
Time bar (total: 12.0s)
| 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)
| 3.6s | 26 232× | 0 | invalid |
| 650.0ms | 5 481× | 0 | valid |
| 538.0ms | 2 775× | 1 | valid |
const: 803.0ms (24.3% of total)ival-tan: 714.0ms (21.6% of total)ival-add: 383.0ms (11.6% of total)ival-<=: 318.0ms (9.6% of total)ival-<: 236.0ms (7.1% of total)ival-mult: 222.0ms (6.7% of total)ival-fabs: 208.0ms (6.3% of total)ival-sub: 189.0ms (5.7% of total)ival-and: 105.0ms (3.2% of total)adjust: 76.0ms (2.3% of total)exact: 40.0ms (1.2% of total)ival-assert: 11.0ms (0.3% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 223 | 1 | (-1.1250245095404491e-234 9.388785750458769e-237) | 2 | (-5.91046744799245e-23 8.546941406357813e-25) | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 3 | 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 | 222 | 6 |
tan.f64 | (tan.f64 (+.f64 x eps)) | sensitivity | 3 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 222 | 3 |
| - | 1 | 30 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 222 | 2 | 1 |
| - | 1 | 4 | 26 |
| number | freq |
|---|---|
| 0 | 33 |
| 1 | 221 |
| 2 | 2 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 37.0ms | 308× | 0 | valid |
| 20.0ms | 204× | 1 | valid |
Compiled 47 to 22 computations (53.2% saved)
ival-sub: 25.0ms (59.4% of total)ival-tan: 9.0ms (21.4% of total)adjust: 4.0ms (9.5% of total)ival-add: 3.0ms (7.1% of total)ival-true: 0.0ms (0% of total)ival-assert: 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 |
|---|---|---|
| ▶ | 59.8% | (-.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 | 0.12667603662424365 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 25.6243997000046 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 10.0ms | 102× | 1 | valid |
| 7.0ms | 154× | 0 | valid |
Compiled 20 to 8 computations (60% saved)
ival-tan: 4.0ms (41.2% of total)adjust: 2.0ms (20.6% of total)ival-add: 2.0ms (20.6% of total)ival-sub: 1.0ms (10.3% of total)ival-true: 0.0ms (0% of total)ival-assert: 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 | |
|---|---|---|---|---|
| 12.0ms | x | @ | -inf | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 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 | 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)
19 alts after pruning (18 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 258 | 18 | 276 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 258 | 19 | 277 |
| Status | Accuracy | Program |
|---|---|---|
| 24.0% | (fma.f64 (pow.f64 (tan.f64 (+.f64 eps 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)) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (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)))))) | |
| 59.7% | (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) | |
| 60.0% | (fma.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)))) (neg.f64 (tan.f64 x))) | |
| 59.7% | (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))) | |
| 60.0% | (/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (*.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))) | |
| ▶ | 59.9% | (/.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 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))) |
| ▶ | 34.7% | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
| ▶ | 59.8% | (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
| 60.0% | (-.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)) | |
| 59.8% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) | |
| 59.2% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| 59.7% | (-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))) | |
| ✓ | 59.8% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 98.1% | #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)))) | |
| 98.6% | #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)) | |
| ▶ | 97.3% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
| 99.2% | #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)) | |
| ▶ | 99.3% | #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)) |
| 98.8% | #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 1 099 to 548 computations (50.1% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 (tan.f64 eps) (tan.f64 x)) | |
| cost-diff | 0 | (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) | |
| cost-diff | 2 | (-.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))) | |
| cost-diff | 9 | (/.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 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))) | |
| cost-diff | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) | |
| cost-diff | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)) | |
| cost-diff | 2 | (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) | |
| cost-diff | 14 | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| cost-diff | 0 | (+.f64 eps x) | |
| cost-diff | 0 | (sin.f64 (-.f64 (+.f64 eps x) x)) | |
| cost-diff | 0 | (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| cost-diff | 4 | (-.f64 (+.f64 eps x) 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 | (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) | |
| 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 | 3 | (*.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)))) | |
| cost-diff | 4 | (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)))))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 63 | 1207 |
| 0 | 121 | 1183 |
| 1 | 230 | 1181 |
| 2 | 575 | 1156 |
| 3 | 2049 | 1117 |
| 0 | 8774 | 1097 |
| 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 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(sin.f64 (-.f64 (+.f64 eps x) x)) |
(-.f64 (+.f64 eps x) x) |
(+.f64 eps x) |
eps |
x |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos.f64 (+.f64 eps x)) |
(cos.f64 x) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.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 x))) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(tan.f64 x) |
x |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.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 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))) |
(-.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 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
eps |
(tan.f64 x) |
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)) |
(neg.f64 (tan.f64 eps)) |
#s(literal 1 binary64) |
(sin.f64 x) |
(*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.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)) (*.f64 (fma.f64 (*.f64 eps eps) (+.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 #s(literal -1/3 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 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 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 (sin.f64 x) (cos.f64 x))) eps)) (*.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)))) 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) |
(*.f64 (fma.f64 (*.f64 eps eps) (+.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 #s(literal -1/3 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 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 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 (sin.f64 x) (cos.f64 x))) eps)) (*.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)))) 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)))) |
(fma.f64 (*.f64 eps eps) (+.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 #s(literal -1/3 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 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 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 (sin.f64 x) (cos.f64 x))) eps)) (*.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 (+.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 #s(literal -1/3 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 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 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 (sin.f64 x) (cos.f64 x))) eps)) 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))))))) |
(+.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 #s(literal -1/3 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 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 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 (sin.f64 x) (cos.f64 x))) eps)) |
(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 #s(literal -1/3 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 (fma.f64 #s(literal -1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 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) (cos.f64 x))) 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)))) (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)))) |
(*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 #s(literal -1/3 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 #s(literal -1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 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))))))) |
(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 #s(literal -1/3 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 (fma.f64 #s(literal -1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 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)) |
(/.f64 (fma.f64 #s(literal -1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 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))))) |
(fma.f64 #s(literal -1/3 binary64) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 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 (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 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(sin.f64 (-.f64 (+.f64 eps x) x)) |
(sin.f64 eps) |
(-.f64 (+.f64 eps x) x) |
eps |
(+.f64 eps x) |
eps |
x |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos.f64 (+.f64 eps x)) |
(cos.f64 x) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) |
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) |
(+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(tan.f64 x) |
x |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (tan.f64 (+.f64 eps x))) |
(/.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 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))) |
(-.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(-.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 (fma.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 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
eps |
(tan.f64 x) |
x |
(cos.f64 x) |
(*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) |
(*.f64 (neg.f64 (fma.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)) |
(neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64))) |
(neg.f64 (tan.f64 eps)) |
#s(literal 1 binary64) |
(sin.f64 x) |
(*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x)) |
(*.f64 (neg.f64 (fma.f64 (tan.f64 eps) (tan.f64 x) #s(literal -1 binary64))) (cos.f64 x)) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.01953125 | (/.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 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))) | |
| accuracy | 0.021816259768442016 | (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) | |
| accuracy | 0.02734375 | (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) | |
| accuracy | 25.611369453282492 | (-.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))) | |
| accuracy | 0.1875 | (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) | |
| accuracy | 0.21875 | (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) | |
| accuracy | 26.181621164799637 | (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) | |
| accuracy | 28.317254210816326 | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| accuracy | 0.015625 | (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| accuracy | 0.03125 | (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) | |
| accuracy | 0.10011884073013777 | (cos.f64 (+.f64 eps x)) | |
| accuracy | 25.748357568802987 | (-.f64 (+.f64 eps x) x) | |
| accuracy | 0.0 | (sin.f64 eps) | |
| accuracy | 0.0 | (cos.f64 eps) | |
| accuracy | 0.00390625 | (/.f64 (sin.f64 eps) (cos.f64 eps)) | |
| accuracy | 1.7367886639738366 | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) | |
| accuracy | 0.037441259768442016 | (pow.f64 (cos.f64 x) #s(literal 2 binary64)) | |
| accuracy | 0.3046875 | (*.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 | 0.33203125 | (*.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)))) | |
| accuracy | 0.44856167886737885 | #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)) |
| 106.0ms | 104× | 1 | valid |
| 66.0ms | 151× | 0 | valid |
| 2.0ms | 1× | 2 | valid |
Compiled 1 160 to 69 computations (94.1% saved)
ival-mult: 36.0ms (26.5% of total)ival-div: 24.0ms (17.6% of total)ival-add: 16.0ms (11.8% of total)adjust: 14.0ms (10.3% of total)ival-tan: 9.0ms (6.6% of total)ival-sub: 7.0ms (5.1% of total)ival-cos: 6.0ms (4.4% of total)ival-neg: 6.0ms (4.4% of total)const: 5.0ms (3.7% of total)ival-pow: 5.0ms (3.7% of total)ival-sin: 5.0ms (3.7% of total)ival-pow2: 3.0ms (2.2% 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 (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)))) |
(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))))))) |
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 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 eps x) x) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(sin.f64 (-.f64 (+.f64 eps x) x)) |
(+.f64 eps x) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.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 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))) |
(-.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 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
#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 (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 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 (+.f64 eps x)) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) |
(*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 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) |
(* -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 |
(+ 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)))) |
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)))))) |
(/ (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 |
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(sin eps) |
(+ eps x) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (* x (+ (* -1 (+ 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 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (* (sin eps) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))))))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(/ 1 x) |
(/ (+ 1 (* -1/3 (pow x 2))) x) |
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x) |
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x) |
(/ (cos eps) (sin eps)) |
(+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps))) |
(+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 2) (+ 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))))))) (pow (sin eps) 2))) (* -1 (/ (* (pow (cos eps) 2) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 2))))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) |
(/ (cos eps) (* x (sin eps))) |
(/ (+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps))) x) |
(/ (+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x) |
(/ (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 3) (* (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* -1 (+ 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))))))) (* 1/3 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (pow (sin eps) 2)))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* (pow x 2) (- (* -1/2 (/ (sin eps) (cos eps))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))) |
(+ (* (pow x 2) (- (+ (* -1/2 (/ (sin eps) (cos eps))) (* (pow x 2) (- (* 1/24 (/ (sin eps) (cos eps))) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))) |
(+ (* (pow x 2) (- (+ (* -1/2 (/ (sin eps) (cos eps))) (* (pow x 2) (- (+ (* 1/24 (/ (sin eps) (cos eps))) (* (pow x 2) (- (* -1/720 (/ (sin eps) (cos eps))) (+ (* -2/15 (/ (sin eps) (cos eps))) (+ (* -1/120 (/ (sin eps) (cos eps))) (* 1/18 (/ (sin eps) (cos eps)))))))) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))) |
(+ x (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* -1/2 (/ (* x (sin eps)) (cos eps))))) (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* x (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/6 x))))) (/ (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))) |
(* 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))))))) |
(+ 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)))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps)))))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))) |
(/ (+ 1 (* -1 (/ (* x (cos eps)) (sin eps)))) x) |
(/ (+ 1 (* x (- (* x (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (cos eps) (sin eps))))) x) |
(/ (+ 1 (* x (- (* x (- (+ (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2))) 1/3)) (/ (cos eps) (sin eps))))) x) |
x |
(* x (+ 1 (* -1 (/ (* x (sin eps)) (cos eps))))) |
(* x (+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1/6 x))))) |
(* x (+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* x (- (* x (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))) 1/6)))))) |
(+ (* -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 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))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(+ 1 (/ (* eps (sin x)) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(* x (+ 1 (/ eps x))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (cos x) (sin x)) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (* (cos x) (cos (+ eps x))) (* (sin x) (sin (+ eps x)))) |
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) |
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) |
(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) |
(+ (/ (sin eps) (cos eps)) (/ (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 (* (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 (cos x) 2) |
