) x) (sin.f64 eps)) x (cos.f64 eps)) |
(* -1 (cos eps)) |
(neg.f64 (cos.f64 eps)) |
(- (* x (sin eps)) (cos eps)) |
(-.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps)) |
(- (* x (+ (sin eps) (* 1/2 (* x (cos eps))))) (cos eps)) |
(-.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal 1/2 binary64) (sin.f64 eps)) x) (cos.f64 eps)) |
(- (* x (+ (sin eps) (* x (- (* -1/6 (* x (sin eps))) (* -1/2 (cos eps)))))) (cos eps)) |
(-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 eps) (*.f64 #s(literal -1/6 binary64) (*.f64 (sin.f64 eps) x))) x (sin.f64 eps)) x) (cos.f64 eps)) |
(* 4/3 x) |
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(* 2/3 eps) |
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(+ (* 2/3 eps) (* 4/3 x)) |
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(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
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(sin.f64 (+.f64 x eps)) |
(+ 1 (/ (* eps (sin x)) (cos x))) |
(fma.f64 (sin.f64 x) (/.f64 eps (cos.f64 x)) #s(literal 1 binary64)) |
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(* x (+ 4/3 (* 2/3 (/ eps x)))) |
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(* -1 (* x (- (* -2/3 (/ eps x)) 4/3))) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(/ -1 (cos x)) |
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(* -1 (sin x)) |
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(sin x) |
(sin.f64 x) |
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(* eps (+ 1 (+ (* eps (+ (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (+ 1 (+ (* eps (+ (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(+ 1 (+ (* eps (+ (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(+ 1 (+ (* eps (+ (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(cos x) |
(cos.f64 x) |
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(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
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(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps (cos.f64 x)) |
(* -1 (cos x)) |
(neg.f64 (cos.f64 x)) |
(- (* eps (sin x)) (cos x)) |
(-.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) |
(- (* eps (+ (sin x) (* 1/2 (* eps (cos x))))) (cos x)) |
(-.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) eps) (cos.f64 x)) |
(- (* eps (+ (sin x) (* eps (- (* -1/6 (* eps (sin x))) (* -1/2 (cos x)))))) (cos x)) |
(-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/6 binary64))) eps (sin.f64 x)) eps) (cos.f64 x)) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
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(- (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
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(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(*.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 eps)) |
(* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(*.f64 (fma.f64 (*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x)) eps (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (neg.f64 eps)) |
(* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))) |
(*.f64 (*.f64 (sin.f64 x) eps) (fma.f64 #s(literal -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))))) |
(* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))) (* 1/3 (/ 1 eps)))) |
(*.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (sin.f64 x) (/.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) eps))) eps) |
(* -1 (* eps (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))) |
(*.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1/3 binary64) (cos.f64 x))))) |
(* eps (- (* 1/3 (/ 1 eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))))) |
(*.f64 (neg.f64 (fma.f64 (fma.f64 #s(literal -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 (/.f64 x eps) eps eps) |
(/ (* eps (sin x)) (cos x)) |
(*.f64 (sin.f64 x) (/.f64 eps (cos.f64 x))) |
(* eps (+ (/ 1 eps) (/ (sin x) (cos x)))) |
(fma.f64 (sin.f64 x) (/.f64 eps (cos.f64 x)) #s(literal 1 binary64)) |
(* -1 (* (pow eps 4) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(*.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) (neg.f64 (sin.f64 x))) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
(*.f64 (fma.f64 (neg.f64 (sin.f64 x)) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (*.f64 eps eps)) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(*.f64 (fma.f64 (neg.f64 (sin.f64 x)) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (*.f64 eps eps))) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) (pow.f64 eps #s(literal 4 binary64))) |
(* -1 (* (pow eps 3) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 (sin.f64 x))) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
(*.f64 (fma.f64 (neg.f64 (sin.f64 x)) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (*.f64 eps eps)) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(*.f64 (fma.f64 (neg.f64 (sin.f64 x)) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) (*.f64 eps eps))) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(*.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(* eps (- (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(*.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) (neg.f64 eps)) |
(* -1 (* (pow eps 2) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(*.f64 (*.f64 eps (neg.f64 eps)) (*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x))) |
(* (pow eps 2) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(*.f64 (*.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) (neg.f64 eps)) eps) |
(* eps (+ 2/3 (* 4/3 (/ x eps)))) |
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) eps) |
(* -1 (* eps (+ (* -1 (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x)))))) (* -1 (/ (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) 1/3) eps))))) |
(*.f64 eps (fma.f64 (fma.f64 #s(literal -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) |
(* -1 (* eps (- (* -1 (/ (- 1/3 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (* -1 (* (sin x) (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* 1/3 (/ 1 (cos x))))))))) |
(*.f64 (neg.f64 (fma.f64 (fma.f64 #s(literal -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x))) (-.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1/3 binary64) (cos.f64 x)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) eps) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* -1 (* eps (- (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) 1))) |
(fma.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (neg.f64 eps) eps) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (/.f64 (neg.f64 x) eps) (neg.f64 eps) eps) |
(/ -1 (cos (- x (* -1 eps)))) |
(/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) |
(* -1 (sin (- x (* -1 eps)))) |
(neg.f64 (sin.f64 (+.f64 x eps))) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 x eps)) |
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps)))) |
(*.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) eps)) (neg.f64 eps)) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) eps)) eps))) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps)) eps))) (pow.f64 eps #s(literal 4 binary64))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) eps) (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (neg.f64 eps)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (neg.f64 eps)) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) (neg.f64 eps)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (neg.f64 eps)))) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 x eps)) |
(* -1 (cos (- x (* -1 eps)))) |
(neg.f64 (cos.f64 (+.f64 x eps))) |
(* -1 (* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(*.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)) (neg.f64 eps)) |
(* -1 (* eps (- (* -4/3 (/ x eps)) 2/3))) |
(*.f64 (fma.f64 (/.f64 x eps) #s(literal -4/3 binary64) #s(literal -2/3 binary64)) (neg.f64 eps)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 90 | 961 |
| 0 | 159 | 949 |
| 1 | 671 | 654 |
| 2 | 6324 | 654 |
| 0 | 9220 | 643 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) |
(neg.f64 (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) |
(fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) |
(fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
(fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) |
(*.f64 x x) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
#s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x)) |
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) |
(neg.f64 (sin.f64 (+.f64 eps x))) |
(sin.f64 (+.f64 eps x)) |
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) |
(*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps) |
(fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) |
(pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(*.f64 (sin.f64 x) (tan.f64 x)) |
(cos.f64 (+.f64 eps x)) |
(neg.f64 (cos.f64 (+.f64 eps x))) |
#s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) |
(*.f64 #s(literal 4/3 binary64) x) |
(*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) |
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) |
| Outputs |
|---|
(*.f64 (-.f64 (pow.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (*.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)))) #s(literal 2 binary64)) (pow.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (-.f64 (*.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x))) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))) |
(*.f64 (+.f64 (pow.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (*.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (-.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (*.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x))))) (pow.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (*.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)))) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (neg.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (neg.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (pow.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) #s(literal 2 binary64))) (-.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (neg.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)))) |
(/.f64 (-.f64 (pow.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (*.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)))) #s(literal 2 binary64))) (-.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (*.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)))))) |
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(neg.f64 (*.f64 (tan.f64 x) (neg.f64 (tan.f64 x)))) |
(-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(-.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 (tan.f64 x)))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 (neg.f64 (tan.f64 x))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(exp.f64 (-.f64 (log.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64)))) |
(exp.f64 (log.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 1/2 binary64))) |
(*.f64 (tan.f64 x) (sin.f64 x)) |
(*.f64 (sin.f64 x) (tan.f64 x)) |
(pow.f64 (*.f64 (tan.f64 x) (sin.f64 x)) #s(literal 1 binary64)) |
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) |
(exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 x) (sin.f64 x))) #s(literal 1 binary64))) |
(*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 (+.f64 x eps)))) |
(*.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) |
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))) (cos.f64 (-.f64 eps x))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))))) |
(neg.f64 (neg.f64 (cos.f64 (+.f64 x eps)))) |
(fma.f64 (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (*.f64 x x) (-.f64 eps x))) (*.f64 (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 eps x))))) |
(fma.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))) (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 eps) (sin.f64 x)))) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 eps) (sin.f64 x)))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 (+.f64 x eps)))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) |
