
Time bar (total: 13.1s)
| 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)
| 3.3s | 25 954× | 0 | invalid |
| 586.0ms | 5 518× | 0 | valid |
| 567.0ms | 2 738× | 1 | valid |
ival-tan: 662.0ms (20.7% of total)const: 643.0ms (20.1% of total)ival-mult: 400.0ms (12.5% of total)ival-<: 273.0ms (8.5% of total)ival-fabs: 250.0ms (7.8% of total)ival-<=: 248.0ms (7.8% of total)ival-add: 237.0ms (7.4% of total)ival-sub: 226.0ms (7.1% of total)ival-and: 104.0ms (3.3% of total)adjust: 92.0ms (2.9% of total)exact: 49.0ms (1.5% of total)ival-assert: 14.0ms (0.4% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 224 | 4 | (1.5947849276100386e-132 1.2208443374928188e-134) | 6 | (9.024504157317816e-72 1.068466416998655e-73) | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 2 | 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 | 10 |
tan.f64 | (tan.f64 (+.f64 x eps)) | sensitivity | 2 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 219 | 5 |
| - | 4 | 28 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 219 | 5 | 0 |
| - | 4 | 5 | 23 |
| number | freq |
|---|---|
| 0 | 33 |
| 1 | 222 |
| 2 | 1 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 17.0ms | 172× | 1 | valid |
| 16.0ms | 334× | 0 | valid |
| 5.0ms | 4× | 2 | valid |
| 1.0ms | 2× | 3 | valid |
Compiled 47 to 22 computations (53.2% saved)
ival-tan: 14.0ms (57% of total)adjust: 4.0ms (16.3% of total)ival-add: 3.0ms (12.2% of total)ival-sub: 3.0ms (12.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 39 |
| 1 | 38 | 35 |
| 2 | 86 | 35 |
| 3 | 169 | 35 |
| 4 | 312 | 35 |
| 5 | 383 | 35 |
| 6 | 469 | 35 |
| 7 | 509 | 35 |
| 8 | 521 | 35 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 13 | 7 |
| 2 | 18 | 7 |
| 3 | 24 | 7 |
| 4 | 32 | 7 |
| 5 | 47 | 7 |
| 6 | 80 | 7 |
| 7 | 110 | 7 |
| 8 | 159 | 7 |
| 9 | 175 | 7 |
| 10 | 183 | 7 |
| 0 | 183 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| Outputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 62.5% | (-.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 | 0.10834297833555283 | (tan.f64 (+.f64 x eps)) | |
| accuracy | 23.906393979708145 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 73.0ms | 86× | 1 | valid |
| 8.0ms | 167× | 0 | valid |
| 2.0ms | 2× | 2 | valid |
| 0.0ms | 1× | 3 | valid |
Compiled 20 to 8 computations (60% saved)
ival-sub: 65.0ms (84.8% of total)ival-tan: 8.0ms (10.4% of total)adjust: 2.0ms (2.6% of total)ival-add: 2.0ms (2.6% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
(tan.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(tan.f64 x) |
| Outputs |
|---|
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
eps |
(+ eps x) |
x |
(* x (+ 1 (* 1/3 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) |
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2)))))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(* x (+ 1 (/ eps x))) |
(/ (sin x) (cos x)) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(* eps (+ 1 (/ x eps))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | eps | @ | 0 | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 2.0ms | x | @ | 0 | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 2.0ms | eps | @ | inf | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 1.0ms | eps | @ | -inf | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 1.0ms | x | @ | inf | ((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) (tan x)) |
| 1× | 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)
15 alts after pruning (14 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 262 | 14 | 276 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 262 | 15 | 277 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 62.5% | (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
| ▶ | 62.5% | (/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
| 26.4% | (/.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))) | |
| 61.3% | (/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) | |
| 62.5% | (/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| ▶ | 62.3% | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
| 62.3% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) | |
| 62.6% | (-.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)) | |
| ✓ | 62.5% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 38.5% | (-.f64 (tan.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))) (tan.f64 x)) | |
| 62.5% | (*.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))) | |
| 98.7% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) | |
| ▶ | 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
| ▶ | 99.7% | #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 (*.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 673 to 372 computations (44.7% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (sin.f64 x) | |
| cost-diff | 0 | (neg.f64 (sin.f64 x)) | |
| cost-diff | 0 | (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) | |
| cost-diff | 6 | (/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| cost-diff | 0 | (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) | |
| cost-diff | 0 | (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))) | |
| cost-diff | 2 | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) | |
| cost-diff | 4 | (-.f64 (+.f64 eps x) x) | |
| cost-diff | 0 | (neg.f64 (cos.f64 x)) | |
| cost-diff | 0 | (sin.f64 x) | |
| cost-diff | 1 | (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) | |
| cost-diff | 1 | (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps 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 | 0 | #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)) | |
| cost-diff | 1 | (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) | |
| cost-diff | 1 | (-.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))) | |
| cost-diff | 8 | (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)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 49 | 575 |
| 0 | 91 | 567 |
| 1 | 152 | 561 |
| 2 | 300 | 554 |
| 3 | 839 | 554 |
| 4 | 3680 | 527 |
| 5 | 6546 | 527 |
| 0 | 8171 | 514 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#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)) |
(*.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) |
(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)))) |
(*.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) |
(-.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))) |
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(sin.f64 x) |
x |
(/.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) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(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)) |
(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))) |
#s(literal 1 binary64) |
#s(literal -1/3 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) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
(sin.f64 x) |
x |
(/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) |
#s(literal 1 binary64) |
(neg.f64 (cos.f64 x)) |
(cos.f64 x) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
#s(literal 1 binary64) |
(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
(cos.f64 x) |
(sin.f64 (-.f64 (+.f64 eps x) x)) |
(-.f64 (+.f64 eps x) x) |
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) |
(neg.f64 (sin.f64 x)) |
(sin.f64 x) |
x |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
(*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) |
(sin.f64 (+.f64 eps x)) |
(cos.f64 x) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
| Outputs |
|---|
#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 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) eps) (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 eps 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)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps)) |
(*.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 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) eps) (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 eps 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)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps) |
(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)))) |
(fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (fma.f64 eps (*.f64 #s(literal 1/3 binary64) eps) (fma.f64 (/.f64 eps (cos.f64 x)) (sin.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 eps 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)))) (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 (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) |
(*.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)))) eps) |
(-.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))) |
(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 (fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(fma.f64 (sin.f64 x) (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(sin.f64 x) |
x |
(/.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) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
(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)) |
(fma.f64 (*.f64 #s(literal -1/3 binary64) (sin.f64 x)) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #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 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
#s(literal 1 binary64) |
#s(literal -1/3 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) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
(-.f64 (tan.f64 (+.f64 eps x)) (/.f64 (sin.f64 x) (cos.f64 x))) |
(sin.f64 x) |
x |
(/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) |
(/.f64 #s(literal -1 binary64) (cos.f64 x)) |
#s(literal 1 binary64) |
(neg.f64 (cos.f64 x)) |
(cos.f64 x) |
(tan.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(literal 1 binary64) |