(cos (+ eps x)) |
(* (cos x) (cos (+ eps x))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) |
(/ (* (cos x) (cos (- eps (* -1 x)))) (* (sin x) (sin (- eps (* -1 x))))) |
(cos (- eps (* -1 x))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- 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))))) |
(* -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 (* 1/3 (pow eps 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))) |
(/ eps (pow (cos x) 2)) |
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) |
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ (* -1 (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (/ (cos x) (sin x))) |
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(/ (pow (cos x) 2) (pow (sin x) 2)) |
(+ (* -1 (/ (* eps (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3))) (/ (pow (cos x) 2) (pow (sin x) 2))) |
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2))) |
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 3) (+ 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))))))) (pow (sin x) 3))) (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))))))) (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2))) |
(/ (* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (cos x)) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))) (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1/3 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2))))))) (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) |
(* eps (- (+ (cos x) (* (pow eps 2) (- (* 1/3 (cos x)) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x))))) |
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (* 2/15 (cos x)) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x))))) |
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (+ (* 2/15 (cos x)) (* (pow eps 2) (- (* 17/315 (cos x)) (* -17/315 (/ (pow (sin x) 2) (cos x)))))) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x))))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* 1/3 (* (pow eps 2) (cos x)))))) |
(+ (sin x) (* eps (+ (cos x) (* (pow eps 2) (+ (* 2/15 (* (pow eps 2) (cos x))) (* 1/3 (cos x))))))) |
(/ (sin x) (cos x)) |
(+ eps (/ (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)))) |
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2)) |
(/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2)) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* eps (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(+ (sin x) (* -1 (/ (* eps (pow (sin x) 2)) (cos x)))) |
(+ (sin x) (* eps (+ (* -1 (/ (pow (sin x) 2) (cos x))) (* -1/3 (/ (* (pow eps 2) (pow (sin x) 2)) (cos x)))))) |
(+ (sin x) (* eps (+ (* -1 (/ (pow (sin x) 2) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (pow (sin x) 2) (cos x))) (* -2/15 (/ (* (pow eps 2) (pow (sin x) 2)) (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 (* 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 (sin x)) (cos x)) |
(* eps (+ (/ 1 eps) (/ (sin x) (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))))) |
(* -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 (- (* -1 (/ (sin x) (cos x))) (/ 1 eps)))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(sin (neg (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))) |
(/ (* (cos x) (cos (- x (* -1 eps)))) (* (sin x) (sin (- x (* -1 eps))))) |
(cos (- x (* -1 eps))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 23.0ms | x | @ | -inf | ((+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (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)))))) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (+ (tan eps) (tan x)) (- (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) (pow (cos x) 2) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) |
| 22.0ms | x | @ | inf | ((+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (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)))))) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (+ (tan eps) (tan x)) (- (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) (pow (cos x) 2) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) |
| 20.0ms | eps | @ | 0 | ((+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (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)))))) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (+ (tan eps) (tan x)) (- (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) (pow (cos x) 2) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) |
| 17.0ms | eps | @ | -inf | ((+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (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)))))) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (+ (tan eps) (tan x)) (- (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) (pow (cos x) 2) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) |
| 16.0ms | x | @ | 0 | ((+ (* (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2)))) (cos x)))) eps) (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (neg (pow (cos x) 2))))) (* (sin x) (+ (* (/ (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (cos x)) -1/3) (/ (+ (* (+ (* (/ (sin x) (pow (cos x) 2)) (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)))))) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (- (+ eps x) x) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (+ eps x) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (* (/ 1 (tan (+ eps x))) (/ 1 (tan x))) (/ (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (cos x))) (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (* (+ (tan eps) (tan x)) (cos x)) (+ (tan eps) (tan x)) (- (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) (pow (cos x) 2) (cos (+ eps x)) (* (cos (+ eps x)) (cos x)) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (tan (+ eps x))) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 963 | 8537 |
| 1 | 3144 | 7981 |
| 0 | 8507 | 7715 |
| 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) |
(* -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 |
(+ 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)))) |
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)))))) |
(/ (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 |
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(sin eps) |
(+ eps x) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (* x (+ (* -1 (+ 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 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (* (sin eps) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))))))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(/ 1 x) |
(/ (+ 1 (* -1/3 (pow x 2))) x) |
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x) |
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x) |
(/ (cos eps) (sin eps)) |
(+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps))) |
(+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 2) (+ 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))))))) (pow (sin eps) 2))) (* -1 (/ (* (pow (cos eps) 2) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 2))))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) |
(/ (cos eps) (* x (sin eps))) |
(/ (+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps))) x) |
(/ (+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x) |
(/ (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 3) (* (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* -1 (+ 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))))))) (* 1/3 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (pow (sin eps) 2)))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* (pow x 2) (- (* -1/2 (/ (sin eps) (cos eps))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))) |
(+ (* (pow x 2) (- (+ (* -1/2 (/ (sin eps) (cos eps))) (* (pow x 2) (- (* 1/24 (/ (sin eps) (cos eps))) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))) |
(+ (* (pow x 2) (- (+ (* -1/2 (/ (sin eps) (cos eps))) (* (pow x 2) (- (+ (* 1/24 (/ (sin eps) (cos eps))) (* (pow x 2) (- (* -1/720 (/ (sin eps) (cos eps))) (+ (* -2/15 (/ (sin eps) (cos eps))) (+ (* -1/120 (/ (sin eps) (cos eps))) (* 1/18 (/ (sin eps) (cos eps)))))))) (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))))) (* -1 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))) |
(+ x (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* -1/2 (/ (* x (sin eps)) (cos eps))))) (/ (sin eps) (cos eps))) |
(+ (* x (+ 1 (* x (+ (* -1/2 (/ (sin eps) (cos eps))) (* -1/6 x))))) (/ (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))) |
(* 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))))))) |
(+ 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)))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps)))))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))) |
(/ (+ 1 (* -1 (/ (* x (cos eps)) (sin eps)))) x) |
(/ (+ 1 (* x (- (* x (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (cos eps) (sin eps))))) x) |
(/ (+ 1 (* x (- (* x (- (+ (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2))) 1/3)) (/ (cos eps) (sin eps))))) x) |
x |
(* x (+ 1 (* -1 (/ (* x (sin eps)) (cos eps))))) |
(* x (+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1/6 x))))) |
(* x (+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* x (- (* x (+ (* -1/3 (/ (sin eps) (cos eps))) (* 1/6 (/ (sin eps) (cos eps))))) 1/6)))))) |
(+ (* -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 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))) (* -2/3 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (cos x))))))))) |
(+ 1 (/ (* eps (sin x)) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(* x (+ 1 (/ eps x))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (cos x) (sin x)) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(/ (* (cos x) (cos (+ eps x))) (* (sin x) (sin (+ eps x)))) |
(/ (- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) |
(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) |
(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) |
(+ (/ (sin eps) (cos eps)) (/ (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 (* (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 (cos x) 2) |
(cos (+ eps x)) |
(* (cos x) (cos (+ eps x))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) |
(/ (* (cos x) (cos (- eps (* -1 x)))) (* (sin x) (sin (- eps (* -1 x))))) |
(cos (- eps (* -1 x))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- 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))))) |
(* -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 (* 1/3 (pow eps 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))) |
(/ eps (pow (cos x) 2)) |
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) |
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ (* -1 (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (/ (cos x) (sin x))) |
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(/ (pow (cos x) 2) (pow (sin x) 2)) |
(+ (* -1 (/ (* eps (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3))) (/ (pow (cos x) 2) (pow (sin x) 2))) |
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2))) |
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 3) (+ 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))))))) (pow (sin x) 3))) (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))))))) (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2))) |
(/ (* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (cos x)) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x)))))) (pow (cos x) 2))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1/3 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2))))))) (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) |
(* eps (- (+ (cos x) (* (pow eps 2) (- (* 1/3 (cos x)) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x))))) |
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (* 2/15 (cos x)) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x))))) |
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (+ (* 2/15 (cos x)) (* (pow eps 2) (- (* 17/315 (cos x)) (* -17/315 (/ (pow (sin x) 2) (cos x)))))) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x))))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* 1/3 (* (pow eps 2) (cos x)))))) |
(+ (sin x) (* eps (+ (cos x) (* (pow eps 2) (+ (* 2/15 (* (pow eps 2) (cos x))) (* 1/3 (cos x))))))) |
(/ (sin x) (cos x)) |
(+ eps (/ (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)))) |
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2)) |
(/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2)) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* eps (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(+ (sin x) (* -1 (/ (* eps (pow (sin x) 2)) (cos x)))) |
(+ (sin x) (* eps (+ (* -1 (/ (pow (sin x) 2) (cos x))) (* -1/3 (/ (* (pow eps 2) (pow (sin x) 2)) (cos x)))))) |
(+ (sin x) (* eps (+ (* -1 (/ (pow (sin x) 2) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (pow (sin x) 2) (cos x))) (* -2/15 (/ (* (pow eps 2) (pow (sin x) 2)) (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 (* 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 (sin x)) (cos x)) |
(* eps (+ (/ 1 eps) (/ (sin x) (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))))) |
(* -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 (- (* -1 (/ (sin x) (cos x))) (/ 1 eps)))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(sin (neg (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))) |
(/ (* (cos x) (cos (- x (* -1 eps)))) (* (sin x) (sin (- x (* -1 eps))))) |
(cos (- x (* -1 eps))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
| Outputs |
|---|
-1/3 |
#s(literal -1/3 binary64) |
(- (* -2/3 (* eps x)) 1/3) |
(fma.f64 (*.f64 eps x) #s(literal -2/3 binary64) #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)) |
(* -2/3 x) |
(*.f64 #s(literal -2/3 binary64) x) |
(* x (- (* -17/9 (pow x 2)) 2/3)) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal -17/9 binary64) #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 |
#s(literal 1/3 binary64) |
(+ 1/3 (* 2/3 (* eps x))) |
(fma.f64 #s(literal 2/3 binary64) (*.f64 eps x) #s(literal 1/3 binary64)) |
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps)))) |
(fma.f64 (fma.f64 #s(literal 4/3 binary64) x (*.f64 #s(literal 2/3 binary64) eps)) 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)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* eps x)) |
(fma.f64 eps x #s(literal 1 binary64)) |
(+ 1 (* x (+ eps (* (pow x 2) (- (* -1/6 eps) (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) (*.f64 x x) 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 (*.f64 #s(literal 1/3 binary64) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) eps))) (*.f64 x x) (*.f64 #s(literal 1/3 binary64) eps)) (*.f64 x x) eps) x #s(literal 1 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 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 1/6 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal -1/2 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))) |
eps |
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (neg.f64 x) (-.f64 (/.f64 (neg.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))) (/.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 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (neg.f64 (fma.f64 (fma.f64 (sin.f64 eps) (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 #s(literal 2/3 binary64) (cos.f64 eps)) (/.f64 (-.f64 (/.f64 (neg.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))) (cos.f64 eps))) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (-.f64 (/.f64 (neg.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))) |
(sin eps) |
(sin.f64 eps) |
(+ eps x) |
(+.f64 eps x) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 1/3 binary64) (fma.f64 (sin.f64 eps) (+.f64 (/.f64 (fma.f64 (pow.f64 (cos.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 (sin.f64 eps) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (cos.f64 eps)) (/.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)))) (cos.f64 eps))) (/.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)))) (cos.f64 eps)) (neg.f64 (sin.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))) |
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(- (* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) (* (sin x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) |
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(* (cos x) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))) |
(*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 x)) |
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(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
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(fma.f64 (/.f64 eps (neg.f64 x)) (neg.f64 x) x) |
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(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) |
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(*.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 (+.f64 eps x)))) |
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(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
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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))))) |
(*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 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))))) |
(*.f64 (fma.f64 eps (/.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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))))) |
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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 (* 1/3 (pow eps 2)))) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps) |
(+ 1 (* -1/2 (pow eps 2))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
(/ eps (pow (cos x) 2)) |
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) |
(*.f64 (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(*.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (/.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) |
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