(cos.f64 (+.f64 x eps)) |
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (*.f64 x x) (-.f64 eps x)))) (*.f64 (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 eps x))))) |
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) |
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) |
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (neg.f64 (*.f64 (sin.f64 eps) (sin.f64 x)))) |
(*.f64 #s(literal -1 binary64) (/.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))) |
(*.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) |
(*.f64 (neg.f64 (cos.f64 (+.f64 x eps))) #s(literal 1 binary64)) |
(*.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)))) (+.f64 #s(literal 0 binary64) (cos.f64 (+.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps)) (*.f64 #s(literal 0 binary64) (cos.f64 (+.f64 x eps)))))) |
(/.f64 (neg.f64 (cos.f64 (+.f64 x eps))) #s(literal 1 binary64)) |
(/.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps)))) |
(neg.f64 (/.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))) |
(neg.f64 (cos.f64 (+.f64 x eps))) |
(-.f64 #s(literal 0 binary64) (/.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))) |
(-.f64 #s(literal 0 binary64) (cos.f64 (+.f64 x eps))) |
(+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (sin.f64 eps) (sin.f64 x))) |
(+.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 (+.f64 x eps)))) |
#s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) |
(*.f64 #s(literal 4/3 binary64) x) |
(*.f64 x #s(literal 4/3 binary64)) |
(*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) |
(*.f64 eps #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) |
(*.f64 (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x)))) |
(*.f64 (fma.f64 #s(literal 64/27 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps)))))) |
(/.f64 (-.f64 (*.f64 #s(literal 16/9 binary64) (*.f64 x x)) (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps))) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps))) |
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x)))) (neg.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x)))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 64/27 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps)))))) |
(/.f64 (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x))) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x))) |
(/.f64 (fma.f64 #s(literal 64/27 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 16/9 binary64) (*.f64 x x) (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 (*.f64 (*.f64 #s(literal 2/3 binary64) eps) #s(literal 4/3 binary64)) x)))) |
(/.f64 (fma.f64 #s(literal 64/27 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x)) (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps)))) (fma.f64 #s(literal 64/27 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)))))) |
(fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 2/3 binary64) eps)) |
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) |
(fma.f64 x #s(literal 4/3 binary64) (*.f64 #s(literal 2/3 binary64) eps)) |
(fma.f64 eps #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) x)) |
(-.f64 (/.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x))) (/.f64 (*.f64 #s(literal 16/9 binary64) (*.f64 x x)) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x)))) |
(+.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 #s(literal 4/3 binary64) x)) |
(+.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps)) |
Compiled 100 471 to 6 524 computations (93.5% saved)
27 alts after pruning (23 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 045 | 11 | 1 056 |
| Fresh | 6 | 12 | 18 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 3 | 3 |
| Total | 1 055 | 27 | 1 082 |
| Status | Accuracy | Program |
|---|---|---|
| 61.0% | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) | |
| ✓ | 61.0% | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
| ▶ | 60.8% | (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) |
| 35.0% | (/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (+.f64 (tan.f64 eps) (tan.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (tan.f64 x))) | |
| 60.9% | (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) | |
| ✓ | 60.8% | (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
| 60.5% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) | |
| ✓ | 60.8% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 60.4% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))) | |
| 99.7% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) | |
| 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) eps (*.f64 (*.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) eps))) | |
| 99.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) | |
| 99.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) | |
| 98.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) | |
| ✓ | 98.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
| 51.4% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps)))) | |
| 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))))) (pow.f64 (*.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) #s(literal 2 binary64))))) | |
| ▶ | 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps)) |
| 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps)) | |
| ▶ | 100.0% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
| 99.9% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 #s(approx (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (fma.f64 (*.f64 x x) #s(literal -4/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) | |
| 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #s(literal 1/3 binary64)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) | |
| ▶ | 98.9% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
| ▶ | 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) | |
| 24.1% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps)) eps))) (pow.f64 eps #s(literal 4 binary64))))) |
Compiled 4 204 to 1 544 computations (63.3% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) | |
| cost-diff | 0 | (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps)) | |
| cost-diff | 9 | (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (cos.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) | |
| cost-diff | 3 | (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) | |
| cost-diff | 0 | #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) | |
| cost-diff | 1 | (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) | |
| cost-diff | 0 | #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) | |
| cost-diff | 0 | (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) | |
| cost-diff | 1 | (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps) | |
| cost-diff | 2 | (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) | |
| cost-diff | 2 | (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) | |
| cost-diff | 5 | (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) | |
| cost-diff | 11 | (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 103 | 1847 |
| 0 | 172 | 1822 |
| 1 | 332 | 1709 |
| 2 | 888 | 1699 |
| 3 | 3996 | 1596 |
| 0 | 8097 | 1541 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
(*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps) |
(fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) |
(*.f64 eps eps) |
eps |
(neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) |
(fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) |
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) |
(fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) |
(tan.f64 x) |
x |
#s(literal 1 binary64) |
(*.f64 eps (tan.f64 x)) |
#s(literal -1/3 binary64) |
(fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) |
(-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
#s(literal 2 binary64) |
(fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) |
(pow.f64 (tan.f64 x) #s(literal 4 binary64)) |
#s(literal 4 binary64) |
(*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) |
(fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
(*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps) |
(+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) |
(*.f64 x x) |
x |
#s(literal 1 binary64) |
eps |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps) |
#s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) |
(fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
(*.f64 eps eps) |
eps |
#s(literal 4/3 binary64) |
#s(literal 1 binary64) |
x |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) |
(pow.f64 eps #s(literal 3 binary64)) |
#s(literal 3 binary64) |
#s(literal 2/3 binary64) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
#s(literal 1/3 binary64) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) |
#s(literal -1 binary64) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(neg.f64 (sin.f64 (+.f64 x eps))) |
(sin.f64 (+.f64 x eps)) |
(neg.f64 (tan.f64 x)) |
(tan.f64 x) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps)) |
(*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps) |
(fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) |
(*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) |
#s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) |
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)) |
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) |
#s(literal 2/3 binary64) |
eps |
(*.f64 #s(literal 4/3 binary64) x) |
#s(literal 4/3 binary64) |
x |
#s(literal 1/3 binary64) |
(*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)))) |
(fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) |
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(sin.f64 x) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
#s(literal 2 binary64) |
#s(literal 1 binary64) |
(/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))) |
(-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) |
(pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) |
(*.f64 eps (tan.f64 x)) |
(tan.f64 x) |
(fma.f64 eps (tan.f64 x) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (-.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64) (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) eps) eps)) (*.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (tan.f64 x)) (*.f64 #s(literal 1/3 binary64) eps)) (*.f64 eps eps))) eps)) |
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#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 eps (fma.f64 (tan.f64 x) eps #s(literal 1 binary64))) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (pow.f64 eps #s(literal 3 binary64))))) |
(*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps) |
(fma.f64 (*.f64 eps (fma.f64 (tan.f64 x) eps #s(literal 1 binary64))) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (pow.f64 eps #s(literal 3 binary64)))) |
(fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) |
(*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) |
#s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) |
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)) |
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) |
#s(literal 2/3 binary64) |
eps |
(*.f64 #s(literal 4/3 binary64) x) |
#s(literal 4/3 binary64) |
x |
#s(literal 1/3 binary64) |
(*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)))) |
(*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) eps #s(literal 1 binary64))) |
(fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) |
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(sin.f64 x) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 x) |
#s(literal 2 binary64) |
#s(literal 1 binary64) |
(/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))) |
(fma.f64 (tan.f64 x) eps #s(literal 1 binary64)) |
(-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) |
(-.f64 (pow.f64 (*.f64 (tan.f64 x) eps) #s(literal 2 binary64)) #s(literal 1 binary64)) |
(pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (tan.f64 x) eps) #s(literal 2 binary64)) |
(*.f64 eps (tan.f64 x)) |
(*.f64 (tan.f64 x) eps) |
(tan.f64 x) |
(fma.f64 eps (tan.f64 x) #s(literal -1 binary64)) |
(fma.f64 (tan.f64 x) eps #s(literal -1 binary64)) |
#s(literal -1 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.23046875 | (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) | |
| accuracy | 0.3125 | (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) | |
| accuracy | 0.3203125 | (*.f64 #s(literal 4/3 binary64) x) | |
| accuracy | 0.6014202425464805 | #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) | |
| accuracy | 0.0 | (neg.f64 (sin.f64 (+.f64 x eps))) | |
| accuracy | 0.021816259768442016 | (sin.f64 (+.f64 x eps)) | |
| accuracy | 0.05424472348973429 | (cos.f64 (+.f64 x eps)) | |
| accuracy | 24.95173741332391 | (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) | |
| accuracy | 0.0078125 | (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) | |
| accuracy | 0.0078125 | (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) | |
| accuracy | 0.01171875 | (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps) | |
| accuracy | 0.5255790727433751 | #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) | |
| accuracy | 0.0 | (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps) | |
| accuracy | 0.0 | (*.f64 x x) | |
| accuracy | 0.5366878961861644 | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) | |
| accuracy | 0.9785646236900496 | #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) | |
| accuracy | 0.015625 | (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) | |
| accuracy | 0.01953125 | (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) | |
| accuracy | 0.0234375 | (pow.f64 (tan.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.03191376953688403 | (pow.f64 (tan.f64 x) #s(literal 4 binary64)) |
| 475.0ms | 101× | 1 | valid |
| 134.0ms | 151× | 0 | valid |
| 10.0ms | 3× | 5 | exit |
| 2.0ms | 1× | 3 | valid |
Compiled 3 340 to 210 computations (93.7% saved)
ival-add: 354.0ms (64.1% of total)ival-mult: 71.0ms (12.9% of total)const: 24.0ms (4.3% of total)adjust: 24.0ms (4.3% of total)ival-div: 24.0ms (4.3% of total)ival-pow2: 13.0ms (2.4% of total)ival-pow: 12.0ms (2.2% of total)ival-neg: 7.0ms (1.3% of total)ival-sub: 5.0ms (0.9% of total)ival-tan: 5.0ms (0.9% of total)ival-cos: 5.0ms (0.9% of total)ival-sin: 5.0ms (0.9% of total)exact: 1.0ms (0.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) |
(-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) |
(fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) |
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) |
(*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
(+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps) |
#s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps)) |
(*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps) |
(fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) |
(pow.f64 (tan.f64 x) #s(literal 4 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) |
(*.f64 x x) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(sin.f64 (+.f64 x eps)) |
(neg.f64 (sin.f64 (+.f64 x eps))) |
#s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) |
(*.f64 #s(literal 4/3 binary64) x) |
(*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) |
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) |
| Outputs |
|---|
-1/3 |
(- (* -1/3 (* eps x)) 1/3) |
(- (* x (+ (* -4/3 x) (* -1/3 eps))) 1/3) |
(- (* x (+ (* -1/3 eps) (* x (- (* -13/9 (* eps x)) 4/3)))) 1/3) |
(- (* -4/3 (pow x 2)) 1/3) |
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3) |
(+ 1 (* 1/3 (pow eps 2))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 2/3 (pow eps 3)))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2))))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (+ eps (+ (* -1 (* (pow eps 2) (+ (* -13/9 eps) (* -4/9 eps)))) (* 1/3 eps)))))))))))) |
(* eps x) |
(* x (+ eps (* 4/3 (* eps (pow x 2))))) |
(* x (+ eps (* (pow x 2) (+ (* 17/15 (* eps (pow x 2))) (* 4/3 eps))))) |
(* x (+ eps (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/315 (* eps (pow x 2))) (* 17/15 eps))))))) |
eps |
(+ eps (* eps (pow x 2))) |
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps)))))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
1 |
(+ 1 (pow x 2)) |
(+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))) |
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
(+ eps (* 2/3 (pow eps 3))) |
(+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2)))))) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3))))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2))))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps))))))))))) |
(/ -1 (cos eps)) |
(- (* -1 (/ (* x (sin eps)) (pow (cos eps) 2))) (/ 1 (cos eps))) |
(- (* x (- (* -1 (* x (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps))) |
(- (* x (- (* x (- (* -1 (* x (+ (* -1/6 (/ (sin eps) (pow (cos eps) 2))) (+ (* 1/2 (/ (sin eps) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3)))) (cos eps)))))) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(+ eps x) |
(+ 1 (* eps x)) |
(+ 1 (* x (- (* 1/3 (* eps (pow x 2))) (* -1 eps)))) |
(+ 1 (* x (- (* (pow x 2) (- (* 2/15 (* eps (pow x 2))) (* -1/3 eps))) (* -1 eps)))) |
(+ (* eps (* x (- (* 2/3 (pow eps 3)) (* -1 eps)))) (* eps (+ 1 (* 1/3 (pow eps 2))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))) (* eps (- (* 2/3 (pow eps 3)) (* -1 eps)))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (- (* 2/3 (pow eps 3)) (* -1 eps))) (* x (+ (* eps (* x (- (* 17/9 (pow eps 3)) (+ (* -1 (* eps (- (* -1 (- (pow eps 2) 1)) (* -1 (pow eps 2))))) (* -1/3 eps))))) (* eps (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (* 2/3 (pow eps 3)) (* -1 eps))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (+ (* 2/3 (pow eps 3)) (* x (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))) (* -1 eps))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (+ (* 2/3 (pow eps 3)) (* x (- (+ (* -1 (- (pow eps 2) 1)) (+ (* 4/3 (pow eps 2)) (* x (- (* 17/9 (pow eps 3)) (+ (* -1 (* eps (- (* -1 (- (pow eps 2) 1)) (* -1 (pow eps 2))))) (* -1/3 eps)))))) (* -1 (pow eps 2))))) (* -1 eps))))) |
(pow x 4) |
(* (pow x 4) (+ 1 (* 4/3 (pow x 2)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2)))))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 6/5 (* 848/945 (pow x 2)))))))) |
(* (pow x 2) (+ 1 (* 5/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2)))))))) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(* -1 (sin eps)) |
(- (* -1 (* x (cos eps))) (sin eps)) |
(- (* x (- (* 1/2 (* x (sin eps))) (cos eps))) (sin eps)) |
(- (* x (- (* x (- (* 1/6 (* x (cos eps))) (* -1/2 (sin eps)))) (cos eps))) (sin eps)) |
1/3 |
(+ 1/3 (* 2/3 (* eps x))) |
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps)))) |
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps)))) |
(* 4/3 x) |
(* 1/3 eps) |
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x))))))) |
(* 2/3 eps) |
(+ (* 2/3 eps) (* 4/3 x)) |
(- (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) |
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) |
(+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x))))))) |
(/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(* x (+ 1 (* 4/3 (pow eps 2)))) |
(* x (+ 1 (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (/ eps x))))) |
(* eps (+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ -1 (cos (+ eps x))) |
(cos (+ eps x)) |
x |
(* x (+ 1 (/ eps x))) |
(/ (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1) (- (/ (* eps (sin x)) (cos x)) 1)) |
(* eps (+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1)) (- (/ (* eps (sin x)) (cos x)) 1)))) |
(+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1)) (- (/ (* eps (sin x)) (cos x)) 1))) |
(/ (pow (sin x) 4) (pow (cos x) 4)) |
(+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) |
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ 1 (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (/ eps x))))) |
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (+ (/ 1 (pow x 2)) (/ eps x))))))) |
(sin (+ eps x)) |
(* -1 (sin (+ eps x))) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) |
(* x (+ 4/3 (* 2/3 (/ eps x)))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(* -1 (* x (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ (+ eps (* 2/3 (pow eps 3))) x))))) |
(/ -1 (cos (- eps (* -1 x)))) |
(cos (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 (+ eps (* 2/3 (pow eps 3)))) (* -1 (/ (+ 1 (* 1/3 (pow eps 2))) x))) x)) (* 4/3 (pow eps 2))))) |
(sin (- eps (* -1 x))) |
(* -1 (sin (- eps (* -1 x)))) |
(* -1 (* x (- (* -2/3 (/ eps x)) 4/3))) |
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ x (* eps (+ 1 (* 4/3 (* eps x))))) |
(+ x (* eps (+ 1 (* eps (+ (* 2/3 eps) (* 4/3 x)))))) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ 1 (+ (* eps (+ (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(/ -1 (cos x)) |
(- (* -1 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x))) |
(- (* eps (- (* -1 (* eps (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos x))) |
(- (* eps (- (* eps (- (* -1 (* eps (+ (* -1/6 (/ (sin x) (pow (cos x) 2))) (+ (* 1/2 (/ (sin x) (pow (cos x) 2))) (/ (* (sin x) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3)))) (cos x)))))) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos x))) |
(cos x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(+ 1 (/ (* eps (sin x)) (cos x))) |
(+ 1 (+ (* eps (- (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (- (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps x) (pow x 2))) |
(+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))) |
(+ 1 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(* -1 (sin x)) |
(- (* -1 (* eps (cos x))) (sin x)) |
(- (* eps (- (* 1/2 (* eps (sin x))) (cos x))) (sin x)) |
(- (* eps (- (* eps (- (* 1/6 (* eps (cos x))) (* -1/2 (sin x)))) (cos x))) (sin x)) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(- (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x)) |
(* eps (- (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) |
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) |
(* 2/3 (pow eps 3)) |
(* (pow eps 3) (+ 2/3 (* 4/3 (/ x eps)))) |
(* (pow eps 3) (+ 2/3 (+ (* 4/3 (/ x eps)) (/ 1 (pow eps 2))))) |
(* (pow eps 3) (+ 2/3 (+ (* 4/3 (/ x eps)) (+ (/ 1 (pow eps 2)) (/ x (pow eps 3)))))) |
(* -1 (* (pow eps 4) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(* -1 (* (pow eps 3) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(* eps (+ 1 (/ x eps))) |
(/ (* eps (sin x)) (cos x)) |
(* eps (+ (/ 1 eps) (/ (sin x) (cos x)))) |
(* 2/3 (* (pow eps 3) x)) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps))))) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3)))))))) |
(* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* eps (- (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* -1 (* (pow eps 2) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 2) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* eps (+ 2/3 (* 4/3 (/ x eps)))) |
(* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* -1 (/ (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) eps))))) |
(* (pow eps 3) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(* -1 (* (pow eps 3) (- (* -4/3 (/ x eps)) 2/3))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 4/3 x) (/ 1 eps)) eps)) 2/3))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x)) eps)) 2/3))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(/ -1 (cos (- x (* -1 eps)))) |
(cos (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (* 4/3 (pow x 2))) eps)) (* -2/3 x)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))) eps)) (* -2/3 x)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (+ 1 (pow x 2)) eps))) eps)) (* 4/3 (pow x 2)))) eps)) (* -2/3 x)))) |
(sin (- x (* -1 eps))) |
(* -1 (sin (- x (* -1 eps)))) |