(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))) |
(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 eps)) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
(cos.f64 x) |
(sin.f64 (-.f64 (+.f64 eps x) x)) |
(sin.f64 eps) |
(-.f64 (+.f64 eps x) x) |
eps |
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) #s(literal 1 binary64) (/.f64 (neg.f64 (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) |
(neg.f64 (sin.f64 x)) |
(sin.f64 x) |
x |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
(*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) |
(sin.f64 (+.f64 eps x)) |
(cos.f64 x) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.01953125 | (/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| accuracy | 0.06528561707679843 | (cos.f64 (+.f64 eps x)) | |
| accuracy | 0.09031686966524144 | (sin.f64 (+.f64 eps x)) | |
| accuracy | 23.87644966822811 | (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) | |
| accuracy | 0.015625 | (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))) | |
| accuracy | 0.06528561707679843 | (cos.f64 (+.f64 eps x)) | |
| accuracy | 0.34815595893597295 | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) | |
| accuracy | 24.013621590949512 | (-.f64 (+.f64 eps x) x) | |
| accuracy | 0.0 | (cos.f64 x) | |
| accuracy | 0.00390625 | (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) | |
| accuracy | 0.10834297833555283 | (tan.f64 (+.f64 eps x)) | |
| accuracy | 23.88395554761824 | (fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) | |
| accuracy | 0.0 | (sin.f64 eps) | |
| accuracy | 0.0 | (cos.f64 eps) | |
| accuracy | 0.0078125 | (/.f64 (sin.f64 eps) (cos.f64 eps)) | |
| accuracy | 1.2567277158709258 | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) | |
| accuracy | 0.015625 | (/.f64 (fma.f64 (sin.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))) | |
| accuracy | 0.02248002930532605 | (pow.f64 (sin.f64 x) #s(literal 4 binary64)) | |
| accuracy | 0.20834789826985745 | #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)) | |
| accuracy | 0.328125 | (*.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) |
| 123.0ms | 91× | 1 | valid |
| 67.0ms | 160× | 0 | valid |
| 7.0ms | 4× | 2 | valid |
| 1.0ms | 1× | 3 | valid |
Compiled 530 to 54 computations (89.8% saved)
ival-div: 51.0ms (30.4% of total)ival-add: 37.0ms (22% of total)ival-mult: 24.0ms (14.3% of total)adjust: 11.0ms (6.6% of total)ival-tan: 10.0ms (6% of total)ival-sin: 8.0ms (4.8% of total)ival-cos: 6.0ms (3.6% of total)const: 5.0ms (3% of total)ival-pow: 5.0ms (3% of total)ival-sub: 4.0ms (2.4% of total)ival-neg: 3.0ms (1.8% of total)ival-pow2: 3.0ms (1.8% 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 (-.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)))) |
(-.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))) |
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (-.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 (sin.f64 eps) (cos.f64 eps))) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(sin.f64 eps) |
(cos.f64 eps) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) |
(sin.f64 x) |
(neg.f64 (cos.f64 x)) |
(-.f64 (+.f64 eps x) x) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) |
(neg.f64 (sin.f64 x)) |
(*.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) |
(pow.f64 (sin.f64 x) #s(literal 4 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))) |
(tan.f64 (+.f64 eps x)) |
(cos.f64 x) |
(cos.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 eps x)) |
| Outputs |
|---|
(+ 1 (* 1/3 (pow eps 2))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps x))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))))) |
1/3 |
(+ 1/3 (* 4/3 (pow x 2))) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2))))) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2))))))) |
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))) |
-1 |
(- (* -1/2 (pow x 2)) 1) |
(- (* (pow x 2) (- (* -5/24 (pow x 2)) 1/2)) 1) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -61/720 (pow x 2)) 5/24)) 1/2)) 1) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(- (* 1/2 (pow x 2)) 1) |
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1) |
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1) |
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))) |
(/ (cos eps) (sin eps)) |
(+ (* -1 x) (/ (cos eps) (sin eps))) |
(+ (* x (- (* -1 (/ (* x (cos eps)) (sin eps))) 1)) (/ (cos eps) (sin eps))) |
(+ (* x (- (* x (+ (* -1 (/ (cos eps) (sin eps))) (* 2/3 x))) 1)) (/ (cos eps) (sin 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 (- (/ (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 (- (+ (* x (- (* -1 (/ (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))) (cos eps))) (+ 2/3 (+ (* -1 (/ (* (sin eps) (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))))))) (/ (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) (* x (+ (cos eps) (* -1 (cos eps))))) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (sin eps)))))))) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (+ (* -1 (sin eps)) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))))))))))) |
(* -1 x) |
(* x (- (* 1/6 (pow x 2)) 1)) |
(* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)) |
(* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1)) |
(* 1/3 eps) |
(+ (* 1/3 eps) (* 4/3 (* eps (pow x 2)))) |
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2)))))) |
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps)))))) |
(pow x 4) |
(* (pow x 4) (+ 1 (* -2/3 (pow x 2)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3)))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 5/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2)))))))) |
(+ (* 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))) |
(+ 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))) |
(+ (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)))) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ 1 (/ (* eps (sin x)) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(/ -1 (cos x)) |
(sin x) |
(* -1 (cos x)) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (* (cos x) (cos (+ eps x))) (sin eps)) |
(* (cos x) (cos (+ eps x))) |
(/ (+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) (* (cos x) (cos (+ eps x)))) |
(+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) |
(* -1 (sin x)) |
(* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(pow (sin x) 4) |
(/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(cos x) |
(cos (+ eps x)) |
(sin (+ eps x)) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) |
(* (cos x) (cos (- eps (* -1 x)))) |
(/ (+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) (* (cos x) (cos (- eps (* -1 x))))) |
(+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(cos (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (- 1 (* -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))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (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)))) |
(+ (* -1 (/ (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 (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)))) |
(/ (pow (cos x) 2) eps) |
(/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps) |
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps) |
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (+ (* -1/2 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/24 (pow (cos x) 2)) (+ (* -1/6 (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))) (* 1/120 (pow (cos x) 2)))))) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps) |
(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)) |
(/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (+ (* 1/2 (/ (sin x) (cos x))) (* eps (- (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/6 (+ (* -1 (/ (* (sin x) (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (* 1/6 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3)))))))))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (pow (cos x) 2) (pow (sin x) 2))) (* (cos x) (sin x)))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x)))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x)))) |
(/ (sin x) (cos x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (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)))) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(/ (* eps (sin x)) (cos x)) |
(* eps (+ (/ 1 eps) (/ (sin x) (cos x)))) |
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps)))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (* (cos x) (cos (- x (* -1 eps)))) (sin (neg (* -1 eps)))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(/ (+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) (* (cos x) (cos (- x (* -1 eps))))) |
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(cos (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 18.0ms | eps | @ | 0 | ((+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (/ 1 (neg (cos x))) (sin x) (neg (cos x)) (- (+ eps x) x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (neg (sin x)) (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) (pow (sin x) 4) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (tan (+ eps x)) (cos x) (cos (+ eps x)) (sin (+ eps x))) |
| 15.0ms | x | @ | inf | ((+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (/ 1 (neg (cos x))) (sin x) (neg (cos x)) (- (+ eps x) x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (neg (sin x)) (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) (pow (sin x) 4) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (tan (+ eps x)) (cos x) (cos (+ eps x)) (sin (+ eps x))) |