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(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1/3 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2))))))) (+ (* -1 (/ (* (pow (sin x) 2) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 3))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) (pow (cos x) 2)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (cos x) (* -1 (/ (pow (sin x) 2) (cos x))))) |
(*.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))) eps) |
(* eps (- (+ (cos x) (* (pow eps 2) (- (* 1/3 (cos x)) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) (*.f64 eps eps) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) eps) |
(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (* 2/15 (cos x)) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (cos x))))) |
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(* eps (- (+ (cos x) (* (pow eps 2) (- (+ (* 1/3 (cos x)) (* (pow eps 2) (- (+ (* 2/15 (cos x)) (* (pow eps 2) (- (* 17/315 (cos x)) (* -17/315 (/ (pow (sin x) 2) (cos x)))))) (* -2/15 (/ (pow (sin x) 2) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (cos x)))))) (* -1 (/ (pow (sin x) 2) (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) (* 1/3 (* (pow eps 2) (cos x)))))) |
(fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) (cos.f64 x)) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* (pow eps 2) (+ (* 2/15 (* (pow eps 2) (cos x))) (* 1/3 (cos x))))))) |
(fma.f64 (fma.f64 (*.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64))) (*.f64 eps eps) (cos.f64 x)) eps (sin.f64 x)) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(+ eps (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 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))))))) |
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(* 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)))))))) |
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(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(fma.f64 (neg.f64 eps) (sin.f64 x) (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)))) |
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(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) |
(fma.f64 (neg.f64 (*.f64 (cos.f64 x) eps)) (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) |
(fma.f64 (-.f64 (*.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps) #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) (sin.f64 x))) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2)) |
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(/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2)) |
(/.f64 (*.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
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(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
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(* 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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(*.f64 (neg.f64 eps) (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)))) |
(* -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 (neg.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)) 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))))) |
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps)))) |
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) 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 (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))) |
(sin (neg (* -1 eps))) |
(sin.f64 eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (/.f64 (neg.f64 x) eps) (neg.f64 eps) eps) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (*.f64 (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))) |
(/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) |
(/ (* (cos x) (cos (- x (* -1 eps)))) (* (sin x) (sin (- x (* -1 eps))))) |
(*.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 (+.f64 eps x)))) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(* (cos x) (cos (- x (* -1 eps)))) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 63 | 674 |
| 0 | 121 | 629 |
| 1 | 527 | 523 |
| 2 | 4769 | 505 |
| 0 | 8218 | 494 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(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)))) |
(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))))))) |
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 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 eps x) x) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(sin.f64 (-.f64 (+.f64 eps x) x)) |
(+.f64 eps x) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.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 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))) |
(-.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 (+.f64 (tan.f64 eps) (tan.f64 x)) (cos.f64 x)) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
#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 (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 (cos.f64 x) #s(literal 2 binary64)) |
(cos.f64 (+.f64 eps x)) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) |
(*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) |
| Outputs |
|---|
(*.f64 (-.f64 (pow.f64 (*.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)))) #s(literal 2 binary64)) (pow.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))) #s(literal 2 binary64))) (pow.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))) (neg.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))))) #s(literal -1 binary64))) |
(*.f64 (+.f64 (pow.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))) #s(literal 3 binary64)) (pow.f64 (*.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)))) #s(literal 3 binary64))) (pow.f64 (fma.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))) (-.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))) (*.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))))) (pow.f64 (*.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)))) #s(literal 2 binary64))) #s(literal -1 binary64))) |
(pow.f64 (/.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))) (neg.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))))) (-.f64 (pow.f64 (*.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)))) #s(literal 2 binary64)) (pow.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))) #s(literal 2 binary64)))) #s(literal -1 binary64)) |
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(*.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(*.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(*.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(*.f64 (cos.f64 x) (cos.f64 x)) |
(pow.f64 (exp.f64 (log.f64 (cos.f64 x))) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(/.f64 (+.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(neg.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(-.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 (cos.f64 x)))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 2 binary64))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64))) (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))) (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))))) |
(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) (neg.f64 (*.f64 (sin.f64 eps) (sin.f64 x)))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.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)))) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) |
(cos.f64 (+.f64 eps x)) |
(+.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)) (neg.f64 (*.f64 (sin.f64 eps) (sin.f64 x)))) |
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) |
(*.f64 (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x))) #s(literal 1/2 binary64)) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal -1 binary64)) |
(/.f64 (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (-.f64 (+.f64 eps x) (neg.f64 x)))) #s(literal 2 binary64)) |
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal -2 binary64)) |
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 eps x) x)) (cos.f64 (-.f64 x (+.f64 eps x)))) #s(literal 2 binary64)) |
(/.f64 (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x))) #s(literal 2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x))))) |
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64))) (pow.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) #s(literal -1 binary64))) |
(*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64))) (pow.f64 (+.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)))) |
(pow.f64 (/.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64)))) #s(literal -1 binary64)) |
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))))) |
(/.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64)) #s(literal -1 binary64))) (+.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (-.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)))) (neg.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64)))) (neg.f64 (+.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))) |
(/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 (+.f64 eps x)))) (*.f64 (neg.f64 (tan.f64 x)) #s(literal -1 binary64))) (*.f64 (neg.f64 (tan.f64 x)) (neg.f64 (tan.f64 (+.f64 eps x))))) |
(/.f64 (-.f64 (neg.f64 (tan.f64 (+.f64 eps x))) (*.f64 (neg.f64 (tan.f64 x)) #s(literal 1 binary64))) (*.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 eps x)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (tan.f64 (+.f64 eps x)))) (*.f64 (tan.f64 x) #s(literal -1 binary64))) (*.f64 (tan.f64 x) (neg.f64 (tan.f64 (+.f64 eps x))))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))) |
(/.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64))) (+.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))) |
(/.f64 (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))) (-.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64))))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (pow.f64 (tan.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(fma.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (cos.f64 x) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(fma.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) |
(fma.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (tan.f64 x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(fma.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) |
(fma.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) |
(fma.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) |
(fma.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(-.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -2 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64)))) (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))))) |
(-.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64)))) (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -3 binary64)) (+.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -2 binary64)) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 (+.f64 eps x)))) (pow.f64 (tan.f64 x) #s(literal -2 binary64))))) |
(-.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) |
(+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) |
(+.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(*.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal -1 binary64)) (cos.f64 (+.f64 eps x))) |
(*.f64 (pow.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.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 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64))) |
(pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (neg.f64 (neg.f64 (tan.f64 (+.f64 eps x)))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) |
(pow.f64 (tan.f64 (+.f64 eps x)) #s(literal -1 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 (+.f64 eps x)))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (tan.f64 (+.f64 eps x))))) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 eps x)))) |
(exp.f64 (*.f64 (log.f64 (tan.f64 (+.f64 eps x))) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (sin.f64 x)) |
(*.f64 (sin.f64 x) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal -1 binary64))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (sin.f64 x)) (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x))) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) |
(/.f64 (*.f64 (sin.f64 x) (-.f64 (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal -1 binary64))) |
(/.f64 (*.f64 (sin.f64 x) (+.f64 (pow.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64))) (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x))) (pow.f64 (*.f64 (tan.f64 eps) (tan.f64 x)) #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) (sin.f64 x) (*.f64 #s(literal 1 binary64) (sin.f64 x))) |
(fma.f64 #s(literal 1 binary64) (sin.f64 x) (*.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) (sin.f64 x))) |
(fma.f64 (sin.f64 x) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) (*.f64 (sin.f64 x) #s(literal 1 binary64))) |
(fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)))) |
(+.f64 (*.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) (sin.f64 x)) (*.f64 #s(literal 1 binary64) (sin.f64 x))) |
(+.f64 (*.f64 (sin.f64 x) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x))) (*.f64 (sin.f64 x) #s(literal 1 binary64))) |
(+.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (*.f64 (sin.f64 x) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)))) |
(+.f64 (*.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) (sin.f64 x))) |
Compiled 73 245 to 5 279 computations (92.8% saved)
22 alts after pruning (20 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 969 | 17 | 986 |
| Fresh | 10 | 3 | 13 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 1 | 1 |
| Total | 983 | 22 | 1 005 |
| Status | Accuracy | Program |
|---|---|---|
| 60.0% | (/.f64 (fma.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (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))) | |
| ▶ | 99.8% | (/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x)) |
| ✓ | 59.9% | (/.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 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))) |
| 34.7% | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) | |
| 35.0% | (/.f64 (sin.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 eps eps (-.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 0 binary64)))))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| 99.5% | (/.f64 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/15 binary64) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))) (*.f64 eps eps) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) eps)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))) | |
| 99.4% | (/.f64 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (*.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) (*.f64 eps eps) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) eps)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))) | |
| 99.8% | (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| ▶ | 60.0% | (-.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)) |
| 59.2% | (-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| ✓ | 59.8% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 99.6% | (*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 eps x))) (pow.f64 (pow.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(literal -1 binary64)) #s(literal -1 binary64))) | |
| 99.8% | (*.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64)) | |
| ▶ | 99.8% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
| 98.5% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) | |
| ▶ | 97.3% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
| 99.3% | #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)) | |
| 98.8% | #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)) | |
| 97.3% | #s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) | |
| ▶ | 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
Compiled 1 217 to 705 computations (42.1% 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)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) | |
| cost-diff | 0 | (-.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)) | |
| cost-diff | 0 | (sin.f64 (+.f64 #s(literal 0 binary64) eps)) | |
| cost-diff | 0 | (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) | |
| cost-diff | 0 | (/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x)) | |
| cost-diff | 2 | (+.f64 #s(literal 0 binary64) eps) | |
| cost-diff | 0 | #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) | |
| cost-diff | 0 | (sin.f64 eps) | |
| cost-diff | 0 | (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) | |
| cost-diff | 0 | (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (/ (sin eps) (cos eps)) (*.f64 (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)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) | |
| cost-diff | 2 | (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps) | |
| cost-diff | 0 | (sin.f64 eps) | |
| cost-diff | 0 | (/.f64 (sin.f64 eps) (cos.f64 x)) | |
| cost-diff | 0 | (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))) | |
| cost-diff | 0 | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 47 | 255 |
| 0 | 72 | 247 |
| 1 | 107 | 243 |
| 2 | 165 | 243 |
| 3 | 413 | 240 |
| 4 | 2125 | 240 |
| 5 | 3430 | 240 |
| 6 | 5705 | 240 |
| 7 | 7792 | 240 |
| 0 | 8080 | 237 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))) |
(/.f64 (sin.f64 eps) (cos.f64 x)) |
(sin.f64 eps) |
eps |
(cos.f64 x) |
x |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
(*.f64 eps eps) |
eps |
#s(literal 1/3 binary64) |
#s(literal 1 binary64) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
(sin.f64 eps) |
eps |
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(*.f64 eps eps) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x)) |
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) |
(sin.f64 (+.f64 #s(literal 0 binary64) eps)) |
(+.f64 #s(literal 0 binary64) eps) |
#s(literal 0 binary64) |
eps |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
x |
(cos.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 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
eps |
(tan.f64 x) |
x |
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) |