(* -1 (* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(* -1 (* eps (- (* -4/3 (/ x eps)) 2/3))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 22.0ms | x | @ | -inf | ((+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4)))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) (* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (/ -1 (cos (+ x eps))) (neg (sin (+ x eps)))) (neg (tan x))) (/ -1 (cos (+ x eps))) (cos (+ x eps)) (+ x eps) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) (pow (tan x) 4) (pow (tan x) 2) (+ (* (tan x) (tan x)) (pow (tan x) 4)) (* x x) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (sin (+ x eps)) (neg (sin (+ x eps))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (* 4/3 x) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (+ (* 2/3 eps) (* 4/3 x))) |
| 16.0ms | x | @ | inf | ((+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4)))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) (* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (/ -1 (cos (+ x eps))) (neg (sin (+ x eps)))) (neg (tan x))) (/ -1 (cos (+ x eps))) (cos (+ x eps)) (+ x eps) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) (pow (tan x) 4) (pow (tan x) 2) (+ (* (tan x) (tan x)) (pow (tan x) 4)) (* x x) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (sin (+ x eps)) (neg (sin (+ x eps))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (* 4/3 x) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (+ (* 2/3 eps) (* 4/3 x))) |
| 14.0ms | eps | @ | inf | ((+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4)))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) (* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (/ -1 (cos (+ x eps))) (neg (sin (+ x eps)))) (neg (tan x))) (/ -1 (cos (+ x eps))) (cos (+ x eps)) (+ x eps) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) (pow (tan x) 4) (pow (tan x) 2) (+ (* (tan x) (tan x)) (pow (tan x) 4)) (* x x) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (sin (+ x eps)) (neg (sin (+ x eps))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (* 4/3 x) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (+ (* 2/3 eps) (* 4/3 x))) |
| 9.0ms | eps | @ | 0 | ((+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4)))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) (* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (/ -1 (cos (+ x eps))) (neg (sin (+ x eps)))) (neg (tan x))) (/ -1 (cos (+ x eps))) (cos (+ x eps)) (+ x eps) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) (pow (tan x) 4) (pow (tan x) 2) (+ (* (tan x) (tan x)) (pow (tan x) 4)) (* x x) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (sin (+ x eps)) (neg (sin (+ x eps))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (* 4/3 x) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (+ (* 2/3 eps) (* 4/3 x))) |
| 9.0ms | eps | @ | -inf | ((+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4)))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) (* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps) (- (tan (+ x eps)) (tan x)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (/ (pow (sin x) 2) (pow (cos x) 2)) (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (/ -1 (cos (+ x eps))) (neg (sin (+ x eps)))) (neg (tan x))) (/ -1 (cos (+ x eps))) (cos (+ x eps)) (+ x eps) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) eps) (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (/ (- (pow (* eps (tan x)) 2) 1) (+ (* eps (tan x)) -1)))) (pow (tan x) 4) (pow (tan x) 2) (+ (* (tan x) (tan x)) (pow (tan x) 4)) (* x x) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (sin (+ x eps)) (neg (sin (+ x eps))) (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (* 4/3 x) (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) (+ (* 2/3 eps) (* 4/3 x))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 922 | 7426 |
| 1 | 3081 | 7213 |
| 0 | 8191 | 6814 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
-1/3 |
(- (* -1/3 (* eps x)) 1/3) |
(- (* x (+ (* -4/3 x) (* -1/3 eps))) 1/3) |
(- (* x (+ (* -1/3 eps) (* x (- (* -13/9 (* eps x)) 4/3)))) 1/3) |
(- (* -4/3 (pow x 2)) 1/3) |
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3) |
(+ 1 (* 1/3 (pow eps 2))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 2/3 (pow eps 3)))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2))))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (+ eps (+ (* -1 (* (pow eps 2) (+ (* -13/9 eps) (* -4/9 eps)))) (* 1/3 eps)))))))))))) |
(* eps x) |
(* x (+ eps (* 4/3 (* eps (pow x 2))))) |
(* x (+ eps (* (pow x 2) (+ (* 17/15 (* eps (pow x 2))) (* 4/3 eps))))) |
(* x (+ eps (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/315 (* eps (pow x 2))) (* 17/15 eps))))))) |
eps |
(+ eps (* eps (pow x 2))) |
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps)))))) |
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
1 |
(+ 1 (pow x 2)) |
(+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))) |
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
(+ eps (* 2/3 (pow eps 3))) |
(+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2)))))) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3))))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2))))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps))))))))))) |
(/ -1 (cos eps)) |
(- (* -1 (/ (* x (sin eps)) (pow (cos eps) 2))) (/ 1 (cos eps))) |
(- (* x (- (* -1 (* x (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps))) |
(- (* x (- (* x (- (* -1 (* x (+ (* -1/6 (/ (sin eps) (pow (cos eps) 2))) (+ (* 1/2 (/ (sin eps) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3)))) (cos eps)))))) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(+ eps x) |
(+ 1 (* eps x)) |
(+ 1 (* x (- (* 1/3 (* eps (pow x 2))) (* -1 eps)))) |
(+ 1 (* x (- (* (pow x 2) (- (* 2/15 (* eps (pow x 2))) (* -1/3 eps))) (* -1 eps)))) |
(+ (* eps (* x (- (* 2/3 (pow eps 3)) (* -1 eps)))) (* eps (+ 1 (* 1/3 (pow eps 2))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))) (* eps (- (* 2/3 (pow eps 3)) (* -1 eps)))))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (- (* 2/3 (pow eps 3)) (* -1 eps))) (* x (+ (* eps (* x (- (* 17/9 (pow eps 3)) (+ (* -1 (* eps (- (* -1 (- (pow eps 2) 1)) (* -1 (pow eps 2))))) (* -1/3 eps))))) (* eps (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (* 2/3 (pow eps 3)) (* -1 eps))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (+ (* 2/3 (pow eps 3)) (* x (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))) (* -1 eps))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (+ (* 2/3 (pow eps 3)) (* x (- (+ (* -1 (- (pow eps 2) 1)) (+ (* 4/3 (pow eps 2)) (* x (- (* 17/9 (pow eps 3)) (+ (* -1 (* eps (- (* -1 (- (pow eps 2) 1)) (* -1 (pow eps 2))))) (* -1/3 eps)))))) (* -1 (pow eps 2))))) (* -1 eps))))) |
(pow x 4) |
(* (pow x 4) (+ 1 (* 4/3 (pow x 2)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2)))))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 6/5 (* 848/945 (pow x 2)))))))) |
(* (pow x 2) (+ 1 (* 5/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2)))))))) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(* -1 (sin eps)) |
(- (* -1 (* x (cos eps))) (sin eps)) |
(- (* x (- (* 1/2 (* x (sin eps))) (cos eps))) (sin eps)) |
(- (* x (- (* x (- (* 1/6 (* x (cos eps))) (* -1/2 (sin eps)))) (cos eps))) (sin eps)) |
1/3 |
(+ 1/3 (* 2/3 (* eps x))) |
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps)))) |
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps)))) |
(* 4/3 x) |
(* 1/3 eps) |
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x))))))) |
(* 2/3 eps) |
(+ (* 2/3 eps) (* 4/3 x)) |
(- (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) |
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) |
(+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x))))))) |
(/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(/ (pow (sin x) 2) (pow (cos x) 2)) |
(* x (+ 1 (* 4/3 (pow eps 2)))) |
(* x (+ 1 (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (/ eps x))))) |
(* eps (+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(/ -1 (cos (+ eps x))) |
(cos (+ eps x)) |
x |
(* x (+ 1 (/ eps x))) |
(/ (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1) (- (/ (* eps (sin x)) (cos x)) 1)) |
(* eps (+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1)) (- (/ (* eps (sin x)) (cos x)) 1)))) |
(+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1)) (- (/ (* eps (sin x)) (cos x)) 1))) |
(/ (pow (sin x) 4) (pow (cos x) 4)) |
(+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) |
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ 1 (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (/ eps x))))) |
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (+ (/ 1 (pow x 2)) (/ eps x))))))) |
(sin (+ eps x)) |
(* -1 (sin (+ eps x))) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) |
(* x (+ 4/3 (* 2/3 (/ eps x)))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(* -1 (* x (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ (+ eps (* 2/3 (pow eps 3))) x))))) |
(/ -1 (cos (- eps (* -1 x)))) |
(cos (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 (+ eps (* 2/3 (pow eps 3)))) (* -1 (/ (+ 1 (* 1/3 (pow eps 2))) x))) x)) (* 4/3 (pow eps 2))))) |
(sin (- eps (* -1 x))) |
(* -1 (sin (- eps (* -1 x)))) |
(* -1 (* x (- (* -2/3 (/ eps x)) 4/3))) |
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ x (* eps (+ 1 (* 4/3 (* eps x))))) |
(+ x (* eps (+ 1 (* eps (+ (* 2/3 eps) (* 4/3 x)))))) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ 1 (+ (* eps (+ (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(/ -1 (cos x)) |
(- (* -1 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x))) |
(- (* eps (- (* -1 (* eps (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos x))) |
(- (* eps (- (* eps (- (* -1 (* eps (+ (* -1/6 (/ (sin x) (pow (cos x) 2))) (+ (* 1/2 (/ (sin x) (pow (cos x) 2))) (/ (* (sin x) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3)))) (cos x)))))) (+ (* 1/2 (/ 1 (cos x))) (/ (pow (sin x) 2) (pow (cos x) 3))))) (/ (sin x) (pow (cos x) 2)))) (/ 1 (cos x))) |
(cos x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(+ 1 (/ (* eps (sin x)) (cos x))) |
(+ 1 (+ (* eps (- (* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (- (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps x) (pow x 2))) |
(+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))) |
(+ 1 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(* -1 (sin x)) |
(- (* -1 (* eps (cos x))) (sin x)) |
(- (* eps (- (* 1/2 (* eps (sin x))) (cos x))) (sin x)) |
(- (* eps (- (* eps (- (* 1/6 (* eps (cos x))) (* -1/2 (sin x)))) (cos x))) (sin x)) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(- (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x)) |
(* eps (- (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) |
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) |
(* 2/3 (pow eps 3)) |
(* (pow eps 3) (+ 2/3 (* 4/3 (/ x eps)))) |
(* (pow eps 3) (+ 2/3 (+ (* 4/3 (/ x eps)) (/ 1 (pow eps 2))))) |
(* (pow eps 3) (+ 2/3 (+ (* 4/3 (/ x eps)) (+ (/ 1 (pow eps 2)) (/ x (pow eps 3)))))) |
(* -1 (* (pow eps 4) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(* -1 (* (pow eps 3) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(* eps (+ 1 (/ x eps))) |
(/ (* eps (sin x)) (cos x)) |
(* eps (+ (/ 1 eps) (/ (sin x) (cos x)))) |
(* 2/3 (* (pow eps 3) x)) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps))))) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3)))))))) |
(* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* eps (- (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* -1 (* (pow eps 2) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(* (pow eps 2) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(* eps (+ 2/3 (* 4/3 (/ x eps)))) |
(* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* -1 (/ (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) eps))))) |
(* (pow eps 3) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(* -1 (* (pow eps 3) (- (* -4/3 (/ x eps)) 2/3))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 4/3 x) (/ 1 eps)) eps)) 2/3))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x)) eps)) 2/3))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(/ -1 (cos (- x (* -1 eps)))) |