| 10.0ms | x | @ | -inf | ((+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (/ 1 (neg (cos x))) (sin x) (neg (cos x)) (- (+ eps x) x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (neg (sin x)) (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) (pow (sin x) 4) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (tan (+ eps x)) (cos x) (cos (+ eps x)) (sin (+ eps x))) |
| 8.0ms | eps | @ | inf | ((+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (/ 1 (neg (cos x))) (sin x) (neg (cos x)) (- (+ eps x) x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (neg (sin x)) (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) (pow (sin x) 4) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (tan (+ eps x)) (cos x) (cos (+ eps x)) (sin (+ eps x))) |
| 7.0ms | eps | @ | -inf | ((+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) (+ (/ (* (sin x) eps) (cos x)) 1) (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x)) (/ (sin eps) (cos eps)) (sin eps) (cos eps) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (/ 1 (neg (cos x))) (sin x) (neg (cos x)) (- (+ eps x) x) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (* (cos (+ eps x)) (cos x)) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (neg (sin x)) (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) (pow (sin x) 4) (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (tan (+ eps x)) (cos x) (cos (+ eps x)) (sin (+ eps x))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 741 | 3968 |
| 1 | 2302 | 3532 |
| 2 | 7176 | 3461 |
| 0 | 8166 | 3253 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ 1 (* 1/3 (pow eps 2))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps x))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))))) |
1/3 |
(+ 1/3 (* 4/3 (pow x 2))) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2))))) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2))))))) |
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))) |
-1 |
(- (* -1/2 (pow x 2)) 1) |
(- (* (pow x 2) (- (* -5/24 (pow x 2)) 1/2)) 1) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -61/720 (pow x 2)) 5/24)) 1/2)) 1) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(- (* 1/2 (pow x 2)) 1) |
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1) |
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1) |
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))) |
(/ (cos eps) (sin eps)) |
(+ (* -1 x) (/ (cos eps) (sin eps))) |
(+ (* x (- (* -1 (/ (* x (cos eps)) (sin eps))) 1)) (/ (cos eps) (sin eps))) |
(+ (* x (- (* x (+ (* -1 (/ (cos eps) (sin eps))) (* 2/3 x))) 1)) (/ (cos eps) (sin 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 (- (/ (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 (- (+ (* x (- (* -1 (/ (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))) (cos eps))) (+ 2/3 (+ (* -1 (/ (* (sin eps) (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))))))) (/ (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) (* x (+ (cos eps) (* -1 (cos eps))))) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (sin eps)))))))) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (+ (* -1 (sin eps)) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))))))))))) |
(* -1 x) |
(* x (- (* 1/6 (pow x 2)) 1)) |
(* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)) |
(* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1)) |
(* 1/3 eps) |
(+ (* 1/3 eps) (* 4/3 (* eps (pow x 2)))) |
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2)))))) |
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps)))))) |
(pow x 4) |
(* (pow x 4) (+ 1 (* -2/3 (pow x 2)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3)))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3)))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 5/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2)))))) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2)))))))) |
(+ (* 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))) |
(+ 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))) |
(+ (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)))) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ 1 (/ (* eps (sin x)) (cos x))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(/ -1 (cos x)) |
(sin x) |
(* -1 (cos x)) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/ (* (cos x) (cos (+ eps x))) (sin eps)) |
(* (cos x) (cos (+ eps x))) |
(/ (+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) (* (cos x) (cos (+ eps x)))) |
(+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) |
(* -1 (sin x)) |
(* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(pow (sin x) 4) |
(/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)) |
(/ (sin (+ eps x)) (cos (+ eps x))) |
(cos x) |
(cos (+ eps x)) |
(sin (+ eps x)) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(/ (* (cos x) (cos (- eps (* -1 x)))) (sin eps)) |
(* (cos x) (cos (- eps (* -1 x)))) |
(/ (+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) (* (cos x) (cos (- eps (* -1 x))))) |
(+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) |
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) |
(cos (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (- 1 (* -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))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (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)))) |
(+ (* -1 (/ (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 (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)))) |
(/ (pow (cos x) 2) eps) |
(/ (+ (* -1 (* eps (* (cos x) (sin x)))) (pow (cos x) 2)) eps) |
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps) |
(/ (+ (* eps (+ (* -1 (* (cos x) (sin x))) (* eps (- (+ (* -1/2 (pow (cos x) 2)) (* (pow eps 2) (- (* 1/24 (pow (cos x) 2)) (+ (* -1/6 (- (* -1/2 (pow (cos x) 2)) (* -1/6 (pow (cos x) 2)))) (* 1/120 (pow (cos x) 2)))))) (* -1/6 (pow (cos x) 2)))))) (pow (cos x) 2)) eps) |
(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)) |
(/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (+ (* 1/2 (/ (sin x) (cos x))) (* eps (- (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/6 (+ (* -1 (/ (* (sin x) (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (* 1/6 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3)))))))))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (pow (cos x) 2) (pow (sin x) 2))) (* (cos x) (sin x)))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x)))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x)))) |
(/ (sin x) (cos x)) |
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) |
(+ (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)))) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(/ (* eps (sin x)) (cos x)) |
(* eps (+ (/ 1 eps) (/ (sin x) (cos x)))) |
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* -1 (* eps (- (* -1 (/ (sin x) (cos x))) (/ 1 eps)))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps))))) |
(/ (* (cos x) (cos (- x (* -1 eps)))) (sin (neg (* -1 eps)))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(/ (+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) (* (cos x) (cos (- x (* -1 eps))))) |
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(cos (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
| Outputs |
|---|
(+ 1 (* 1/3 (pow eps 2))) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps x))) |
(fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
1/3 |
#s(literal 1/3 binary64) |
(+ 1/3 (* 4/3 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2))))) |
(fma.f64 (fma.f64 #s(literal 17/9 binary64) (*.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) |
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2))))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 248/135 binary64) (*.f64 x x) #s(literal 17/9 binary64)) (*.f64 x x) #s(literal 4/3 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) |
1 |
#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 (*.f64 x x) #s(literal 1/3 binary64)) eps eps) x #s(literal 1 binary64)) |
(+ 1 (* x (+ eps (* (pow x 2) (- (+ (* -1/6 eps) (* (pow x 2) (- (* 1/120 eps) (+ (* -1/2 (- (* -1/6 eps) (* -1/2 eps))) (* 1/24 eps))))) (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) eps) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal -1/6 binary64) eps))) (*.f64 x x) (*.f64 #s(literal 1/3 binary64) eps)) (*.f64 x x) eps) x #s(literal 1 binary64)) |
(/ (sin eps) (cos eps)) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (/.f64 x (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 (fma.f64 (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))) (*.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))) |
-1 |
#s(literal -1 binary64) |
(- (* -1/2 (pow x 2)) 1) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64)) |
(- (* (pow x 2) (- (* -5/24 (pow x 2)) 1/2)) 1) |
(fma.f64 (fma.f64 #s(literal -5/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -61/720 (pow x 2)) 5/24)) 1/2)) 1) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -61/720 binary64) (*.f64 x x) #s(literal -5/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) x) |
(- (* 1/2 (pow x 2)) 1) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) |
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1) |
(fma.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) |
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) |
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) (fma.f64 (sin.f64 eps) (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 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (-.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (/.f64 (neg.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))) |
(/ (cos eps) (sin eps)) |
(/.f64 (cos.f64 eps) (sin.f64 eps)) |
(+ (* -1 x) (/ (cos eps) (sin eps))) |