(neg.f64 (tan.f64 eps)) |
#s(literal 1 binary64) |
| Outputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x)) |
(/.f64 (sin.f64 eps) (cos.f64 x)) |
(sin.f64 eps) |
eps |
(cos.f64 x) |
x |
(cos.f64 (+.f64 eps x)) |
(cos.f64 (+.f64 x eps)) |
(+.f64 eps x) |
(+.f64 x eps) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))) |
#s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)) |
#s(approx (/ (sin eps) (cos eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) |
(*.f64 eps eps) |
eps |
#s(literal 1/3 binary64) |
#s(literal 1 binary64) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64))))) |
(/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
(/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) |
(sin.f64 eps) |
eps |
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
#s(approx (cos eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps eps) #s(literal 1 binary64)) |
(*.f64 eps eps) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x)) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x)) |
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) |
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) |
(sin.f64 (+.f64 #s(literal 0 binary64) eps)) |
(sin.f64 eps) |
(+.f64 #s(literal 0 binary64) eps) |
eps |
#s(literal 0 binary64) |
eps |
(cos.f64 (+.f64 eps x)) |
(cos.f64 (+.f64 x eps)) |
(+.f64 eps x) |
(+.f64 x eps) |
x |
(cos.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 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal -1 binary64)))) (tan.f64 x)) |
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) |
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal -1 binary64)))) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(+.f64 (tan.f64 x) (tan.f64 eps)) |
(tan.f64 eps) |
eps |
(tan.f64 x) |
x |
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) |
(neg.f64 (fma.f64 (tan.f64 x) (tan.f64 eps) #s(literal -1 binary64))) |
(neg.f64 (tan.f64 eps)) |
#s(literal 1 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) | |
| accuracy | 0.015625 | (+.f64 (tan.f64 eps) (tan.f64 x)) | |
| accuracy | 0.021816259768442016 | (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) | |
| accuracy | 25.6243997000046 | (-.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)) | |
| accuracy | 0.0 | (sin.f64 (+.f64 #s(literal 0 binary64) eps)) | |
| accuracy | 0.0 | (cos.f64 x) | |
| accuracy | 0.03125 | (/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x)) | |
| accuracy | 0.10011884073013777 | (cos.f64 (+.f64 eps x)) | |
| accuracy | 0.0 | (sin.f64 eps) | |
| accuracy | 0.00390625 | (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) | |
| accuracy | 0.33152299922042383 | #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) | |
| accuracy | 1.7367886639738366 | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) | |
| accuracy | 0.0 | (*.f64 eps eps) | |
| accuracy | 0.0078125 | (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps) | |
| accuracy | 0.38405655789567417 | #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)) | |
| accuracy | 1.7367886639738366 | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) | |
| accuracy | 0.0 | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) | |
| accuracy | 0.0078125 | (/.f64 (sin.f64 eps) (cos.f64 x)) | |
| accuracy | 0.0234375 | (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))) | |
| accuracy | 0.10011884073013777 | (cos.f64 (+.f64 eps x)) |
| 46.0ms | 102× | 1 | valid |
| 40.0ms | 153× | 0 | valid |
| 1.0ms | 1× | 2 | valid |
Compiled 201 to 41 computations (79.6% saved)
ival-div: 10.0ms (15.7% of total)adjust: 9.0ms (14.1% of total)ival-add: 9.0ms (14.1% of total)ival-mult: 9.0ms (14.1% of total)ival-tan: 8.0ms (12.5% of total)ival-cos: 5.0ms (7.8% of total)ival-sin: 5.0ms (7.8% of total)ival-sub: 4.0ms (6.3% of total)const: 4.0ms (6.3% of total)ival-neg: 1.0ms (1.6% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))) |
(/.f64 (sin.f64 eps) (cos.f64 x)) |
(sin.f64 eps) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(+.f64 #s(literal 0 binary64) eps) |
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x)) |
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) |
(sin.f64 (+.f64 #s(literal 0 binary64) eps)) |
(-.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 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
(cos.f64 (+.f64 eps x)) |
(*.f64 eps eps) |
(cos.f64 x) |
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) |
| Outputs |
|---|
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(sin eps) |
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps)))) |
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps))))) |
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin 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))) |
(+ (* 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 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -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 (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (* -1/3 (/ (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 (/ (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))) |
(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 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(+ 1 (* -1 (/ (* x (sin eps)) (cos eps)))) |
(+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1/3 (/ (* (pow x 2) (sin eps)) (cos eps)))))) |
(+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* -1/3 (/ (sin eps) (cos eps))) (* -2/15 (/ (* (pow x 2) (sin eps)) (cos eps)))))))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (cos x)) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin eps) (cos (+ eps x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(cos (+ eps x)) |
(cos x) |
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (sin eps) (cos (- eps (* -1 x)))) |
(cos (- eps (* -1 x))) |
(/ eps (pow (cos x) 2)) |
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) |
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(/ eps (cos x)) |
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x)))) |
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x)))) |
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x)))) |
eps |
(* 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)))) |
(* eps (+ 1 (* 1/3 (pow eps 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)))))))) |
(+ 1 (* 1/3 (pow eps 2))) |
(+ 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))) |
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2)))) |
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))) |
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))) |
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 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 (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (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 (/ (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))) |
(+ (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) |
(+ 1 (* -1 (/ (* eps (sin x)) (cos x)))) |
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1/3 (/ (* (pow eps 2) (sin x)) (cos x)))))) |
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (sin x) (cos x))) (* -2/15 (/ (* (pow eps 2) (sin x)) (cos x)))))))) |
(* 1/3 (pow eps 3)) |
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2)))) |
(* 1/3 (pow eps 2)) |
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2)))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps)))) |
(sin (neg (* -1 eps))) |
(cos (- x (* -1 eps))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 20.0ms | eps | @ | 0 | ((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (cos (+ eps x))) (/ (sin eps) (cos x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (cos eps) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (cos (+ eps x)) (* eps eps) (cos x) (+ (* (neg (tan eps)) (tan x)) 1)) |
| 9.0ms | x | @ | inf | ((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (cos (+ eps x))) (/ (sin eps) (cos x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (cos eps) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (cos (+ eps x)) (* eps eps) (cos x) (+ (* (neg (tan eps)) (tan x)) 1)) |
| 6.0ms | eps | @ | -inf | ((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (cos (+ eps x))) (/ (sin eps) (cos x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (cos eps) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (cos (+ eps x)) (* eps eps) (cos x) (+ (* (neg (tan eps)) (tan x)) 1)) |
| 6.0ms | eps | @ | inf | ((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (cos (+ eps x))) (/ (sin eps) (cos x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (cos eps) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (cos (+ eps x)) (* eps eps) (cos x) (+ (* (neg (tan eps)) (tan x)) 1)) |
| 5.0ms | x | @ | -inf | ((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (cos (+ eps x))) (/ (sin eps) (cos x)) (sin eps) (* (+ (* (* eps eps) 1/3) 1) eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (cos eps) (+ 0 eps) (/ (/ (sin (+ 0 eps)) (cos (+ eps x))) (cos x)) (/ (sin (+ 0 eps)) (cos (+ eps x))) (sin (+ 0 eps)) (- (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (tan x)) (/ (+ (tan eps) (tan x)) (+ (* (neg (tan eps)) (tan x)) 1)) (+ (tan eps) (tan x)) (tan eps) (cos (+ eps x)) (* eps eps) (cos x) (+ (* (neg (tan eps)) (tan x)) 1)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 523 | 2556 |
| 1 | 1630 | 2383 |
| 2 | 5366 | 2254 |
| 0 | 8162 | 2135 |
| 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 (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(sin eps) |
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps)))) |
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps))))) |
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin 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))) |
(+ (* 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 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -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 (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (* -1/3 (/ (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 (/ (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))) |
(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 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(+ 1 (* -1 (/ (* x (sin eps)) (cos eps)))) |
(+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1/3 (/ (* (pow x 2) (sin eps)) (cos eps)))))) |
(+ 1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* -1/3 (/ (sin eps) (cos eps))) (* -2/15 (/ (* (pow x 2) (sin eps)) (cos eps)))))))) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (cos x)) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin eps) (cos (+ eps x))) |
(- (+ (/ (sin eps) (* (cos eps) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))) (/ (sin x) (* (cos x) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (/ (sin x) (cos x))) |
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) |
(cos (+ eps x)) |
(cos x) |
(+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (sin eps) (cos (- eps (* -1 x)))) |
(cos (- eps (* -1 x))) |
(/ eps (pow (cos x) 2)) |
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) |
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(/ eps (cos x)) |
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x)))) |
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x)))) |
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x)))) |
eps |
(* 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)))) |
(* eps (+ 1 (* 1/3 (pow eps 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)))))))) |
(+ 1 (* 1/3 (pow eps 2))) |
(+ 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))) |
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2)))) |
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))) |
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))) |
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 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 (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (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 (/ (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))) |
(+ (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) |
(+ 1 (* -1 (/ (* eps (sin x)) (cos x)))) |
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1/3 (/ (* (pow eps 2) (sin x)) (cos x)))))) |
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (sin x) (cos x))) (* -2/15 (/ (* (pow eps 2) (sin x)) (cos x)))))))) |
(* 1/3 (pow eps 3)) |
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2)))) |
(* 1/3 (pow eps 2)) |
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2)))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps)))) |
(sin (neg (* -1 eps))) |
(cos (- x (* -1 eps))) |
| 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 (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 (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 eps) (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 (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (*.f64 (sin.f64 eps) (-.f64 (fma.f64 (sin.f64 eps) (/.f64 #s(literal 2/3 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (-.f64 (neg.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 eps))) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (+.f64 (pow.f64 (/.f64 (sin.f64 eps) (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))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps)))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps)) |
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps))))) |
(fma.f64 (neg.f64 (*.f64 (sin.f64 eps) (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))) (*.f64 x x) (sin.f64 eps)) |
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 x) x) (*.f64 (sin.f64 eps) #s(literal -61/720 binary64)) (*.f64 #s(literal 5/24 binary64) (sin.f64 eps))) (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (sin.f64 eps))) (*.f64 x x) (sin.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)) (/.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 (- (* -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 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 eps)) (sin.f64 eps) (*.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 (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 #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))))) 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 (* x (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (-.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (*.f64 (sin.f64 eps) (/.f64 #s(literal -1/2 binary64) (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 (- (* -1 (* x (+ (* -1/2 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps))))) (cos eps)))))) (+ (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))) (* -1/2 (/ (sin eps) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
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1 |
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(/ (sin eps) (cos x)) |
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(/ (sin eps) (cos (+ eps x))) |
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) |
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(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (+ 1 (* -1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) |
(/.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (fma.f64 (/.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (/.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 1 binary64))) |
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(cos x) |
(cos.f64 x) |
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(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 x eps)) |
(/ eps (pow (cos x) 2)) |
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) |
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(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
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(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
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(/ eps (cos x)) |
(/.f64 eps (cos.f64 x)) |
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x)))) |
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (cos.f64 x)) #s(literal -1/6 binary64) (/.f64 eps (cos.f64 x))) |
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64))) (/.f64 eps (cos.f64 x))) |
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 eps (/.f64 eps (cos.f64 x))) (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) (/.f64 #s(literal -1/6 binary64) (cos.f64 x))) (/.f64 eps (cos.f64 x))) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 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))))) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) (+.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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))))) |
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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 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #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 (* -1/2 (pow eps 2))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
(* eps (+ (/ 1 (cos x)) (/ (* eps (sin x)) (pow (cos x) 2)))) |
(fma.f64 (*.f64 (sin.f64 x) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps (/.f64 eps (cos.f64 x))) |
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))) |
(fma.f64 (*.f64 (fma.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) eps (/.f64 eps (cos.f64 x))) |
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (cos x))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 2))) (* 1/6 (/ (sin x) (pow (cos x) 2))))))) (* 1/2 (/ 1 (cos x)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 3))) (* 1/6 (/ 1 (cos x)))))) (* -1 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x)))) |
(fma.f64 (*.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) eps (/.f64 eps (cos.f64 x))) |
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 (fma.f64 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps) |
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps) |