(cos (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (* 4/3 (pow x 2))) eps)) (* -2/3 x)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))) eps)) (* -2/3 x)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (+ 1 (pow x 2)) eps))) eps)) (* 4/3 (pow x 2)))) eps)) (* -2/3 x)))) |
(sin (- x (* -1 eps))) |
(* -1 (sin (- x (* -1 eps)))) |
(* -1 (* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(* -1 (* eps (- (* -4/3 (/ x eps)) 2/3))) |
| Outputs |
|---|
-1/3 |
#s(literal -1/3 binary64) |
(- (* -1/3 (* eps x)) 1/3) |
(fma.f64 (*.f64 eps x) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) |
(- (* x (+ (* -4/3 x) (* -1/3 eps))) 1/3) |
(fma.f64 (fma.f64 #s(literal -4/3 binary64) x (*.f64 #s(literal -1/3 binary64) eps)) x #s(literal -1/3 binary64)) |
(- (* x (+ (* -1/3 eps) (* x (- (* -13/9 (* eps x)) 4/3)))) 1/3) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -13/9 binary64) (*.f64 eps x) #s(literal -4/3 binary64)) x (*.f64 #s(literal -1/3 binary64) eps)) x #s(literal -1/3 binary64)) |
(- (* -4/3 (pow x 2)) 1/3) |
(fma.f64 (*.f64 x x) #s(literal -4/3 binary64) #s(literal -1/3 binary64)) |
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3) |
(fma.f64 (fma.f64 #s(literal -17/9 binary64) (*.f64 x x) #s(literal -4/3 binary64)) (*.f64 x x) #s(literal -1/3 binary64)) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -248/135 binary64) (*.f64 x x) #s(literal -17/9 binary64)) (*.f64 x x) #s(literal -4/3 binary64)) (*.f64 x x) #s(literal -1/3 binary64)) |
(+ 1 (* 1/3 (pow eps 2))) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* 2/3 (pow eps 3)))))) |
(fma.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (+ eps (+ (* -1 (* (pow eps 2) (+ (* -13/9 eps) (* -4/9 eps)))) (* 1/3 eps)))))))))))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(* eps x) |
(*.f64 eps x) |
(* x (+ eps (* 4/3 (* eps (pow x 2))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 4/3 binary64) eps) x) |
(* x (+ eps (* (pow x 2) (+ (* 17/15 (* eps (pow x 2))) (* 4/3 eps))))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 17/15 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 4/3 binary64) eps)) (*.f64 x x) eps) x) |
(* x (+ eps (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/315 (* eps (pow x 2))) (* 17/15 eps))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 248/315 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 17/15 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 4/3 binary64) eps)) (*.f64 x x) eps) x) |
eps |
(+ eps (* eps (pow x 2))) |
(fma.f64 (*.f64 x x) eps eps) |
(+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 2/3 binary64) eps) (*.f64 x x) eps) |
(+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps)))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 2/3 binary64) eps)) (*.f64 x x) eps) (*.f64 x x) eps) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(fma.f64 x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 x (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
1 |
#s(literal 1 binary64) |
(+ 1 (pow x 2)) |
(fma.f64 x x #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))) |
(fma.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2/3 (pow x 2)))) |
(*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2)))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x)) |
(+ eps (* 2/3 (pow eps 3))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) |
(+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (* 4/3 (pow eps 2)))))) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps) |
(+ (* eps (* x (+ eps (* 2/3 (pow eps 3))))) (* eps (+ 1 (* 1/3 (pow eps 2))))) |
(*.f64 eps (fma.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* eps (+ eps (* 2/3 (pow eps 3))))))) |
(fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (+ eps (* 2/3 (pow eps 3)))) (* x (+ (* eps (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2))))))))) |
(fma.f64 (fma.f64 (*.f64 eps (fma.f64 (fma.f64 #s(literal 5/6 binary64) eps (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 17/9 binary64) (*.f64 #s(literal 1/2 binary64) eps))) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)))) x (*.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) eps)) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (+ (* 2/3 (pow eps 3)) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (+ (* -1/6 eps) (* 17/9 (pow eps 3)))) (* -1/2 eps))))))))))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 5/6 binary64) eps (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 17/9 binary64) (*.f64 #s(literal 1/2 binary64) eps))) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(/ -1 (cos eps)) |
(/.f64 #s(literal -1 binary64) (cos.f64 eps)) |
(- (* -1 (/ (* x (sin eps)) (pow (cos eps) 2))) (/ 1 (cos eps))) |
(neg.f64 (fma.f64 x (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 eps)))) |
(- (* x (- (* -1 (* x (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps))) |
(fma.f64 (neg.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (cos.f64 eps))) x (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) x (/.f64 #s(literal -1 binary64) (cos.f64 eps))) |
(- (* x (- (* x (- (* -1 (* x (+ (* -1/6 (/ (sin eps) (pow (cos eps) 2))) (+ (* 1/2 (/ (sin eps) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3)))) (cos eps)))))) (+ (* 1/2 (/ 1 (cos eps))) (/ (pow (sin eps) 2) (pow (cos eps) 3))))) (/ (sin eps) (pow (cos eps) 2)))) (/ 1 (cos eps))) |
(fma.f64 (fma.f64 (neg.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1/3 binary64) (/.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (cos.f64 eps))) (sin.f64 eps)) (cos.f64 eps))) x (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (cos.f64 eps))))) x (/.f64 (neg.f64 (sin.f64 eps)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 #s(literal -1 binary64) (cos.f64 eps))) |
(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/2 binary64)) (sin.f64 eps)) x (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) x) (sin.f64 eps)) x (cos.f64 eps)) |
(+ eps x) |
(+.f64 eps x) |
(+ 1 (* eps x)) |
(fma.f64 eps x #s(literal 1 binary64)) |
(+ 1 (* x (- (* 1/3 (* eps (pow x 2))) (* -1 eps)))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/3 binary64) eps) x #s(literal 1 binary64)) |
(+ 1 (* x (- (* (pow x 2) (- (* 2/15 (* eps (pow x 2))) (* -1/3 eps))) (* -1 eps)))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/3 binary64) eps)) (*.f64 x x) eps) x #s(literal 1 binary64)) |
(+ (* eps (* x (- (* 2/3 (pow eps 3)) (* -1 eps)))) (* eps (+ 1 (* 1/3 (pow eps 2))))) |
(*.f64 eps (fma.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))) (* eps (- (* 2/3 (pow eps 3)) (* -1 eps)))))) |
(fma.f64 (*.f64 eps (fma.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) #s(literal -1 binary64) (*.f64 (*.f64 eps eps) #s(literal 7/3 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (- (* 2/3 (pow eps 3)) (* -1 eps))) (* x (+ (* eps (* x (- (* 17/9 (pow eps 3)) (+ (* -1 (* eps (- (* -1 (- (pow eps 2) 1)) (* -1 (pow eps 2))))) (* -1/3 eps))))) (* eps (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))))))) |
(fma.f64 (fma.f64 (*.f64 eps (fma.f64 (-.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 17/9 binary64) (fma.f64 (fma.f64 (neg.f64 eps) eps #s(literal 1 binary64)) eps (pow.f64 eps #s(literal 3 binary64)))) (*.f64 #s(literal -1/3 binary64) eps)) x (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) #s(literal -1 binary64) (*.f64 (*.f64 eps eps) #s(literal 7/3 binary64))))) x (*.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) eps)) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (* 2/3 (pow eps 3)) (* -1 eps))))) |
(fma.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (+ (* 2/3 (pow eps 3)) (* x (- (+ (* -1 (- (pow eps 2) 1)) (* 4/3 (pow eps 2))) (* -1 (pow eps 2))))) (* -1 eps))))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) #s(literal -1 binary64) (*.f64 (*.f64 eps eps) #s(literal 7/3 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (- (+ (* 2/3 (pow eps 3)) (* x (- (+ (* -1 (- (pow eps 2) 1)) (+ (* 4/3 (pow eps 2)) (* x (- (* 17/9 (pow eps 3)) (+ (* -1 (* eps (- (* -1 (- (pow eps 2) 1)) (* -1 (pow eps 2))))) (* -1/3 eps)))))) (* -1 (pow eps 2))))) (* -1 eps))))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 17/9 binary64) (fma.f64 (fma.f64 (neg.f64 eps) eps #s(literal 1 binary64)) eps (pow.f64 eps #s(literal 3 binary64)))) (*.f64 #s(literal -1/3 binary64) eps)) x (fma.f64 (fma.f64 eps eps #s(literal -1 binary64)) #s(literal -1 binary64) (*.f64 (*.f64 eps eps) #s(literal 7/3 binary64)))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(pow x 4) |
(pow.f64 x #s(literal 4 binary64)) |
(* (pow x 4) (+ 1 (* 4/3 (pow x 2)))) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* 6/5 (pow x 2)))))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 6/5 binary64) (*.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 4) (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 6/5 (* 848/945 (pow x 2)))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 848/945 binary64) (*.f64 x x) #s(literal 6/5 binary64)) (*.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 2) (+ 1 (* 5/3 (pow x 2)))) |
(*.f64 (fma.f64 #s(literal 5/3 binary64) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2)))))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 77/45 binary64) (*.f64 x x) #s(literal 5/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x)) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2)))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 88/63 binary64) (*.f64 x x) #s(literal 77/45 binary64)) (*.f64 x x) #s(literal 5/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (*.f64 x x)) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (cos eps))) |
(fma.f64 (cos.f64 eps) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (cos.f64 eps)) x (sin.f64 eps)) |
(* -1 (sin eps)) |
(neg.f64 (sin.f64 eps)) |
(- (* -1 (* x (cos eps))) (sin eps)) |
(neg.f64 (fma.f64 (cos.f64 eps) x (sin.f64 eps))) |
(- (* x (- (* 1/2 (* x (sin eps))) (cos eps))) (sin eps)) |
(fma.f64 (-.f64 (*.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/2 binary64)) (cos.f64 eps)) x (neg.f64 (sin.f64 eps))) |
(- (* x (- (* x (- (* 1/6 (* x (cos eps))) (* -1/2 (sin eps)))) (cos eps))) (sin eps)) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (cos.f64 eps) (*.f64 #s(literal 1/2 binary64) (sin.f64 eps))) x (neg.f64 (cos.f64 eps))) x (neg.f64 (sin.f64 eps))) |
1/3 |
#s(literal 1/3 binary64) |
(+ 1/3 (* 2/3 (* eps x))) |
(fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x #s(literal 1/3 binary64)) |
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps)))) |
(fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)) |
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps)))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 17/9 binary64) (*.f64 eps x) #s(literal 4/3 binary64)) x (*.f64 #s(literal 2/3 binary64) eps)) x #s(literal 1/3 binary64)) |
(* 4/3 x) |
(*.f64 #s(literal 4/3 binary64) x) |
(* 1/3 eps) |
(*.f64 #s(literal 1/3 binary64) eps) |
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x))) |
(fma.f64 (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps)) x (*.f64 #s(literal 1/3 binary64) eps)) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))) x (*.f64 #s(literal 1/3 binary64) eps)) |
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 17/9 binary64) (*.f64 #s(literal 4/3 binary64) eps)) x (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))) x (*.f64 #s(literal 1/3 binary64) eps)) |
(* 2/3 eps) |
(*.f64 #s(literal 2/3 binary64) eps) |
(+ (* 2/3 eps) (* 4/3 x)) |
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) |
(- (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) |
(fma.f64 eps (*.f64 (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))) (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) |
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