(-.f64 (/.f64 (cos.f64 eps) (sin.f64 eps)) x) |
(+ (* x (- (* -1 (/ (* x (cos eps)) (sin eps))) 1)) (/ (cos eps) (sin eps))) |
(fma.f64 (fma.f64 (neg.f64 x) (/.f64 (cos.f64 eps) (sin.f64 eps)) #s(literal -1 binary64)) x (/.f64 (cos.f64 eps) (sin.f64 eps))) |
(+ (* x (- (* x (+ (* -1 (/ (cos eps) (sin eps))) (* 2/3 x))) 1)) (/ (cos eps) (sin eps))) |
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/3 binary64) x) (/.f64 (cos.f64 eps) (sin.f64 eps))) x #s(literal -1 binary64)) x (/.f64 (cos.f64 eps) (sin.f64 eps))) |
(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(fma.f64 (neg.f64 (sin.f64 eps)) x (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 (- (/ (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 (- (+ (* x (- (* -1 (/ (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))) (cos eps))) (+ 2/3 (+ (* -1 (/ (* (sin eps) (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))))))) (/ (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 (-.f64 (fma.f64 (/.f64 (cos.f64 eps) (cos.f64 eps)) #s(literal 2/3 binary64) #s(literal -2/3 binary64)) (fma.f64 (sin.f64 eps) (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 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) x (+.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) (* x (+ (cos eps) (* -1 (cos eps))))) |
(fma.f64 #s(literal 0 binary64) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (sin eps)))))))) |
(fma.f64 (fma.f64 #s(literal 0 binary64) x #s(literal 0 binary64)) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (+ (* -1 (sin eps)) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))))))))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 0 binary64) x #s(literal 0 binary64)) x #s(literal 0 binary64)) x (sin.f64 eps)) |
(* -1 x) |
(neg.f64 x) |
(* x (- (* 1/6 (pow x 2)) 1)) |
(*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64)) x) |
(* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1)) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x) |
(* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1)) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)) x) |
(* 1/3 eps) |
(*.f64 #s(literal 1/3 binary64) eps) |
(+ (* 1/3 eps) (* 4/3 (* eps (pow x 2)))) |
(fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 4/3 binary64) (*.f64 #s(literal 1/3 binary64) eps)) |
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* 17/9 (* eps (pow x 2)))))) |
(fma.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 17/9 binary64) (*.f64 #s(literal 4/3 binary64) eps)) x) x (*.f64 #s(literal 1/3 binary64) eps)) |
(+ (* 1/3 eps) (* (pow x 2) (+ (* 4/3 eps) (* (pow x 2) (+ (* 248/135 (* eps (pow x 2))) (* 17/9 eps)))))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 248/135 binary64) (*.f64 #s(literal 17/9 binary64) eps)) x) x (*.f64 #s(literal 4/3 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/3 binary64) eps)) |
(pow x 4) |
(pow.f64 x #s(literal 4 binary64)) |
(* (pow x 4) (+ 1 (* -2/3 (pow x 2)))) |
(*.f64 (fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* 1/5 (pow x 2)) 2/3)))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/5 binary64) (*.f64 x x) #s(literal -2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 4) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/5 (* -34/945 (pow x 2)))) 2/3)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -34/945 binary64) (*.f64 x x) #s(literal 1/5 binary64)) (*.f64 x x) #s(literal -2/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 5/3 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal 5/3 binary64) (*.f64 x x) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2)))))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 77/45 binary64) (*.f64 x x) #s(literal 5/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x) |
(* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2)))))))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 88/63 binary64) (*.f64 x x) #s(literal 77/45 binary64)) (*.f64 x x) #s(literal 5/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) x) |
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (/.f64 x (cos.f64 eps)) (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (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 1/6 binary64))) (neg.f64 x) (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(fma.f64 (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (cos.f64 eps) (neg.f64 (sin.f64 eps))) x (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
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(+ (sin eps) (* x (cos eps))) |
(fma.f64 (cos.f64 eps) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) #s(literal -1/2 binary64)) x (cos.f64 eps)) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) #s(literal -1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) x (sin.f64 eps)) |
(+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
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(- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(+ 1 (/ (* eps (sin x)) (cos x))) |
(fma.f64 (sin.f64 x) (/.f64 eps (cos.f64 x)) #s(literal 1 binary64)) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
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(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(/ -1 (cos x)) |
(/.f64 #s(literal -1 binary64) (cos.f64 x)) |
(sin x) |
(sin.f64 x) |
(* -1 (cos x)) |
(neg.f64 (cos.f64 x)) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/ (* (cos x) (cos (+ eps x))) (sin eps)) |
(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 eps)) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(/ (+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) (* (cos x) (cos (+ eps x)))) |
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(+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) |
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) |
(* -1 (sin x)) |
(neg.f64 (sin.f64 x)) |
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(pow (sin x) 4) |
(pow.f64 (sin.f64 x) #s(literal 4 binary64)) |
(/ (+ (/ (pow (sin x) 4) (pow (cos x) 2)) (pow (sin x) 2)) (pow (cos x) 2)) |
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(cos x) |
(cos.f64 x) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
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(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 eps)) |
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(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
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(+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) |
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) |
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(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(+ 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 (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))))) |
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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 (* 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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(* 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)))) |
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(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
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(+ 1 (* -1/2 (pow eps 2))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
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(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x))) |
#s(literal 0 binary64) |
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(fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps #s(literal 0 binary64)) |
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(/ 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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(pow (cos x) 2) |
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eps |
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(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) |
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) |
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 49 | 367 |
| 0 | 91 | 343 |
| 1 | 390 | 273 |
| 2 | 3401 | 263 |
| 0 | 8762 | 256 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(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)))) |
(-.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))) |
(+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (*.f64 (-.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 (sin.f64 eps) (cos.f64 eps))) |
(/.f64 (sin.f64 eps) (cos.f64 eps)) |
(sin.f64 eps) |
(cos.f64 eps) |
(fma.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (tan.f64 (+.f64 eps x))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) |
(sin.f64 x) |
(neg.f64 (cos.f64 x)) |
(-.f64 (+.f64 eps x) x) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x))) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) |
(neg.f64 (sin.f64 x)) |
(*.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) |
(pow.f64 (sin.f64 x) #s(literal 4 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))) |
(tan.f64 (+.f64 eps x)) |
(cos.f64 x) |
(cos.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 eps x)) |
| Outputs |
|---|