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sin.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal -1/3 binary64) (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) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (*.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) #s(literal -1/3 binary64)))) (-.f64 #s(literal 1/3 binary64) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -4/3 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) eps) |
(/ (sin x) (cos x)) |
(/.f64 (sin.f64 x) (cos.f64 x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(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))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) (+.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (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 (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (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 (fma.f64 (-.f64 #s(literal 1/3 binary64) (-.f64 (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.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)))))) eps (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (sin.f64 x))) eps (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 (/ (sin x) (cos x))) |
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) |
(+.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x))) |
(+.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps) (/.f64 (sin.f64 x) (cos.f64 x))) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(fma.f64 (neg.f64 eps) (sin.f64 x) (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 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps (cos.f64 x)) |
(pow eps 2) |
(*.f64 eps eps) |
(+ 1 (* -1 (/ (* eps (sin x)) (cos x)))) |
(fma.f64 (neg.f64 eps) (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 1 binary64)) |
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1/3 (/ (* (pow eps 2) (sin x)) (cos x)))))) |
(fma.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (*.f64 eps eps) #s(literal -1/3 binary64) #s(literal -1 binary64))) eps #s(literal 1 binary64)) |
(+ 1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* (pow eps 2) (+ (* -1/3 (/ (sin x) (cos x))) (* -2/15 (/ (* (pow eps 2) (sin x)) (cos x)))))))) |
(fma.f64 (neg.f64 eps) (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 #s(literal -2/15 binary64) (*.f64 eps eps) #s(literal -1/3 binary64))) #s(literal 1 binary64))) |
(* 1/3 (pow eps 3)) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64)) |
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) |
(* 1/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2)))) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x)) |
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x)) |
(- (/ (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))) |
(/ (sin (neg (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) |
(sin (neg (* -1 eps))) |
(sin.f64 eps) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 x eps)) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 47 | 213 |
| 0 | 72 | 193 |
| 1 | 293 | 165 |
| 2 | 2500 | 165 |
| 0 | 8201 | 165 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))) |
(/.f64 (sin.f64 eps) (cos.f64 x)) |
(sin.f64 eps) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps)) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(+.f64 #s(literal 0 binary64) eps) |
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x)) |
(/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) |
(sin.f64 (+.f64 #s(literal 0 binary64) eps)) |
(-.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 (+.f64 (tan.f64 eps) (tan.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64))) |
(+.f64 (tan.f64 eps) (tan.f64 x)) |
(tan.f64 eps) |
(cos.f64 (+.f64 eps x)) |
(*.f64 eps eps) |
(cos.f64 x) |
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) |
| Outputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(*.f64 (pow.f64 (/.f64 (cos.f64 (+.f64 x eps)) (neg.f64 (sin.f64 eps))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (cos.f64 x) (neg.f64 (sin.f64 eps))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (cos.f64 (+.f64 x eps))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64)) |
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 x eps))) (pow.f64 (pow.f64 (sin.f64 eps) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 x eps))) (sin.f64 eps)) |
(*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 x))) |
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps)))) |
(*.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (pow.f64 (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (pow.f64 (neg.f64 (cos.f64 (+.f64 x eps))) #s(literal -1 binary64))) |
(*.f64 (neg.f64 (sin.f64 eps)) (pow.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 (+.f64 x eps))) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64))) |
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (pow.f64 (cos.f64 x) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64))) |
(*.f64 (sin.f64 eps) (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 x eps)))) |
(pow.f64 (/.f64 (pow.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64)) |
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eps |
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(/.f64 (-.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal -1 binary64))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x))) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal -1 binary64)) (-.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x))) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64)))) |
(fma.f64 (*.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 eps) #s(literal 1 binary64)) |
(fma.f64 #s(literal -1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 1 binary64)) |
(fma.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 1 binary64) #s(literal 1 binary64)) |
(fma.f64 (neg.f64 (tan.f64 eps)) (*.f64 (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) |
(fma.f64 (tan.f64 x) (*.f64 (neg.f64 (tan.f64 eps)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(fma.f64 (tan.f64 x) (neg.f64 (tan.f64 eps)) #s(literal 1 binary64)) |
(fma.f64 (tan.f64 eps) (neg.f64 (tan.f64 x)) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 1 binary64)) |
(-.f64 (/.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) #s(literal 2 binary64)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal -1 binary64))) (pow.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) |
(+.f64 (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x)) #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 x)) (tan.f64 eps))) |
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x))) |
Compiled 24 350 to 3 263 computations (86.6% saved)
29 alts after pruning (24 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 743 | 17 | 760 |
| Fresh | 8 | 7 | 15 |
| Picked | 1 | 4 | 5 |
| Done | 1 | 1 | 2 |
| Total | 753 | 29 | 782 |
| Status | Accuracy | Program |
|---|---|---|
| 60.0% | (/.f64 (fma.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (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))) | |
| 35.0% | (/.f64 (/.f64 (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))) (cos.f64 (+.f64 eps x))) (cos.f64 x)) | |
| 90.9% | (/.f64 (/.f64 (sin.f64 (exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))) (cos.f64 x)) | |
| 99.8% | (/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x)) | |
| 99.6% | (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) (cos.f64 x)) | |
| ▶ | 34.7% | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
| 99.8% | (/.f64 (*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (sin.f64 eps)) (cos.f64 x)) | |
| ▶ | 99.8% | (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
| ✓ | 60.0% | (-.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)) |
| ✓ | 59.8% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| ▶ | 100.0% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))) |
| 100.0% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))) | |
| ✓ | 99.8% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
| 99.3% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x))))) | |
| 98.1% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x)))) | |
| 99.0% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x)))) | |
| 98.0% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))) (cos.f64 (+.f64 eps x)))) | |
| 98.5% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) | |
| 99.8% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64))) | |
| ✓ | 97.3% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
| 97.3% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) | |
| 97.3% | #s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) | |
| 32.5% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)))) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64))))) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) | |
| ✓ | 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
| ▶ | 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
| ▶ | 6.2% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) |
Compiled 1 308 to 861 computations (34.2% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) | |
| cost-diff | 2 | (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)) | |
| cost-diff | 2 | (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) | |
| cost-diff | 14 | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) | |
| cost-diff | 0 | (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) | |
| cost-diff | 0 | (sin.f64 eps) | |
| cost-diff | 0 | #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) | |
| cost-diff | 0 | (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) | |
| cost-diff | 1 | (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) | |
| cost-diff | 1 | (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) | |
| cost-diff | 2 | (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps) | |
| cost-diff | 0 | #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps) | |
| cost-diff | 0 | #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) | |
| cost-diff | 0 | (sin.f64 eps) | |
| cost-diff | 0 | (/.f64 (sin.f64 eps) (cos.f64 x)) | |
| cost-diff | 0 | (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) | |
| cost-diff | 0 | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 63 | 431 |
| 0 | 97 | 419 |
| 1 | 169 | 411 |
| 2 | 283 | 400 |
| 3 | 561 | 393 |
| 4 | 1836 | 387 |
| 5 | 5863 | 387 |
| 0 | 8380 | 373 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) |
(/.f64 (sin.f64 eps) (cos.f64 x)) |
(sin.f64 eps) |
eps |
(cos.f64 x) |
x |
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) |
(cos.f64 eps) |
(*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) |
(neg.f64 (sin.f64 eps)) |
(sin.f64 x) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) |
#s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps) |
#s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(*.f64 eps eps) |
eps |
#s(literal 1/3 binary64) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) |
#s(literal 1 binary64) |
(*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64))) |
#s(literal 1/9 binary64) |
(pow.f64 eps #s(literal 4 binary64)) |
eps |
#s(literal 4 binary64) |
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
#s(literal 1/3 binary64) |
(*.f64 eps eps) |
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) |
(sin.f64 eps) |
eps |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
x |
(cos.f64 x) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.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 x))) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(tan.f64 x) |
x |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
(/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) |
(*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) |
| Outputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))))) (cos.f64 x))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) |
(/.f64 (/.f64 (sin.f64 eps) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))))) (cos.f64 x)) |
(/.f64 (sin.f64 eps) (cos.f64 x)) |
(sin.f64 eps) |
eps |
(cos.f64 x) |
x |
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)))) |
(cos.f64 eps) |
(*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) |
(*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) |
(neg.f64 (sin.f64 eps)) |
(sin.f64 x) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) |
#s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps) |
#s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(*.f64 eps eps) |
eps |
#s(literal 1/3 binary64) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (fma.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1/9 binary64) eps) (fma.f64 #s(literal -1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))))) |
#s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
#s(approx (/ (sin eps) (cos eps)) (/.f64 (fma.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1/9 binary64) eps) (fma.f64 #s(literal -1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps) |
(/.f64 (fma.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1/9 binary64) eps) (fma.f64 #s(literal -1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) |
(/.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps #s(literal -1 binary64))) |
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) |
(fma.f64 #s(literal -1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/9 binary64)) |
#s(literal 1/9 binary64) |
(pow.f64 eps #s(literal 4 binary64)) |
eps |
#s(literal 4 binary64) |
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
(fma.f64 #s(literal -1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
#s(literal 1/3 binary64) |
(*.f64 eps eps) |
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps))) |
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) |
(sin.f64 eps) |
eps |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(cos.f64 (+.f64 eps x)) |
(cos.f64 (+.f64 x eps)) |
(+.f64 eps x) |
(+.f64 x eps) |
x |
(cos.f64 x) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) |
(-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (tan.f64 x)) |
(tan.f64 x) |
x |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(tan.f64 (+.f64 eps x)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 eps x) |
(+.f64 x eps) |
eps |
(/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) |
(/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (tan.f64 (+.f64 x eps))) |
(*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) |
(*.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.1328125 | (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) | |
| accuracy | 0.21875 | (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) | |
| accuracy | 26.181621164799637 | (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) | |
| accuracy | 28.317254210816326 | (/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) | |
| accuracy | 0.0 | #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) | |
| accuracy | 0.015625 | (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| accuracy | 0.03125 | (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) | |
| accuracy | 0.10011884073013777 | (cos.f64 (+.f64 eps x)) | |
| accuracy | 0.0859375 | (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64))) | |
| accuracy | 0.2109375 | (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) | |
| accuracy | 0.38405655789567417 | #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) | |
| accuracy | 1.7367886639738366 | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) | |
| accuracy | 0.2109375 | (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) | |
| accuracy | 0.38405655789567417 | #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)) | |
| accuracy | 1.7367886639738366 | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) | |
| accuracy | 61.2632633060152 | #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) | |
| accuracy | 0.00390625 | (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) | |
| accuracy | 0.00390625 | (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) | |
| accuracy | 0.0078125 | (/.f64 (sin.f64 eps) (cos.f64 x)) | |
| accuracy | 0.0234375 | (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) |
| 82.0ms | 102× | 1 | valid |
| 66.0ms | 154× | 0 | valid |
Compiled 319 to 49 computations (84.6% saved)
ival-div: 25.0ms (26.2% of total)ival-mult: 18.0ms (18.8% of total)adjust: 9.0ms (9.4% of total)ival-sub: 9.0ms (9.4% of total)ival-tan: 7.0ms (7.3% of total)ival-cos: 6.0ms (6.3% of total)const: 6.0ms (6.3% of total)ival-add: 6.0ms (6.3% of total)ival-sin: 5.0ms (5.2% of total)ival-pow: 3.0ms (3.1% of total)ival-neg: 1.0ms (1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) |
(/.f64 (sin.f64 eps) (cos.f64 x)) |
(sin.f64 eps) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) |
#s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps) |
#s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps) |
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) |
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)) |
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) |
(*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
#s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64))) |
(cos.f64 (+.f64 eps x)) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) |
(/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) |
| Outputs |
|---|
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(sin eps) |
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps)))) |
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps))))) |
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin 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))) |
(+ (* 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))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps)))))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (* x (+ (* -1 (+ 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 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (* (sin eps) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))))))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(/ 1 x) |