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(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* x (+ 1 (* 4/3 (pow eps 2)))) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x) |
(* x (+ 1 (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (/ eps x))))) |
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(* eps (+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
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(+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(/ -1 (cos (+ eps x))) |
(/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
x |
(* x (+ 1 (/ eps x))) |
(fma.f64 (/.f64 eps x) x x) |
(/ (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1) (- (/ (* eps (sin x)) (cos x)) 1)) |
(/.f64 (fma.f64 (*.f64 eps eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (fma.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64))) |
(* eps (+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1)) (- (/ (* eps (sin x)) (cos x)) 1)))) |
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(+ (* -1 (* (pow eps 2) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) (/ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (- (/ (* (pow eps 2) (pow (sin x) 2)) (pow (cos x) 2)) 1)) (- (/ (* eps (sin x)) (cos x)) 1))) |
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(/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) |
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(* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)) |
(* (pow x 2) (+ 1 (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (/ eps x))))) |
(*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (/.f64 eps x))) #s(literal 1 binary64)) (*.f64 x x)) |
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 2/3 (/ (pow eps 3) x)) (+ (* 4/3 (pow eps 2)) (+ (/ 1 (pow x 2)) (/ eps x))))))) |
(*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 eps x)))) (fma.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64))) (*.f64 x x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(* -1 (sin (+ eps x))) |
(neg.f64 (sin.f64 (+.f64 eps x))) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
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(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (+ (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))))) |
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(* x (+ 4/3 (* 2/3 (/ eps x)))) |
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(cos (- eps (* -1 x))) |
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(fma.f64 (/.f64 (neg.f64 eps) x) (neg.f64 x) x) |
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(sin (- eps (* -1 x))) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (+ 1 (+ (* eps (+ (* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(cos x) |
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(+ 1 (+ (* eps x) (pow x 2))) |
(fma.f64 x (+.f64 eps x) #s(literal 1 binary64)) |
(+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))) |
(+ 1 (+ (* eps (+ x (* eps (+ 1/3 (+ (* 2/3 (* eps x)) (* 4/3 (pow x 2))))))) (pow x 2))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))) |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* eps (cos x))) |
(fma.f64 (cos.f64 x) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (sin.f64 x)) |
(* -1 (sin x)) |
(neg.f64 (sin.f64 x)) |
(- (* -1 (* eps (cos x))) (sin x)) |
(neg.f64 (fma.f64 (cos.f64 x) eps (sin.f64 x))) |
(- (* eps (- (* 1/2 (* eps (sin x))) (cos x))) (sin x)) |
(fma.f64 (-.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) |
(- (* eps (- (* eps (- (* 1/6 (* eps (cos x))) (* -1/2 (sin x)))) (cos x))) (sin x)) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (cos.f64 x) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps (neg.f64 (cos.f64 x))) eps (neg.f64 (sin.f64 x))) |
(* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(neg.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(- (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(neg.f64 (fma.f64 (*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x)) eps (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) |
(* -1 (* eps (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(*.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 eps)) |
(* eps (+ (* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x)) eps (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps) |
(/ (* eps (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))))) (cos x)) |
(/.f64 (*.f64 (*.f64 (sin.f64 x) eps) (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) |
(* eps (- (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))))) |
(*.f64 (fma.f64 (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal -1/3 binary64) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (neg.f64 (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))))) eps) |
(* -1 (* (pow eps 3) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal -1/3 binary64)))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) |
(*.f64 (-.f64 (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps)) (fma.f64 #s(literal -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) |
(*.f64 (-.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (+.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 #s(literal 1/3 binary64) eps))) (fma.f64 #s(literal -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (- (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))))) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) |
(*.f64 (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) eps) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (fma.f64 #s(literal -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))))) (pow.f64 eps #s(literal 3 binary64))) |
(* 2/3 (pow eps 3)) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64)) |
(* (pow eps 3) (+ 2/3 (* 4/3 (/ x eps)))) |
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (+ 2/3 (+ (* 4/3 (/ x eps)) (/ 1 (pow eps 2))))) |
(*.f64 (+.f64 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 2/3 binary64)) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (+ 2/3 (+ (* 4/3 (/ x eps)) (+ (/ 1 (pow eps 2)) (/ x (pow eps 3)))))) |
(*.f64 (+.f64 (+.f64 (/.f64 x (pow.f64 eps #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 4) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(*.f64 (neg.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) (sin.f64 x))) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
(*.f64 (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x)) (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)))) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(*.f64 (fma.f64 (neg.f64 (sin.f64 x)) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) (pow.f64 eps #s(literal 4 binary64))) |
(* -1 (* (pow eps 3) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(*.f64 (neg.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (sin.f64 x))) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x)))))) |
(*.f64 (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 eps eps)) (/.f64 (sin.f64 x) (cos.f64 x)) (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps)))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (+ (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (+ (/ 1 (pow eps 3)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (cos x))) (/ (pow (sin x) 2) (* (pow eps 3) (pow (cos x) 2)))))))) |
(*.f64 (fma.f64 (neg.f64 (sin.f64 x)) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) (pow.f64 eps #s(literal 3 binary64))) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 (/.f64 x eps) eps eps) |
(/ (* eps (sin x)) (cos x)) |
(/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) |
(* eps (+ (/ 1 eps) (/ (sin x) (cos x)))) |
(fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps #s(literal 1 binary64)) |
(* 2/3 (* (pow eps 3) x)) |
(*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64)) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (* 1/3 (/ 1 eps))))) |
(*.f64 (fma.f64 #s(literal 2/3 binary64) x (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 4/3 binary64) (/.f64 #s(literal 1/3 binary64) eps))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))) |
(*.f64 (fma.f64 #s(literal 2/3 binary64) x (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 4/3 binary64) (+.f64 (/.f64 x (*.f64 eps eps)) (/.f64 #s(literal 1/3 binary64) eps)))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (+ (* 2/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (+ (/ x (pow eps 2)) (/ (pow x 2) (pow eps 3)))))))) |
(*.f64 (+.f64 (fma.f64 #s(literal 2/3 binary64) x (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 4/3 binary64) (/.f64 #s(literal 1/3 binary64) eps))) (+.f64 (+.f64 (/.f64 (*.f64 x x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 x (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* eps (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(*.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(* eps (- (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) eps) |
(* -1 (* (pow eps 2) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))) |
(*.f64 (neg.f64 (*.f64 (*.f64 eps eps) (sin.f64 x))) (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) |
(* (pow eps 2) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) eps)))) |
(*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) (*.f64 eps eps)) |
(* eps (+ 2/3 (* 4/3 (/ x eps)))) |
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 2/3 binary64)) eps) |
(* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* -1 (/ (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) eps))))) |
(*.f64 (neg.f64 (fma.f64 (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) (neg.f64 eps)) |
(* (pow eps 3) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))) |
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(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))))) |
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(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))))) |
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(* -1 (* (pow eps 3) (- (* -1 (/ (- (+ 1/3 (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (+ (* -1 (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))) (* 1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (-.f64 (/.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 (neg.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) eps)) (-.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (neg.f64 eps)) (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (*.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) (sin.f64 x)) (cos.f64 x)) #s(literal 1/3 binary64))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* -1 (* (pow eps 3) (- (* -4/3 (/ x eps)) 2/3))) |
(*.f64 (neg.f64 (fma.f64 (/.f64 x eps) #s(literal -4/3 binary64) #s(literal -2/3 binary64))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 4/3 x) (/ 1 eps)) eps)) 2/3))) |
(*.f64 (neg.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps) #s(literal -1 binary64) #s(literal -2/3 binary64))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x)) eps)) 2/3))) |
(*.f64 (neg.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 (fma.f64 (/.f64 (neg.f64 x) eps) #s(literal -1 binary64) #s(literal 1 binary64)) eps)) eps) #s(literal -1 binary64) #s(literal -2/3 binary64))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
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(* (pow eps 4) (+ (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))) (* -1 (/ (+ (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps)) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) eps)))) |
(*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) eps))) eps)) eps))) (pow.f64 eps #s(literal 4 binary64))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (+ (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (-.f64 (/.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) eps) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps))))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