(*.f64 (-.f64 (*.f64 (pow.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64))) (pow.f64 (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) (*.f64 (neg.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64))) (pow.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) (*.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))))))) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) (*.f64 (neg.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))) (-.f64 (*.f64 (pow.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) (*.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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 eps #s(literal 6 binary64)) (pow.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 (pow.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))))) (neg.f64 (-.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) (*.f64 (neg.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)) (*.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (-.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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)))))))))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 (pow.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)))) (-.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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)))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (*.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))) (*.f64 (neg.f64 (fma.f64 eps (tan.f64 x) #s(literal 1 binary64))) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)))))) |
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.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)))))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.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))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.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)))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.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))))) |
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64)))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(neg.f64 (/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (*.f64 (sin.f64 x) (tan.f64 x)) #s(literal 2 binary64))) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) |
(exp.f64 (*.f64 (log.f64 (/.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))))) #s(literal -1 binary64))) |
(*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x))) #s(literal -1 binary64))) |
(*.f64 (sin.f64 (+.f64 eps x)) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x))) (+.f64 (tan.f64 eps) (tan.f64 x))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (neg.f64 (+.f64 (tan.f64 eps) (tan.f64 x)))) (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x)))))) |
(/.f64 (neg.f64 (neg.f64 (sin.f64 (+.f64 eps x)))) (neg.f64 (neg.f64 (cos.f64 (+.f64 eps x))))) |
(/.f64 (neg.f64 (+.f64 (tan.f64 eps) (tan.f64 x))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x))))) |
(/.f64 (neg.f64 (sin.f64 (+.f64 eps x))) (neg.f64 (cos.f64 (+.f64 eps x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x))) (+.f64 (tan.f64 eps) (tan.f64 x))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))))) |
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x)))) |
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x))) (+.f64 (tan.f64 eps) (tan.f64 x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x)))) |
(tan.f64 (+.f64 eps x)) |
(*.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x))) |
(*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x))) |
(*.f64 #s(literal 1 binary64) (cos.f64 x)) |
(pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (cos.f64 x) #s(literal 1 binary64)) |
(neg.f64 (neg.f64 (cos.f64 x))) |
(fma.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (cos.f64 x)) #s(literal 1 binary64)) (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
(fma.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
(fma.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 x))) |
(cos.f64 (neg.f64 x)) |
(cos.f64 x) |
(+.f64 (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
(exp.f64 (log.f64 (cos.f64 x))) |
(/.f64 (neg.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)))) (neg.f64 (cos.f64 (-.f64 eps x)))) |
(/.f64 (neg.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)))) (neg.f64 (+.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))))))) |
(/.f64 (-.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 eps x))) (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps 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 (neg.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)))) (neg.f64 (sin.f64 (-.f64 eps x)))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x))))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64))) (sin.f64 (-.f64 eps x))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x)))))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (sin.f64 eps) (cos.f64 x))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (cos.f64 eps) (sin.f64 x))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) |
(sin.f64 (+.f64 eps x)) |
(-.f64 (*.f64 (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (*.f64 x x) (-.f64 eps x)))) (*.f64 (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 eps x))))) |
(-.f64 (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (*.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) |
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (cos.f64 x))) |
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x))) |
Compiled 49 947 to 4 712 computations (90.6% saved)
19 alts after pruning (18 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 037 | 18 | 1 055 |
| Fresh | 9 | 0 | 9 |
| Picked | 5 | 0 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 051 | 19 | 1 070 |
| Status | Accuracy | Program |
|---|---|---|
| 99.9% | (/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x))) | |
| 99.8% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| ▶ | 99.9% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
| ▶ | 99.2% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
| ▶ | 58.9% | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))))))) |
| 99.3% | (/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (fma.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps) #s(literal -1/3 binary64) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))) | |
| 99.4% | (/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 x) (*.f64 (fma.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/24 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/18 binary64) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/120 binary64)))) (*.f64 eps eps) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))) | |
| 98.7% | (/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (neg.f64 (*.f64 (cos.f64 x) eps)) (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))) | |
| ✓ | 62.5% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 99.9% | (*.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)) | |
| 98.7% | #s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) | |
| 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))))) | |
| 99.7% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))))) eps)) | |
| ▶ | 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
| 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) | |
| 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) | |
| 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) | |
| 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) | |
| ▶ | 5.3% | #s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
Compiled 1 493 to 824 computations (44.8% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 2 | (+.f64 #s(literal 0 binary64) eps) | |
| cost-diff | 2 | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))))))) | |
| cost-diff | 4 | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)))) | |
| cost-diff | 8 | (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))) | |
| cost-diff | 0 | (cos.f64 (+.f64 eps x)) | |
| cost-diff | 0 | (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) | |
| cost-diff | 0 | #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) | |
| cost-diff | 0 | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) | |
| cost-diff | 1 | (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) | |
| cost-diff | 3 | (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) | |
| cost-diff | 0 | #s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) | |
| cost-diff | 0 | (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) | |
| cost-diff | 0 | (sin.f64 eps) | |
| cost-diff | 0 | #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) | |
| cost-diff | 0 | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 73 | 622 |
| 0 | 103 | 580 |
| 1 | 199 | 528 |
| 2 | 481 | 521 |
| 3 | 1398 | 511 |
| 4 | 3717 | 511 |
| 5 | 7520 | 511 |
| 0 | 8028 | 490 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos 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) |
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(literal 0 binary64) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) |
(fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) |
(*.f64 #s(literal 4/3 binary64) eps) |
#s(literal 4/3 binary64) |
eps |
(fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) |
x |
#s(literal 1 binary64) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
(*.f64 eps eps) |
#s(literal 1/3 binary64) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) |
eps |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
x |
(cos.f64 x) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))))))) |
#s(literal 1 binary64) |
(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)))))) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
(cos.f64 x) |
(sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)))) |
(/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))) |
(+.f64 (+.f64 eps x) x) |
(*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)) |
(+.f64 #s(literal 0 binary64) eps) |
#s(literal 0 binary64) |
| Outputs |
|---|
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos 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) |