(/ (+ 1 (* -1/3 (pow x 2))) x) |
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x) |
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x) |
(/ (cos eps) (sin eps)) |
(+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps))) |
(+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 2) (+ 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))))))) (pow (sin eps) 2))) (* -1 (/ (* (pow (cos eps) 2) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 2))))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) |
(/ (+ 1 (* -1 (/ (* x (cos eps)) (sin eps)))) x) |
(/ (+ 1 (* x (- (* x (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (cos eps) (sin eps))))) x) |
(/ (+ 1 (* x (- (* x (- (+ (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2))) 1/3)) (/ (cos eps) (sin eps))))) x) |
(* -1 (* x (sin eps))) |
(* x (+ (* -1 (sin eps)) (* 1/6 (* (pow x 2) (sin eps))))) |
(* x (+ (* -1 (sin eps)) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin eps))) (* 1/6 (sin eps)))))) |
(* x (+ (* -1 (sin eps)) (* (pow x 2) (+ (* 1/6 (sin eps)) (* (pow x 2) (+ (* -1/120 (sin eps)) (* 1/5040 (* (pow x 2) (sin eps))))))))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1/2 (* x (cos eps)))))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1/2 (cos eps)) (* 1/6 (* 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)))) |
(/ (cos eps) (* x (sin eps))) |
(/ (+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps))) x) |
(/ (+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x) |
(/ (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 3) (* (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* -1 (+ 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))))))) (* 1/3 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (pow (sin eps) 2)))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))))) |
(/ (sin eps) (cos x)) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(* (cos x) (cos (+ eps x))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (cos x) (sin x)) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(* -1 (* (sin eps) (sin x))) |
(+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))) |
(cos (+ eps x)) |
(/ (* (cos x) (cos (+ eps x))) (* (sin x) (sin (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) |
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))) |
(cos (- eps (* -1 x))) |
(/ (* (cos x) (cos (- eps (* -1 x)))) (* (sin x) (sin (- eps (* -1 x))))) |
(/ eps (pow (cos x) 2)) |
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) |
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(/ eps (cos x)) |
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x)))) |
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x)))) |
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x)))) |
eps |
(* 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)))) |
(* 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 (* 1/3 (pow eps 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)))))))) |
1 |
(+ 1 (* 1/3 (pow eps 2))) |
(+ 1 (* -1/9 (pow eps 4))) |
(+ 1 (* -1/3 (pow eps 2))) |
(pow (cos x) 2) |
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2)) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ (* -1 (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (/ (cos x) (sin x))) |
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2)) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* eps (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(* -1 (* eps (sin x))) |
(* eps (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))) |
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* -1/120 (* (pow eps 2) (sin x))) (* 1/6 (sin x)))))) |
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* 1/6 (sin x)) (* (pow eps 2) (+ (* -1/120 (sin x)) (* 1/5040 (* (pow eps 2) (sin x))))))))) |
(cos x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))) |
(+ (cos x) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))) |
(* 1/3 (pow eps 2)) |
(* 1/9 (pow eps 4)) |
(+ (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 (cos x) 2) (pow (sin x) 2)) |
(+ (* -1 (/ (* eps (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3))) (/ (pow (cos x) 2) (pow (sin x) 2))) |
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2))) |
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 3) (+ 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))))))) (pow (sin x) 3))) (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))))))) (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2))) |
(* 1/3 (pow eps 3)) |
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2)))) |
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2)))) |
(* -1/9 (pow eps 4)) |
(* (pow eps 4) (- (/ 1 (pow eps 4)) 1/9)) |
(* -1/3 (pow eps 2)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/3)) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(sin (neg (* -1 eps))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(cos (- x (* -1 eps))) |
(/ (* (cos x) (cos (- x (* -1 eps)))) (* (sin x) (sin (- x (* -1 eps))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 12.0ms | eps | @ | -inf | ((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/ (sin eps) (cos x)) (sin eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* (/ (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps)))) eps) (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps))) (- (tan (+ x eps)) (tan x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (* (tan (+ eps x)) (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (* eps eps) 1/3) (/ (sin eps) (cos eps)) (* 1/3 (* eps eps)) (* 1/9 (pow eps 4)) (cos (+ eps x)) (/ 1 (tan (+ eps x))) (/ 1 (* (tan (+ eps x)) (tan x)))) |
| 7.0ms | eps | @ | inf | ((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/ (sin eps) (cos x)) (sin eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* (/ (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps)))) eps) (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps))) (- (tan (+ x eps)) (tan x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (* (tan (+ eps x)) (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (* eps eps) 1/3) (/ (sin eps) (cos eps)) (* 1/3 (* eps eps)) (* 1/9 (pow eps 4)) (cos (+ eps x)) (/ 1 (tan (+ eps x))) (/ 1 (* (tan (+ eps x)) (tan x)))) |
| 5.0ms | x | @ | inf | ((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/ (sin eps) (cos x)) (sin eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* (/ (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps)))) eps) (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps))) (- (tan (+ x eps)) (tan x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (* (tan (+ eps x)) (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (* eps eps) 1/3) (/ (sin eps) (cos eps)) (* 1/3 (* eps eps)) (* 1/9 (pow eps 4)) (cos (+ eps x)) (/ 1 (tan (+ eps x))) (/ 1 (* (tan (+ eps x)) (tan x)))) |
| 5.0ms | x | @ | -inf | ((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/ (sin eps) (cos x)) (sin eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* (/ (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps)))) eps) (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps))) (- (tan (+ x eps)) (tan x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (* (tan (+ eps x)) (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (* eps eps) 1/3) (/ (sin eps) (cos eps)) (* 1/3 (* eps eps)) (* 1/9 (pow eps 4)) (cos (+ eps x)) (/ 1 (tan (+ eps x))) (/ 1 (* (tan (+ eps x)) (tan x)))) |
| 4.0ms | eps | @ | 0 | ((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/ (sin eps) (cos x)) (sin eps) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (* (+ (* (* eps eps) 1/3) 1) eps) (+ (* (* eps eps) 1/3) 1) (* (/ (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps)))) eps) (- 1 (* 1/9 (pow eps 4))) (- 1 (* 1/3 (* eps eps))) (- (tan (+ x eps)) (tan x)) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x)) (/ (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (/ 1 (* (tan (+ eps x)) (tan x)))) (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1) (- (* 1 (/ 1 (tan x))) (* (/ 1 (tan (+ eps x))) 1)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* (* eps eps) 1/3) (/ (sin eps) (cos eps)) (* 1/3 (* eps eps)) (* 1/9 (pow eps 4)) (cos (+ eps x)) (/ 1 (tan (+ eps x))) (/ 1 (* (tan (+ eps x)) (tan x)))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 707 | 6465 |
| 1 | 2311 | 5981 |
| 0 | 8406 | 5816 |
| 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 (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(sin eps) |
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps)))) |
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps))))) |
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin 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))) |
(+ (* 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))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps)))))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (* x (+ (* -1 (+ 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 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (* (sin eps) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))))))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(/ 1 x) |
(/ (+ 1 (* -1/3 (pow x 2))) x) |
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x) |
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x) |
(/ (cos eps) (sin eps)) |
(+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps))) |
(+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 2) (+ 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))))))) (pow (sin eps) 2))) (* -1 (/ (* (pow (cos eps) 2) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 2))))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) |
(/ (+ 1 (* -1 (/ (* x (cos eps)) (sin eps)))) x) |
(/ (+ 1 (* x (- (* x (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (cos eps) (sin eps))))) x) |
(/ (+ 1 (* x (- (* x (- (+ (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2))) 1/3)) (/ (cos eps) (sin eps))))) x) |
(* -1 (* x (sin eps))) |
(* x (+ (* -1 (sin eps)) (* 1/6 (* (pow x 2) (sin eps))))) |
(* x (+ (* -1 (sin eps)) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin eps))) (* 1/6 (sin eps)))))) |
(* x (+ (* -1 (sin eps)) (* (pow x 2) (+ (* 1/6 (sin eps)) (* (pow x 2) (+ (* -1/120 (sin eps)) (* 1/5040 (* (pow x 2) (sin eps))))))))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1/2 (* x (cos eps)))))) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1/2 (cos eps)) (* 1/6 (* 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)))) |
(/ (cos eps) (* x (sin eps))) |
(/ (+ (* -1 (/ (* x (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 2))) (/ (cos eps) (sin eps))) x) |
(/ (+ (* x (- (* -1 (* x (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x) |
(/ (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* (cos eps) (* (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (sin eps))) (+ (* -1 (/ (* (pow (cos eps) 3) (* (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* -1 (+ 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))))))) (* 1/3 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (pow (sin eps) 2)))))) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (pow (cos eps) 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))) (pow (sin eps) 2))))) (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)))) (/ (cos eps) (sin eps))) x) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (sin eps) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))))) |
(/ (sin eps) (cos x)) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(* (cos x) (cos (+ eps x))) |
(/ (* (sin x) (* (sin (+ eps x)) (- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))))) (* (cos x) (cos (+ eps x)))) |
(/ (cos x) (sin x)) |
(/ (cos (+ eps x)) (sin (+ eps x))) |
(- (/ (cos x) (sin x)) (/ (cos (+ eps x)) (sin (+ eps x)))) |
(* -1 (* (sin eps) (sin x))) |
(+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))) |
(cos (+ eps x)) |
(/ (* (cos x) (cos (+ eps x))) (* (sin x) (sin (+ eps x)))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(/ (* (sin x) (* (sin (- eps (* -1 x))) (- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))))) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x)))) |
(- (/ (cos x) (sin x)) (/ (cos (- eps (* -1 x))) (sin (- eps (* -1 x))))) |
(cos (- eps (* -1 x))) |
(/ (* (cos x) (cos (- eps (* -1 x)))) (* (sin x) (sin (- eps (* -1 x))))) |
(/ eps (pow (cos x) 2)) |
(* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))) |
(* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2)))) |
(/ eps (cos x)) |
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x)))) |
(* eps (+ (* (pow eps 2) (- (* 1/120 (/ (pow eps 2) (cos x))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x)))) |
(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x)))) |
eps |
(* 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)))) |
(* 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 (* 1/3 (pow eps 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)))))))) |
1 |
(+ 1 (* 1/3 (pow eps 2))) |
(+ 1 (* -1/9 (pow eps 4))) |
(+ 1 (* -1/3 (pow eps 2))) |
(pow (cos x) 2) |
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2)) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ (* -1 (/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (/ (cos x) (sin x))) |
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))))) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) (/ (cos x) (sin x))) |
(/ (* eps (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2)) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(* eps (+ (* eps (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (+ (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (+ (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))) (* eps (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))))))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2)))) |
(* -1 (* eps (sin x))) |
(* eps (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))) |
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* -1/120 (* (pow eps 2) (sin x))) (* 1/6 (sin x)))))) |
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* 1/6 (sin x)) (* (pow eps 2) (+ (* -1/120 (sin x)) (* 1/5040 (* (pow eps 2) (sin x))))))))) |
(cos x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))) |
(+ (cos x) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))) |
(* 1/3 (pow eps 2)) |
(* 1/9 (pow eps 4)) |
(+ (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 (cos x) 2) (pow (sin x) 2)) |
(+ (* -1 (/ (* eps (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3))) (/ (pow (cos x) 2) (pow (sin x) 2))) |
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2))) |
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 3) (+ 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))))))) (pow (sin x) 3))) (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))))))) (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2))) |
(* 1/3 (pow eps 3)) |
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2)))) |
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2)))) |
(* -1/9 (pow eps 4)) |
(* (pow eps 4) (- (/ 1 (pow eps 4)) 1/9)) |
(* -1/3 (pow eps 2)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/3)) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(sin (neg (* -1 eps))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(cos (- x (* -1 eps))) |
(/ (* (cos x) (cos (- x (* -1 eps)))) (* (sin x) (sin (- x (* -1 eps))))) |
| 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 (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 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 x (+.f64 (/.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)))) (/.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 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (neg.f64 (fma.f64 (fma.f64 (sin.f64 eps) (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 #s(literal 2/3 binary64) (cos.f64 eps)) (/.f64 (-.f64 (/.f64 (neg.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))) (cos.f64 eps))) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (-.f64 (/.f64 (neg.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))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* 1/2 (* (pow x 2) (sin eps)))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps)) |
(+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps))))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) #s(literal 5/24 binary64)) (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (sin.f64 eps))) (*.f64 x x) (sin.f64 eps)) |
(+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (neg.f64 x) x) (fma.f64 (sin.f64 eps) #s(literal 7/360 binary64) (*.f64 (sin.f64 eps) #s(literal -5/48 binary64))) (*.f64 (sin.f64 eps) #s(literal 5/24 binary64))) (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (sin.f64 eps))) (*.f64 x x) (sin.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 (sin.f64 eps) x) (/.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)))) (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 (+.f64 #s(literal 1 binary64) (/.f64 (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 #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))) |
(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 (sin eps)) (* -1 (* x (cos eps)))))) |
(fma.f64 (neg.f64 (fma.f64 (cos.f64 eps) x (sin.f64 eps))) x (cos.f64 eps)) |
(+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 2/3 binary64) (neg.f64 (cos.f64 eps))) x (neg.f64 (sin.f64 eps))) x (cos.f64 eps)) |