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(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps))) eps)) (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x)))))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (neg.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (neg.f64 (fma.f64 (sin.f64 x) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) eps)) (neg.f64 eps)))) |
(/ -1 (cos (- x (* -1 eps)))) |
(/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (/.f64 (neg.f64 x) eps) (neg.f64 eps) eps) |
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps)))) |
(*.f64 (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) eps)) (neg.f64 eps)) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (* 4/3 (pow x 2))) eps)) (* -2/3 x)))) |
(*.f64 (neg.f64 (fma.f64 #s(literal -2/3 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) (neg.f64 eps)))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps))) eps)) (* -2/3 x)))) |
(*.f64 (neg.f64 (fma.f64 #s(literal -2/3 binary64) x (/.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) (/.f64 x eps)) #s(literal -1 binary64) #s(literal -1/3 binary64)) eps))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (+ 1 (pow x 2)) eps))) eps)) (* 4/3 (pow x 2)))) eps)) (* -2/3 x)))) |
(*.f64 (neg.f64 (fma.f64 #s(literal -2/3 binary64) x (/.f64 (fma.f64 (/.f64 (neg.f64 (+.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) eps) x)) eps) #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) (neg.f64 eps)))) (pow.f64 eps #s(literal 3 binary64))) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(* -1 (sin (- x (* -1 eps)))) |
(neg.f64 (sin.f64 (+.f64 eps x))) |
(* -1 (* eps (- (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (* eps (pow (cos x) 2)))) (* -1/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) (* -1 (* (sin x) (+ (* -1 (/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 3))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(*.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (-.f64 (/.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) eps) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)))) (neg.f64 eps)) |
(* -1 (* eps (- (* -4/3 (/ x eps)) 2/3))) |
(*.f64 (fma.f64 (/.f64 x eps) #s(literal -4/3 binary64) #s(literal -2/3 binary64)) (neg.f64 eps)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 101 | 1411 |
| 0 | 169 | 1395 |
| 1 | 775 | 1097 |
| 2 | 7417 | 1097 |
| 0 | 8449 | 1069 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) |
(-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) |
(fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) |
(*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) |
(*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
(+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) |
#s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps) |
#s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps)) |
(*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps) |
(fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) |
(pow.f64 (tan.f64 x) #s(literal 4 binary64)) |
(pow.f64 (tan.f64 x) #s(literal 2 binary64)) |
(fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) |
(*.f64 x x) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(sin.f64 (+.f64 x eps)) |
(neg.f64 (sin.f64 (+.f64 x eps))) |
#s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) |
(*.f64 #s(literal 4/3 binary64) x) |
(*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) |
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) |
| Outputs |
|---|
(*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) |
(*.f64 (+.f64 (pow.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 (pow.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (*.f64 (*.f64 eps (tan.f64 x)) (pow.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)))) (pow.f64 (*.f64 (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) #s(literal 2 binary64))))) |
(*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) |
(/.f64 (-.f64 (*.f64 (fma.f64 (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (fma.f64 (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (pow.f64 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 2 binary64))) (+.f64 (fma.f64 (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) |
(/.f64 (-.f64 (pow.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))) #s(literal 2 binary64))) (-.f64 (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) |
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(fma.f64 #s(literal -1 binary64) (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 #s(literal -1 binary64) (*.f64 (sin.f64 eps) (cos.f64 x)))) |
(-.f64 (-.f64 #s(literal 0 binary64) (*.f64 (cos.f64 eps) (sin.f64 x))) (*.f64 (sin.f64 eps) (cos.f64 x))) |
(-.f64 #s(literal 0 binary64) (sin.f64 (+.f64 eps x))) |
(+.f64 (neg.f64 (*.f64 (cos.f64 eps) (sin.f64 x))) (neg.f64 (*.f64 (sin.f64 eps) (cos.f64 x)))) |
(+.f64 (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal -1 binary64)) (*.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal -1 binary64))) |
(+.f64 (*.f64 #s(literal -1 binary64) (*.f64 (cos.f64 eps) (sin.f64 x))) (*.f64 #s(literal -1 binary64) (*.f64 (sin.f64 eps) (cos.f64 x)))) |
(+.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 (+.f64 eps x)))) |
#s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) |
(*.f64 #s(literal 4/3 binary64) x) |
(*.f64 x #s(literal 4/3 binary64)) |
(*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) |
(*.f64 eps #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) |
(*.f64 (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x)))) |
(*.f64 (fma.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 4/3 binary64) x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps)))))) |
(/.f64 (-.f64 (*.f64 #s(literal 16/9 binary64) (*.f64 x x)) (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps))) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps))) |
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x)))) (neg.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x)))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 4/3 binary64) x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps)))))) |
(/.f64 (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x))) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x))) |
(/.f64 (fma.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 4/3 binary64) x) #s(literal 3 binary64))) (fma.f64 #s(literal 16/9 binary64) (*.f64 x x) (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 (*.f64 (*.f64 #s(literal 2/3 binary64) eps) #s(literal 4/3 binary64)) x)))) |
(/.f64 (fma.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 4/3 binary64) x) #s(literal 3 binary64))) (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x)) (-.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (*.f64 #s(literal 16/9 binary64) (*.f64 x x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 4/9 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 4/3 binary64) x) (-.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps)))) (fma.f64 #s(literal 8/27 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 4/3 binary64) x) #s(literal 3 binary64))))) |
(fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) |
(fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 2/3 binary64) eps)) |
(fma.f64 eps #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) x)) |
(fma.f64 x #s(literal 4/3 binary64) (*.f64 #s(literal 2/3 binary64) eps)) |
(-.f64 (/.f64 (*.f64 #s(literal 4/9 binary64) (*.f64 eps eps)) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x))) (/.f64 (*.f64 #s(literal 16/9 binary64) (*.f64 x x)) (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal -4/3 binary64) x)))) |
(+.f64 (*.f64 #s(literal 2/3 binary64) eps) (*.f64 #s(literal 4/3 binary64) x)) |
(+.f64 (*.f64 #s(literal 4/3 binary64) x) (*.f64 #s(literal 2/3 binary64) eps)) |
Compiled 105 537 to 6 430 computations (93.9% saved)
30 alts after pruning (26 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 003 | 14 | 1 017 |
| Fresh | 6 | 12 | 18 |
| Picked | 5 | 0 | 5 |
| Done | 0 | 4 | 4 |
| Total | 1 014 | 30 | 1 044 |
| Status | Accuracy | Program |
|---|---|---|
| 61.0% | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) | |
| ✓ | 61.0% | (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
| 60.9% | (-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) | |
| ✓ | 60.8% | (-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
| 60.5% | (-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) | |
| ✓ | 60.8% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 60.4% | (-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))) | |
| 60.8% | (neg.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) (tan.f64 x))) | |
| 99.7% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) | |
| 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) eps (*.f64 (*.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) eps))) | |
| 99.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) | |
| 99.0% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) | |
| 98.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) | |
| ✓ | 98.9% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
| 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) (pow.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 2 binary64))))) | |
| 100.0% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))) eps)) | |
| 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) eps)) | |
| 100.0% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) (tan.f64 x) (+.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))))) eps)) | |
| 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps)) | |
| 99.8% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #s(literal 1/3 binary64)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) | |
| 98.9% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) | |
| 98.4% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) | |
| 99.1% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) | |
| 6.5% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps)) | |
| 6.5% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (/.f64 eps x))) #s(literal 1 binary64)) (*.f64 x x)))) eps)) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) | |
| 99.2% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))) |
Compiled 7 913 to 1 517 computations (80.8% saved)
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (/.f64 eps x))) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) eps eps)) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) |
(-.f64 (tan.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
(neg.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) (tan.f64 x))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) |
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x))) |
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#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.f64 eps (tan.f64 x))) #s(literal -1/3 binary64) (fma.f64 (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 eps (tan.f64 x)) (-.f64 (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) (neg.f64 (fma.f64 (*.f64 eps (sin.f64 x)) (fma.f64 #s(literal -1/3 binary64) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))) (cos.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64) #s(literal -1/3 binary64))))) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (*.f64 (neg.f64 (fma.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -2/3 binary64) #s(literal -2/3 binary64)) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x) (/.f64 (-.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64) #s(literal -1/3 binary64)) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps)) eps))) (pow.f64 eps #s(literal 4 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (fma.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) eps (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) #s(literal -1/3 binary64) (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) (tan.f64 x) (+.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))))) eps)) |