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(literal 0 binary64) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(fma.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) |
(*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) (+.f64 eps x)) |
(fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) |
(fma.f64 (*.f64 #s(literal 4/3 binary64) eps) (+.f64 eps x) #s(literal 1 binary64)) |
(*.f64 #s(literal 4/3 binary64) eps) |
#s(literal 4/3 binary64) |
eps |
(fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) |
x |
#s(literal 1 binary64) |
(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) |
#s(literal 1/3 binary64) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) |
eps |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
x |
(cos.f64 x) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(literal 1 binary64) |
(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)))))) |
(/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 eps)) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos.f64 (+.f64 eps x)) |
(+.f64 eps x) |
eps |
x |
(cos.f64 x) |
(sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))))) |
(sin.f64 eps) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)))) |
eps |
(/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))) |
(/.f64 #s(literal 1 binary64) eps) |
(+.f64 (+.f64 eps x) x) |
(fma.f64 #s(literal 2 binary64) x eps) |
(*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)) |
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) |
(+.f64 #s(literal 0 binary64) eps) |
eps |
#s(literal 0 binary64) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.25390625 | (+.f64 (+.f64 eps x) x) | |
| accuracy | 0.34815595893597295 | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))))))) | |
| accuracy | 0.35206220893597295 | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)))) | |
| accuracy | 26.111650247599812 | (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))) | |
| accuracy | 0.00390625 | (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) | |
| accuracy | 0.01953125 | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| accuracy | 0.06528561707679843 | (cos.f64 (+.f64 eps x)) | |
| accuracy | 0.43705820201513584 | #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) | |
| accuracy | 0.0234375 | (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) | |
| accuracy | 0.20834789826985745 | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) | |
| accuracy | 0.3359375 | (*.f64 #s(literal 4/3 binary64) eps) | |
| accuracy | 1.0750440035070712 | #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) | |
| accuracy | 60.62189398736709 | #s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) | |
| accuracy | 0.0 | #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) | |
| accuracy | 0.00390625 | (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) | |
| accuracy | 0.01953125 | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| accuracy | 0.06528561707679843 | (cos.f64 (+.f64 eps x)) |
| 130.0ms | 91× | 1 | valid |
| 74.0ms | 162× | 0 | valid |
| 2.0ms | 2× | 2 | valid |
| 1.0ms | 1× | 3 | valid |
Compiled 490 to 70 computations (85.7% saved)
ival-add: 51.0ms (28.6% of total)ival-mult: 40.0ms (22.5% of total)ival-div: 20.0ms (11.2% of total)ival-sin: 15.0ms (8.4% of total)const: 13.0ms (7.3% of total)adjust: 13.0ms (7.3% of total)ival-tan: 6.0ms (3.4% of total)ival-cos: 5.0ms (2.8% of total)ival-pow: 5.0ms (2.8% of total)ival-sub: 3.0ms (1.7% of total)ival-neg: 3.0ms (1.7% of total)ival-pow2: 3.0ms (1.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) |
(sin.f64 eps) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
(fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) |
(cos.f64 (+.f64 eps x)) |
(/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))))))) |
(+.f64 #s(literal 0 binary64) eps) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) |
(*.f64 #s(literal 4/3 binary64) eps) |
(+.f64 (+.f64 eps x) x) |
| Outputs |
|---|
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (* x (- (/ (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 (- (+ (* x (- (* -1 (/ (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))) (cos eps))) (+ 2/3 (+ (* -1 (/ (* (sin eps) (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))))))) (/ (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) (* x (+ (cos eps) (* -1 (cos eps))))) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (sin eps)))))))) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (+ (* -1 (sin eps)) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (+ (* -1/2 (cos eps)) (* -1/6 (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 (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ 1 (* 4/3 (pow eps 2))) |
(+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))) |
eps |
(+ eps (* x (+ 1 (* 4/3 (pow eps 2))))) |
(+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x)) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))) |
(+ (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 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))) |
(+ 1 (* 1/3 (pow eps 2))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps x))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))))) |
(+ eps (* 2 x)) |
(/ (+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) (* (cos x) (cos (+ eps x)))) |
(+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) |
(* (cos x) (cos (+ eps x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(* 4/3 (* eps x)) |
(* x (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (/ 1 x)))) |
(* 4/3 (* eps (pow x 2))) |
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (/ 1 x)))) |
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (+ (/ 1 x) (/ eps (pow x 2)))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(* eps (+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(cos (+ eps x)) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(* 2 x) |
(* x (+ 2 (/ eps x))) |
(/ (+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) (* (cos x) (cos (- eps (* -1 x))))) |
(+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(* -1 (* x (+ (* -4/3 eps) (* -1 (/ (+ 1 (* 4/3 (pow eps 2))) x))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))) x)) (* 4/3 eps))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(cos (- eps (* -1 x))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(* -1 (* x (- (* -1 (/ eps x)) 2))) |
(/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (+ (* 1/2 (/ (sin x) (cos x))) (* eps (- (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/6 (+ (* -1 (/ (* (sin x) (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (* 1/6 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3)))))))))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (pow (cos x) 2) (pow (sin x) 2))) (* (cos x) (sin x)))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x)))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x)))) |
(* 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)))) |
(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)) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (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)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
1 |
(+ 1 (* 4/3 (* eps x))) |
(+ 1 (* eps (+ (* 4/3 eps) (* 4/3 x)))) |
x |
(+ x (* eps (+ 1 (* 4/3 (pow x 2))))) |
(+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2)))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(cos x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(/ 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)))) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* 4/3 eps) |
(* 4/3 (pow eps 2)) |
(* (pow eps 2) (+ 4/3 (* 4/3 (/ x eps)))) |
(* (pow eps 2) (+ 4/3 (+ (* 4/3 (/ x eps)) (/ 1 (pow eps 2))))) |
(* 4/3 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2)))))) |
(* (pow eps 3) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* eps (+ 1 (* 2 (/ x eps)))) |
(/ (+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) (* (cos x) (cos (- x (* -1 eps))))) |
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(* (pow eps 2) (+ 4/3 (* -1 (/ (- (* -4/3 x) (/ 1 eps)) eps)))) |
(* (pow eps 2) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1) eps)) (* 4/3 x))) |
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1) eps)) (* 4/3 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps))))) |
(cos (- x (* -1 eps))) |
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps))))) |
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* -1 (* eps (- (* -2 (/ x eps)) 1))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | x | @ | inf | ((/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin eps) (* (cos (+ eps x)) (cos x)) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (cos (+ eps x)) (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps))) (/ 1 (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps)))) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (/ 1 (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps))))))) (+ 0 eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (* 4/3 eps) (+ (+ eps x) x)) |
| 6.0ms | x | @ | -inf | ((/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin eps) (* (cos (+ eps x)) (cos x)) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (cos (+ eps x)) (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps))) (/ 1 (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps)))) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (/ 1 (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps))))))) (+ 0 eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (* 4/3 eps) (+ (+ eps x) x)) |