(+ (* x (+ (* x (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps)))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (+.f64 (/.f64 (fma.f64 (pow.f64 (cos.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 (sin.f64 eps) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (cos.f64 eps)) (/.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)))) (cos.f64 eps))) (/.f64 (*.f64 (neg.f64 (cos.f64 eps)) (+.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)))) 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 (+ (* -1 (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps))) (+ (* 1/3 (/ (sin eps) (cos eps))) (+ (* x (+ (* -1 (+ 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 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (+ (* 1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (/ (* (sin eps) (+ (* -1 (/ (* (pow (cos eps) 3) (pow (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) 2)) (pow (sin eps) 3))) (/ (* (cos eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (sin eps)))) (cos eps))))))) (+ (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)) (/ (* (sin eps) (- (/ (* (pow (cos eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (sin eps) 2)) 1/3)) (cos eps))))))) (/ (pow (sin eps) 2) (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) |
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(cos (+ eps x)) |
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(/ eps (cos x)) |
(/.f64 eps (cos.f64 x)) |
(* eps (+ (* -1/6 (/ (pow eps 2) (cos x))) (/ 1 (cos x)))) |
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(* eps (+ (* (pow eps 2) (- (* (pow eps 2) (+ (* -1/5040 (/ (pow eps 2) (cos x))) (* 1/120 (/ 1 (cos x))))) (* 1/6 (/ 1 (cos x))))) (/ 1 (cos x)))) |
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eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
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(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* 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 (* 1/3 (pow eps 2)))) |
(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)))))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2)))))))) |
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1 |
#s(literal 1 binary64) |
(+ 1 (* 1/3 (pow eps 2))) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
(+ 1 (* -1/9 (pow eps 4))) |
(fma.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/9 binary64) #s(literal 1 binary64)) |
(+ 1 (* -1/3 (pow eps 2))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/3 binary64) #s(literal 1 binary64)) |
(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) |
(fma.f64 (neg.f64 (*.f64 (cos.f64 x) eps)) (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* -1/2 (* eps (pow (cos x) 2))))) (pow (cos x) 2)) |
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(+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (+ (* -1/2 (pow (cos x) 2)) (* 1/6 (* eps (* (cos x) (sin x)))))))) (pow (cos x) 2)) |
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(* eps (- (+ 1 (/ (* eps (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (* eps (+ (/ (* eps (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x)))))) (cos x)) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (- (+ 1 (* eps (+ (* eps (+ (/ (* eps (* (sin x) (+ (* -1 (/ (* (pow (cos x) 2) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (sin x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x)) (/ (* (sin x) (+ (* -1 (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2))))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ (* -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))))) (pow (sin x) 2))) (/ (* (pow (cos x) 3) (* (+ 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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (pow (sin x) 3)))))) (cos x))))))) (cos x)) (/ (* (sin x) (+ (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (+ (/ (* (cos x) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (sin x)) (/ (* (sin x) (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 2) (+ 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))))))) (pow (sin x) 2))) (* -1 (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))))) (cos x))))) (cos x)))) (/ (* (sin x) (+ (/ (* (sin x) (+ (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))) (/ (* (cos x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (sin x)))) (cos x)) (/ (* (pow (cos x) 2) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 2)))) (cos x))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(fma.f64 (neg.f64 (fma.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.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)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (/.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)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) eps (/.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)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) eps (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) |
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (cos x) (* (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (sin x))) (+ (* -1 (/ (* (pow (cos x) 3) (+ 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))))))) (pow (sin x) 3))) (* -1 (/ (* (pow (cos x) 3) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 3))))))) (+ (* -1 (/ (* (pow (cos x) 4) (pow (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))) 2)) (pow (sin x) 4))) (/ (* (pow (cos x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 2))))) (/ (* (pow (cos x) 3) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (sin x) 3)))) (/ (pow (cos x) 2) (pow (sin x) 2))) |
(fma.f64 (fma.f64 (neg.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (/.f64 (fma.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.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)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (fma.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)))) #s(literal -1/2 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal 1/6 binary64))) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 (pow.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)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))))) (/.f64 (*.f64 (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.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)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (/.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)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (*.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))) (sin.f64 x))) eps (fma.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (pow.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)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (/.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)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))))) eps (/.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)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) eps (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) |
(* 1/3 (pow eps 3)) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64)) |
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) |
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2)))) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
(* -1/9 (pow eps 4)) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/9 binary64)) |
(* (pow eps 4) (- (/ 1 (pow eps 4)) 1/9)) |
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/9 binary64)) (pow.f64 eps #s(literal 4 binary64))) |
(* -1/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/3 binary64)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/3)) |
(fma.f64 (*.f64 eps eps) #s(literal -1/3 binary64) #s(literal 1 binary64)) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x 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))) |
(sin (neg (* -1 eps))) |
(sin.f64 eps) |
(* (cos x) (cos (- x (* -1 eps)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) |
(/ (* (sin x) (* (sin (- x (* -1 eps))) (- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (*.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps))))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) |
(/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps)))) |
(/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps))) |
(- (/ (cos x) (sin x)) (/ (cos (- x (* -1 eps))) (sin (- x (* -1 eps))))) |
(-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 x eps)))) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 x eps)) |
(/ (* (cos x) (cos (- x (* -1 eps)))) (* (sin x) (sin (- x (* -1 eps))))) |
(*.f64 (/.f64 (cos.f64 x) (sin.f64 (+.f64 x eps))) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 x))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 63 | 357 |
| 0 | 97 | 340 |
| 1 | 372 | 275 |
| 2 | 2827 | 273 |
| 0 | 8825 | 264 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) |
(/.f64 (sin.f64 eps) (cos.f64 x)) |
(sin.f64 eps) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) |
#s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps) |
#s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps) |
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) |
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64)) |
(-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) |
(*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
#s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps)) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64))) |
(cos.f64 (+.f64 eps x)) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) |
(/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))) |
(*.f64 (pow.f64 (/.f64 (cos.f64 (+.f64 x eps)) (neg.f64 (sin.f64 eps))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) #s(literal -1 binary64)) (pow.f64 (cos.f64 x) #s(literal -1 binary64))) |
(*.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 eps x)))) (cos.f64 (-.f64 eps x))) |
(*.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 eps) (cos.f64 x))) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 x))) |
(*.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (pow.f64 (neg.f64 (cos.f64 (+.f64 x eps))) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x))) |
(*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64))) |
(*.f64 (sin.f64 eps) (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 x eps)))) |
(pow.f64 (/.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps)) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (/.f64 (cos.f64 x) (sin.f64 eps)) (cos.f64 (+.f64 x eps))) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x)) #s(literal -1 binary64)) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x)) |
(/.f64 (*.f64 (neg.f64 (sin.f64 eps)) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64))) (neg.f64 (cos.f64 x))) |
(/.f64 (*.f64 (sin.f64 eps) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64))) (cos.f64 x)) |
(/.f64 (*.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 1 binary64)) (cos.f64 (+.f64 x eps))) |
(/.f64 (*.f64 (neg.f64 (sin.f64 eps)) #s(literal 1 binary64)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))) |
(/.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) |
(/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (/.f64 (cos.f64 x) (sin.f64 eps))) |
(/.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (neg.f64 (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (sin.f64 eps))) |
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (cos.f64 x) (sin.f64 eps)) (cos.f64 (+.f64 x eps)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x))) |
(/.f64 (neg.f64 (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (neg.f64 (neg.f64 (cos.f64 (+.f64 x eps))))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 x eps))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) |
(neg.f64 (/.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 x eps)))) |
(neg.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (neg.f64 (cos.f64 (+.f64 x eps))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps)) (cos.f64 x))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (pow.f64 (pow.f64 (sin.f64 eps) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (sin.f64 eps)) |
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))) |
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (cos.f64 x))) |
(*.f64 (neg.f64 (sin.f64 eps)) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal -1 binary64))) |
(*.f64 (sin.f64 eps) (pow.f64 (cos.f64 x) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (/.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (cos.f64 x) (sin.f64 eps)) #s(literal -1 binary64)) |
(/.f64 (-.f64 #s(literal 0 binary64) (neg.f64 (neg.f64 (sin.f64 eps)))) (neg.f64 (cos.f64 x))) |
(/.f64 (neg.f64 (neg.f64 (sin.f64 eps))) (neg.f64 (neg.f64 (cos.f64 x)))) |
(/.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (cos.f64 x)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (cos.f64 x) (sin.f64 eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) (sin.f64 eps))) |
(/.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (cos.f64 x))) |
(/.f64 (sin.f64 eps) (cos.f64 x)) |
(neg.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 x))) (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 x) (sin.f64 eps))) #s(literal -1 binary64))) |
(sin.f64 eps) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) |
#s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps) |
(*.f64 eps #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) |
#s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(*.f64 (/.f64 (*.f64 (fma.f64 #s(literal -1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1 binary64)) eps) (fma.f64 #s(literal -1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64))) |
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(*.f64 (*.f64 (fma.f64 #s(literal -1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal 1 binary64)) eps) (pow.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) #s(literal -1 binary64))) |
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(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 1 binary64))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(*.f64 eps (*.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 1 binary64))) |
(*.f64 eps (*.f64 #s(literal 1/3 binary64) eps)) |
#s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64)) eps)) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) eps)) eps) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 1/3 binary64)) |
(*.f64 (*.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal 1/3 binary64) eps)) |
(*.f64 (*.f64 #s(literal 1/3 binary64) eps) (*.f64 eps #s(literal 1 binary64))) |
(*.f64 (*.f64 #s(literal 1/3 binary64) eps) eps) |
(*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 1 binary64))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) |
(*.f64 eps (*.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 1 binary64))) |
(*.f64 eps (*.f64 #s(literal 1/3 binary64) eps)) |
(*.f64 (pow.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) eps)) #s(literal 2 binary64)) (*.f64 eps eps)) |
(*.f64 (pow.f64 (*.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 2 binary64)) #s(literal 1/9 binary64)) |
(*.f64 (pow.f64 (*.f64 #s(literal 1 binary64) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps) |
(*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps)) #s(literal 1/3 binary64)) |
(*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) (*.f64 eps eps)) |
(*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) eps) (*.f64 #s(literal 1/3 binary64) eps)) |
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/9 binary64)) |
(*.f64 (*.f64 #s(literal 1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps)) |
(*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 eps #s(literal 1 binary64)) #s(literal 2 binary64))) |
(*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps)) |
(*.f64 (*.f64 #s(literal 1/3 binary64) eps) (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) |
(*.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) |
(*.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/9 binary64)) #s(literal 1 binary64)) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/9 binary64)) |
(*.f64 #s(literal 1/9 binary64) (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64))) |
(*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) |
(*.f64 (*.f64 eps eps) (pow.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(*.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) |
(*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal 1/9 binary64))) |
(*.f64 (*.f64 eps eps) (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64))) |
(*.f64 #s(literal 1 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/9 binary64))) |
(*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) |
(*.f64 eps (*.f64 (*.f64 #s(literal 1/3 binary64) eps) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)))) |
(pow.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 2 binary64)) |
(exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) #s(literal 2 binary64))) |
(*.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 eps x))) (pow.f64 (cos.f64 (-.f64 eps x)) #s(literal -1 binary64))) |
(*.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 eps) (cos.f64 x))) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (cos.f64 (-.f64 eps x)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 eps x)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 eps) (cos.f64 x))) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)))) #s(literal -1 binary64)) |
(/.f64 (-.f64 (+.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 x eps))) (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 x eps)))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (-.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 eps) (cos.f64 x)))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))) |
(/.f64 (neg.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 eps x)))) (neg.f64 (cos.f64 (-.f64 eps x)))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 eps) (cos.f64 x))) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64))))) |
(/.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 eps x))) (cos.f64 (-.f64 eps x))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 x)) (neg.f64 (sin.f64 eps)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 eps) (cos.f64 x))) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (-.f64 eps x)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 eps x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 eps) (cos.f64 x))) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64))))) |