3 calls:
| 17.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 16.0ms | x |
| 15.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | eps |
| 100.0% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (/.f64 eps x))) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) eps eps)) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) |
(-.f64 (tan.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
(neg.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) (tan.f64 x))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) |
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x))) |
(*.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #s(literal 1/3 binary64)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) eps (*.f64 (*.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x)))) (tan.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (neg.f64 (sin.f64 x)))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x))) |
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) #s(literal 1/3 binary64)) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps)) |
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 x (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) (pow.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 2 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))))) (pow.f64 (*.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) #s(literal 2 binary64))))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))) eps)) |
3 calls:
| 160.0ms | x |
| 13.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 12.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | eps |
| 100.0% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
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(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 x (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) (pow.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 2 binary64))))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) (pow.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 2 binary64))))) |
3 calls:
| 25.0ms | x |
| 18.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 12.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
| 99.8% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (/.f64 eps x))) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) eps eps)) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) |
(-.f64 (tan.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
(neg.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) (tan.f64 x))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) |
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x))) |
(*.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #s(literal 1/3 binary64)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) eps (*.f64 (*.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x)))) (tan.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (neg.f64 (sin.f64 x)))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x))) |
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) #s(literal 1/3 binary64)) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal -1 binary64))))) eps)) |
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (tan.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (/.f64 x (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps)))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) eps)) |
3 calls:
| 15.0ms | x |
| 12.0ms | eps |
| 12.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
| 99.8% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (/.f64 eps x))) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) eps eps)) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) |
(-.f64 (tan.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
(neg.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) (tan.f64 x))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) |
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x))) |
(*.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #s(literal 1/3 binary64)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) eps (*.f64 (*.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) #s(approx (cos (+ eps x)) (fma.f64 (sin.f64 x) (neg.f64 eps) (cos.f64 x)))) (tan.f64 x)) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) (tan.f64 x)) |
(/.f64 (fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (neg.f64 (sin.f64 x)))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (cos.f64 x))) |
(/.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) #s(literal 1/3 binary64)) eps) eps (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)))) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps)) |
3 calls:
| 14.0ms | eps |
| 10.0ms | x |
| 10.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
| 99.8% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (/.f64 eps x))) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) eps eps)) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) |
(-.f64 (tan.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
(neg.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) (tan.f64 x))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) |
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x))) |
(*.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #s(literal 1/3 binary64)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #s(literal 1/3 binary64)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
3 calls:
| 10.0ms | eps |
| 8.0ms | x |
| 8.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
| 99.8% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2/3 binary64) (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) (/.f64 eps x))) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* eps eps) (neg (+ (* (* (+ (* (tan x) (tan x)) 1) (* eps (tan x))) -1/3) (+ (* (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))) (* eps (tan x))) (- (+ (* (pow (tan x) 2) -1/3) -1/3) (+ (* (tan x) (tan x)) (pow (tan x) 4))))))) (* (+ (* eps (tan x)) 1) (+ (* (tan x) (tan x)) 1))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 eps) eps) (*.f64 eps #s(literal -17/9 binary64)) (fma.f64 #s(literal 1/3 binary64) eps eps)) x (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/3 binary64) x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(approx (pow (cos x) 2) #s(literal 1 binary64))) eps eps)) |
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x)))) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) x))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) |
(-.f64 (tan.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (tan.f64 x)) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (tan.f64 x)) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
(neg.f64 (fma.f64 (sin.f64 (+.f64 eps x)) (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps x))) (tan.f64 x))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 (+.f64 x eps))) (neg.f64 (sin.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) |
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps x)))) (neg.f64 (tan.f64 x))) |
(*.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))) |
3 calls:
| 11.0ms | eps |
| 8.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 8.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.2% | 1 | x |
| 99.2% | 1 | eps |
| 99.2% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 62/315 binary64) (*.f64 x x) #s(literal 17/45 binary64)) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps (neg.f64 eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
3 calls:
| 4.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 4.0ms | eps |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.2% | 1 | x |
| 99.2% | 1 | eps |
| 99.2% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/45 binary64) (*.f64 x x) #s(literal 2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
3 calls:
| 28.0ms | eps |
| 3.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.2% | 1 | x |
| 99.2% | 1 | eps |
| 99.2% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 (*.f64 (fma.f64 #s(literal 2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x)) eps eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
3 calls:
| 2.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 2.0ms | x |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.1% | 1 | x |
| 99.1% | 1 | eps |
| 99.1% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 #s(approx (/ (pow (sin x) 2) (pow (cos x) 2)) (*.f64 x x)) #s(literal 1 binary64)) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) |
3 calls:
| 2.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 2.0ms | x |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 1 | x |
| 98.9% | 1 | eps |
| 98.9% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
3 calls:
| 1.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 1.0ms | x |
| 1.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.4% | 1 | eps |
| 98.4% | 1 | x |
| 98.4% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| 1× | egg-herbie |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 174 | 1617 |
| 1 | 313 | 1596 |
| 2 | 794 | 1584 |
| 3 | 2955 | 1532 |
| 1× | node limit |
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) (tan.f64 x) (+.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) (pow.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 2 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #s(literal 1/3 binary64)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) (tan.f64 x) (+.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (tan.f64 x)) (tan.f64 x) (-.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 (neg.f64 eps) eps) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (*.f64 eps (tan.f64 x)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) (pow.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps)) #s(literal 2 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (-.f64 (pow.f64 (*.f64 eps (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 eps (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) (*.f64 eps eps))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 #s(approx (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) (fma.f64 (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x)) x #s(literal 1/3 binary64))) eps) eps (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 eps eps) #s(approx (neg (+ (* (* eps (sin x)) (+ (* -1/3 (/ (+ (* (tan x) (tan x)) 1) (cos x))) (/ (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)) (cos x)))) (+ (* (neg (pow (cos x) -2)) (+ (* (sin x) (sin x)) (pow (* (sin x) (tan x)) 2))) (+ (* (pow (tan x) 2) -1/3) -1/3)))) #s(literal 1/3 binary64)) (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2/3 binary64) eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/3 binary64) eps) x (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64))) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (neg (+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))))) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) (+ (* (pow eps 3) 2/3) eps)) x) (+ (* (* eps eps) 1/3) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) (fma.f64 x x #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) #s(literal 1 binary64)) eps)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 57 | 665 |
| 0 | 110 | 649 |
| 1 | 485 | 546 |
| 2 | 4365 | 526 |
| 0 | 8147 | 515 |
| 0 | 922 | 7426 |
| 1 | 3081 | 7213 |
| 0 | 8191 | 6814 |
| 0 | 747 | 5061 |
| 1 | 2418 | 4868 |
| 0 | 8010 | 4589 |
| 0 | 90 | 961 |
| 0 | 159 | 949 |
| 1 | 671 | 654 |
| 2 | 6324 | 654 |
| 0 | 9220 | 643 |
| 0 | 157 | 950 |
| 1 | 464 | 884 |
| 2 | 1539 | 873 |
| 3 | 6077 | 710 |
| 0 | 8335 | 686 |
| 0 | 726 | 5927 |
| 1 | 2368 | 5709 |
| 2 | 7941 | 5650 |
| 0 | 8117 | 5392 |
| 0 | 101 | 1411 |
| 0 | 169 | 1395 |
| 1 | 775 | 1097 |
| 2 | 7417 | 1097 |
| 0 | 8449 | 1069 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 2 363 to 515 computations (78.2% saved)
Compiled 3 368 to 392 computations (88.4% saved)
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