| 5.0ms | eps | @ | -inf | ((/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin eps) (* (cos (+ eps x)) (cos x)) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (cos (+ eps x)) (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps))) (/ 1 (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps)))) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (/ 1 (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps))))))) (+ 0 eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (* 4/3 eps) (+ (+ eps x) x)) |
| 4.0ms | eps | @ | inf | ((/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin eps) (* (cos (+ eps x)) (cos x)) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (cos (+ eps x)) (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps))) (/ 1 (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps)))) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (/ 1 (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps))))))) (+ 0 eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (* 4/3 eps) (+ (+ eps x) x)) |
| 3.0ms | eps | @ | 0 | ((/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin eps) (* (cos (+ eps x)) (cos x)) (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (cos (+ eps x)) (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps))) (/ 1 (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps)))) (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (/ 1 (/ (+ (+ eps x) x) (* (+ (+ eps x) x) (+ 0 eps))))))) (+ 0 eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (* 4/3 eps) (+ (+ eps x) x)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 600 | 3604 |
| 1 | 1984 | 3149 |
| 2 | 6711 | 3092 |
| 0 | 8102 | 2938 |
| 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) (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 (- (+ (* x (- (* -1 (/ (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))) (cos eps))) (+ 2/3 (+ (* -1 (/ (* (sin eps) (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))))))) (/ (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) (* x (+ (cos eps) (* -1 (cos eps))))) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (sin eps)))))))) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (+ (* -1 (sin eps)) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (+ (* -1/2 (cos eps)) (* -1/6 (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 (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(+ 1 (* 4/3 (pow eps 2))) |
(+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))) |
eps |
(+ eps (* x (+ 1 (* 4/3 (pow eps 2))))) |
(+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x)) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))) |
(+ (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 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))) |
(+ 1 (* 1/3 (pow eps 2))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps x))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))))) |
(+ eps (* 2 x)) |
(/ (+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) (* (cos x) (cos (+ eps x)))) |
(+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) |
(* (cos x) (cos (+ eps x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(* 4/3 (* eps x)) |
(* x (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (/ 1 x)))) |
(* 4/3 (* eps (pow x 2))) |
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (/ 1 x)))) |
(* (pow x 2) (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (+ (/ 1 x) (/ eps (pow x 2)))))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(* eps (+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(cos (+ eps x)) |
(/ (sin eps) (* (cos x) (cos (+ eps x)))) |
(+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(* 2 x) |
(* x (+ 2 (/ eps x))) |
(/ (+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) (* (cos x) (cos (- eps (* -1 x))))) |
(+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))) |
(* -1 (* x (+ (* -4/3 eps) (* -1 (/ (+ 1 (* 4/3 (pow eps 2))) x))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))) x)) (* 4/3 eps))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(cos (- eps (* -1 x))) |
(/ (sin eps) (* (cos x) (cos (- eps (* -1 x))))) |
(* -1 (* x (- (* -1 (/ eps x)) 2))) |
(/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (+ (* 1/2 (/ (sin x) (cos x))) (* eps (- (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/6 (+ (* -1 (/ (* (sin x) (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (* 1/6 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3)))))))))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (pow (cos x) 2) (pow (sin x) 2))) (* (cos x) (sin x)))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x)))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x)))) |
(* 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)))) |
(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)) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin x) (cos x))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (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)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))) |
1 |
(+ 1 (* 4/3 (* eps x))) |
(+ 1 (* eps (+ (* 4/3 eps) (* 4/3 x)))) |
x |
(+ x (* eps (+ 1 (* 4/3 (pow x 2))))) |
(+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2)))))) |
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(cos x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(/ 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)))) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* 4/3 eps) |
(* 4/3 (pow eps 2)) |
(* (pow eps 2) (+ 4/3 (* 4/3 (/ x eps)))) |
(* (pow eps 2) (+ 4/3 (+ (* 4/3 (/ x eps)) (/ 1 (pow eps 2))))) |
(* 4/3 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2)))))) |
(* (pow eps 3) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* eps (+ 1 (* 2 (/ x eps)))) |
(/ (+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) (* (cos x) (cos (- x (* -1 eps))))) |
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(* (pow eps 2) (+ 4/3 (* -1 (/ (- (* -4/3 x) (/ 1 eps)) eps)))) |
(* (pow eps 2) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1) eps)) (* 4/3 x))) |
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1) eps)) (* 4/3 x))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps))))) |
(cos (- x (* -1 eps))) |
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps))))) |
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* -1 (* eps (- (* -2 (/ 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 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (/.f64 x (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (* x (- (/ (sin eps) (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 (- (+ (* x (- (* -1 (/ (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))) (cos eps))) (+ 2/3 (+ (* -1 (/ (* (sin eps) (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))))))) (/ (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 (fma.f64 (/.f64 (cos.f64 eps) (cos.f64 eps)) #s(literal 2/3 binary64) (-.f64 #s(literal -2/3 binary64) (fma.f64 (sin.f64 eps) (fma.f64 (sin.f64 eps) (/.f64 #s(literal 2/3 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (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 (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) (* x (+ (cos eps) (* -1 (cos eps))))) |
(fma.f64 #s(literal 0 binary64) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (sin eps)))))))) |
(fma.f64 (fma.f64 #s(literal 0 binary64) x #s(literal 0 binary64)) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (+ (* -1 (sin eps)) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))))))))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 0 binary64) x #s(literal 0 binary64)) x #s(literal 0 binary64)) x (sin.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 x) (fma.f64 (cos.f64 eps) x (sin.f64 eps)) (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 (* (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))) |
(+ 1 (* 4/3 (pow eps 2))) |
(fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
(+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))) |
(fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
eps |
(+ eps (* x (+ 1 (* 4/3 (pow eps 2))))) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) |
(+ eps (* x (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow eps 2)))))) |
(fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x 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 (* 1/3 (pow eps 2)))) (* (pow eps 2) x)) |
(fma.f64 (*.f64 eps x) eps (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))) |
(fma.f64 (*.f64 eps (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 eps) (neg.f64 (sin.f64 eps))) x (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) x (neg.f64 (sin.f64 eps))) x (cos.f64 eps)) |
(/ 1 eps) |
(/.f64 #s(literal 1 binary64) 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) (fma.f64 (sin.f64 eps) (fma.f64 (sin.f64 eps) (/.f64 #s(literal 2/3 binary64) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 (neg.f64 (sin.f64 eps)) (cos.f64 eps)) (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64))) (cos.f64 eps))) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (-.f64 (pow.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) #s(literal 3 binary64)) (/.f64 (neg.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))) |
(+ 1 (* 1/3 (pow eps 2))) |
(fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps x))) |
(fma.f64 eps x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) |
(+ eps (* 2 x)) |
(fma.f64 #s(literal 2 binary64) x eps) |
(/ (+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) (* (cos x) (cos (+ eps x)))) |
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x)))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) |
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x)))) |