(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 (/.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 (*.f64 (sin.f64 x) #s(literal -1 binary64)) (sin.f64 eps) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(fma.f64 #s(literal -1 binary64) (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(fma.f64 (+.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 x eps))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)))) |
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)))) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)))) |
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 eps x))) (/.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (cos.f64 (-.f64 eps x)))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))) |
(cos.f64 (+.f64 x eps)) |
(+.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 (/.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 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)))) |
(+.f64 (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(*.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) |
(*.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal -1 binary64)) (cos.f64 (+.f64 x eps))) |
(*.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -1/2 binary64)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -1/2 binary64))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps)))) |
(*.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -1 binary64)) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -1 binary64))) |
(pow.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (neg.f64 (neg.f64 (tan.f64 (+.f64 x eps)))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) |
(pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -1 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (tan.f64 (+.f64 x eps)))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (tan.f64 (+.f64 x eps))))) |
(/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps)))) |
(exp.f64 (neg.f64 (log.f64 (tan.f64 (+.f64 x eps))))) |
(*.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -1 binary64)) (sin.f64 x)) (cos.f64 x)) |
(*.f64 (pow.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal -1/2 binary64))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(*.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64)) |
(*.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -1 binary64)) (pow.f64 (tan.f64 x) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 (+.f64 x eps)))) |
(pow.f64 (exp.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (/.f64 (tan.f64 x) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -1 binary64))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) |
(pow.f64 (neg.f64 (*.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 x eps)))) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (neg.f64 (tan.f64 x)) (neg.f64 (tan.f64 (+.f64 x eps)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 (+.f64 x eps))) #s(literal 1 binary64)) |
(pow.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) #s(literal -1 binary64)) |
(/.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (tan.f64 (+.f64 x eps)))) |
(/.f64 (/.f64 #s(literal -1 binary64) (tan.f64 (+.f64 x eps))) (neg.f64 (tan.f64 x))) |
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 x eps)))) |
(/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -1 binary64)) (tan.f64 x)) |
(/.f64 (pow.f64 (tan.f64 x) #s(literal -1 binary64)) (tan.f64 (+.f64 x eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 (tan.f64 x) (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (neg.f64 (tan.f64 x)) (tan.f64 (+.f64 x eps))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (tan.f64 x)) (neg.f64 (tan.f64 (+.f64 x eps))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) |
(exp.f64 (fma.f64 (log.f64 (tan.f64 (+.f64 x eps))) #s(literal -1 binary64) (neg.f64 (log.f64 (tan.f64 x))))) |
(exp.f64 (+.f64 (neg.f64 (log.f64 (tan.f64 x))) (neg.f64 (log.f64 (tan.f64 (+.f64 x eps)))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) #s(literal -1 binary64))) |
Compiled 21 174 to 2 358 computations (88.9% saved)
30 alts after pruning (24 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 514 | 8 | 522 |
| Fresh | 3 | 16 | 19 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 5 | 5 |
| Total | 521 | 30 | 551 |
| Status | Accuracy | Program |
|---|---|---|
| 60.0% | (/.f64 (fma.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (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))) | |
| 35.0% | (/.f64 (/.f64 (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))) (cos.f64 (+.f64 eps x))) (cos.f64 x)) | |
| 90.9% | (/.f64 (/.f64 (sin.f64 (exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))) (cos.f64 x)) | |
| 99.8% | (/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x)) | |
| 99.6% | (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) (cos.f64 x)) | |
| 34.7% | (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) | |
| 99.8% | (/.f64 (*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (sin.f64 eps)) (cos.f64 x)) | |
| ✓ | 99.8% | (/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
| ✓ | 60.0% | (-.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)) |
| ✓ | 59.8% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 99.6% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (*.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) eps))))) | |
| 99.3% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x)))))) | |
| ✓ | 99.8% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
| 98.1% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x)))) | |
| 99.0% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x)))) | |
| 98.0% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))) (cos.f64 (+.f64 eps x)))) | |
| 98.5% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) | |
| 99.8% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64))) | |
| 100.0% | #s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/.f64 (sin.f64 eps) (*.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))))) | |
| ✓ | 97.3% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
| 97.3% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) | |
| 97.3% | #s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) | |
| 32.5% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)))) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) | |
| ✓ | 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) | |
| 97.4% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps))) |
Compiled 2 588 to 895 computations (65.4% saved)
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))) (cos.f64 (+.f64 eps x)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))) |
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.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 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64)) |
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) (cos.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)) |
(/.f64 (*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (sin.f64 eps)) (cos.f64 x)) |
(/.f64 (/.f64 (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))) (cos.f64 (+.f64 eps x))) (cos.f64 x)) |
(/.f64 (sin.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 eps eps (-.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 0 binary64)))))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (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 (/.f64 (sin.f64 (exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))) (cos.f64 x)) |
(fma.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)))) (neg.f64 (tan.f64 x))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x)))))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x))))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (*.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) eps))))) |
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 eps x))) (pow.f64 (pow.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(literal -1 binary64)) #s(literal -1 binary64))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/.f64 (sin.f64 eps) (*.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.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)) |
(/.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 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))) |
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (*.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 (fma.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (neg.f64 (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 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (*.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) (*.f64 eps eps) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) eps)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))) |
#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)))) |
(fma.f64 (pow.f64 (tan.f64 (+.f64 eps 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)) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (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 #s(approx (- (* (+ (tan eps) (tan x)) (cos x)) (* (+ (* (neg (tan eps)) (tan x)) 1) (sin x))) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 2/15 binary64) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))) (*.f64 eps eps) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))) eps)) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (cos.f64 x))) |
#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)) |
#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)) (*.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 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))) |
3 calls:
| 19.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 18.0ms | x |
| 14.0ms | 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)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))) (cos.f64 (+.f64 eps x)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))) |
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.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 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64)) |
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) (cos.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)) |
(/.f64 (*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (sin.f64 eps)) (cos.f64 x)) |
(/.f64 (/.f64 (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))) (cos.f64 (+.f64 eps x))) (cos.f64 x)) |
(/.f64 (sin.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 eps eps (-.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 0 binary64)))))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (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 (/.f64 (sin.f64 (exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))) (cos.f64 x)) |
(fma.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)))) (neg.f64 (tan.f64 x))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x)))))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x))))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (*.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) eps))))) |
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 eps x))) (pow.f64 (pow.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(literal -1 binary64)) #s(literal -1 binary64))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/.f64 (sin.f64 eps) (*.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))))) |
| Outputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/.f64 (sin.f64 eps) (*.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))))) |
3 calls:
| 13.0ms | eps |
| 12.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 12.0ms | x |
| 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)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))) (cos.f64 (+.f64 eps x)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 (+.f64 x eps))) (cos.f64 x)) |
(-.f64 (tan.f64 (+.f64 x eps)) (*.f64 (neg.f64 (sin.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))))) |
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 eps x))) (cos.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 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (+.f64 (cos.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 (+.f64 (+.f64 eps x) x)))) #s(literal 2 binary64)) |
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 x eps)) (sin.f64 eps))) (cos.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)) |
(/.f64 (*.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal -1 binary64)) (sin.f64 eps)) (cos.f64 x)) |
(/.f64 (/.f64 (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))) (cos.f64 (+.f64 eps x))) (cos.f64 x)) |
(/.f64 (sin.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 eps eps (-.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 0 binary64)))))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (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 (/.f64 (sin.f64 (exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x))) (cos.f64 x)) |
(fma.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)))) (neg.f64 (tan.f64 x))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x)))))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (+ eps x)) (fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x))))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) #s(approx (* (neg (sin eps)) (sin x)) (*.f64 (*.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) eps))))) |
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 eps x))) (pow.f64 (pow.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) #s(literal -1 binary64)) #s(literal -1 binary64))) |
| Outputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
3 calls:
| 12.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 11.0ms | eps |
| 11.0ms | 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)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))) (cos.f64 (+.f64 eps x)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 (/.f64 (sin.f64 eps) (+.f64 (cos.f64 (+.f64 (+.f64 x eps) x)) (cos.f64 eps))) #s(literal 2 binary64))) |
| Outputs |
|---|
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
3 calls:
| 8.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 6.0ms | eps |
| 6.0ms | 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)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64)) (sin.f64 eps))) (cos.f64 (+.f64 eps x)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (cos.f64 (+.f64 eps x)))) |
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x))) |
| Outputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x)))) |
3 calls:
| 8.0ms | x |
| 6.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.0% | 1 | x |
| 99.0% | 1 | eps |
| 99.0% | 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)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
| Outputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
3 calls:
| 5.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 5.0ms | x |
| 4.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.5% | 1 | x |
| 98.5% | 1 | eps |
| 98.5% | 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)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 eps eps) #s(literal 2/15 binary64)) (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/9 binary64) (*.f64 eps eps)) (*.f64 eps eps) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64)) (*.f64 #s(literal 1/3 binary64) eps)) eps)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 #s(approx (sin eps) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps)) #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))) eps))) |
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
3 calls:
| 4.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 4.0ms | x |
| 4.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.4% | 1 | x |
| 97.4% | 1 | eps |
| 97.4% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
Total -58.3b remaining (-3447%)
Threshold costs -58.3b (-3447%)
| Inputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) (*.f64 (*.f64 eps eps) #s(literal 1/3 binary64))) eps))) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 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 |
|---|---|---|
| 97.4% | 1 | x |
| 97.4% | 1 | eps |
| 97.4% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| 1× | egg-herbie |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 68 | 223 |
| 1 | 99 | 210 |
| 2 | 139 | 198 |
| 3 | 226 | 198 |
| 4 | 638 | 198 |
| 5 | 4464 | 198 |
| 6 | 7913 | 198 |
| 1× | node limit |
| Inputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/.f64 (sin.f64 eps) (*.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps))) |
| Outputs |
|---|
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ (/ (sin eps) (cos x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x)))) (/.f64 (sin.f64 eps) (*.f64 (fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
(/.f64 #s(approx (sin (- (+ eps x) x)) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 #s(approx (/ (sin eps) (cos x)) (/.f64 eps (cos.f64 x))) (cos.f64 (+.f64 eps x)))) |
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (/ (sin eps) (cos eps)) (*.f64 #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64)) eps))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 157 | 950 |
| 1 | 464 | 884 |
| 2 | 1539 | 873 |
| 3 | 6077 | 710 |
| 0 | 8335 | 686 |
| 0 | 523 | 2556 |
| 1 | 1630 | 2383 |
| 2 | 5366 | 2254 |
| 0 | 8162 | 2135 |
| 0 | 47 | 213 |
| 0 | 72 | 193 |
| 1 | 293 | 165 |
| 2 | 2500 | 165 |
| 0 | 8201 | 165 |
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 50 | 16 |
| 2 | 402 | 16 |
| 3 | 6137 | 16 |
| 0 | 8166 | 16 |
| 0 | 707 | 6465 |
| 1 | 2311 | 5981 |
| 0 | 8406 | 5816 |
| 0 | 963 | 8537 |
| 1 | 3144 | 7981 |
| 0 | 8507 | 7715 |
| 1× | fuel |
| 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× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 482 to 259 computations (46.3% saved)
Compiled 478 to 164 computations (65.7% saved)
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