(* (cos x) (cos (+ eps x))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (+ eps x)) (cos (+ eps x)))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* 4/3 (* eps x)) |
(*.f64 (*.f64 eps x) #s(literal 4/3 binary64)) |
(* x (+ (* 4/3 eps) (+ (* 4/3 (/ (pow eps 2) x)) (/ 1 x)))) |
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(* 4/3 (* eps (pow x 2))) |
(*.f64 (*.f64 (*.f64 #s(literal 4/3 binary64) x) x) eps) |
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(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
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(cos (+ eps x)) |
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(* 2 x) |
(*.f64 #s(literal 2 binary64) x) |
(* x (+ 2 (/ eps x))) |
(*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x) |
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(+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) |
#s(literal 0 binary64) |
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eps |
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(fma.f64 (fma.f64 #s(literal 0 binary64) eps #s(literal 1 binary64)) eps #s(literal 0 binary64)) |
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(* eps (+ 1 (* -1/6 (pow eps 2)))) |
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(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
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(pow (cos x) 2) |
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#s(literal 0 binary64) |
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1 |
#s(literal 1 binary64) |
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(+ 1 (* eps (+ (* 4/3 eps) (* 4/3 x)))) |
(fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
x |
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(fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x #s(literal 1 binary64)) eps x) |
(+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) |
(* 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))))) |
(*.f64 (fma.f64 (fma.f64 (neg.f64 (fma.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/3 binary64) (*.f64 (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 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))))) (/.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (sin.f64 x) (cos.f64 x)))) eps (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 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))))) (/.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (sin.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (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 (/ (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 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(fma.f64 (fma.f64 (fma.f64 (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 -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps) |
(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 #s(literal -1/2 binary64) (cos.f64 x)) eps) (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 eps (sin.f64 x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps (cos.f64 x)) |
(/ 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)))) |
(fma.f64 (*.f64 (sin.f64 x) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(* 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)))) |
(fma.f64 (*.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) eps (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(* 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)))) |
(fma.f64 (*.f64 (fma.f64 (fma.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sin.f64 x)) (/.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))))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (-.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) eps (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) |
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(+ 1 (+ (* eps (+ (* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 #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 -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64))))) eps (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(* 4/3 eps) |
(*.f64 #s(literal 4/3 binary64) eps) |
(* 4/3 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 4/3 binary64)) |
(* (pow eps 2) (+ 4/3 (* 4/3 (/ x eps)))) |
(*.f64 (*.f64 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) #s(literal 4/3 binary64)) eps) eps) |
(* (pow eps 2) (+ 4/3 (+ (* 4/3 (/ x eps)) (/ 1 (pow eps 2))))) |
(*.f64 (*.f64 (+.f64 (fma.f64 (/.f64 x eps) #s(literal 4/3 binary64) (/.f64 (/.f64 #s(literal 1 binary64) eps) eps)) #s(literal 4/3 binary64)) eps) eps) |
(* 4/3 (* (pow eps 2) x)) |
(*.f64 (*.f64 (*.f64 eps x) eps) #s(literal 4/3 binary64)) |
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps)))) |
(*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (+.f64 x (*.f64 x (/.f64 x eps))) (/.f64 #s(literal 1 binary64) eps)) eps) eps) |
(* (pow eps 2) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2)))))) |
(*.f64 (fma.f64 #s(literal 4/3 binary64) (+.f64 x (*.f64 x (/.f64 x eps))) (+.f64 (/.f64 (/.f64 x eps) eps) (/.f64 #s(literal 1 binary64) eps))) (*.f64 eps eps)) |
(* (pow eps 3) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (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 -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64)))))) |
(* (pow eps 3) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(*.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 -1/3 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (*.f64 (cos.f64 x) eps)) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64)))))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(*.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 -1/3 binary64) (+.f64 (+.f64 (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (*.f64 (cos.f64 x) eps)) (/.f64 (/.f64 #s(literal 1 binary64) eps) eps)) (fma.f64 (/.f64 (sin.f64 x) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) (/.f64 (sin.f64 x) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 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 4 binary64))))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(*.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 -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64))))) (*.f64 eps eps)) |
(* (pow eps 2) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(*.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 -1/3 binary64) (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (*.f64 (cos.f64 x) eps)) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64)))))) (*.f64 eps eps)) |
(* (pow eps 2) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(*.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 -1/3 binary64) (+.f64 (+.f64 (+.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (*.f64 (cos.f64 x) eps)) (/.f64 (/.f64 #s(literal 1 binary64) eps) eps)) (fma.f64 (/.f64 (sin.f64 x) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps)) (/.f64 (sin.f64 x) eps) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 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 4 binary64))))) (*.f64 eps eps)) |
(* eps (+ 1 (* 2 (/ x eps)))) |
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps) |
(/ (+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x)))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) |
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x)))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(+ (* -1 (/ (sin x) (cos x))) (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))) |
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x))) |
(* (pow eps 2) (+ 4/3 (* -1 (/ (- (* -4/3 x) (/ 1 eps)) eps)))) |
(*.f64 (-.f64 #s(literal 4/3 binary64) (/.f64 (fma.f64 #s(literal -4/3 binary64) x (/.f64 #s(literal -1 binary64) eps)) eps)) (*.f64 eps eps)) |
(* (pow eps 2) (+ (* -1 (/ (- (* -4/3 (pow x 2)) 1) eps)) (* 4/3 x))) |
(*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 (fma.f64 (*.f64 #s(literal -4/3 binary64) x) x #s(literal -1 binary64)) (neg.f64 eps))) eps) eps) |
(* (pow eps 2) (+ (* -1 (/ (- (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) 1) eps)) (* 4/3 x))) |
(*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -4/3 binary64) x) x (/.f64 (neg.f64 x) eps)) #s(literal -1 binary64) #s(literal 1 binary64)) eps)) eps) 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))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (-.f64 (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (neg.f64 (*.f64 (cos.f64 x) eps))) (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 -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (-.f64 (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) (neg.f64 eps)) (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 -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64))))))) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(/ (sin eps) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(*.f64 (-.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 -1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64))))) (/.f64 (-.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)))) eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps)) (*.f64 eps eps)) |
(* -1 (* eps (- (* -2 (/ x eps)) 1))) |
(fma.f64 (*.f64 #s(literal -2 binary64) (/.f64 x eps)) (neg.f64 eps) eps) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 73 | 481 |
| 0 | 103 | 448 |
| 1 | 512 | 310 |
| 2 | 4931 | 310 |
| 0 | 8294 | 292 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) |
(sin.f64 eps) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
(fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) |
(cos.f64 (+.f64 eps x)) |
(/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))))))) |
(+.f64 #s(literal 0 binary64) eps) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) |
(*.f64 #s(literal 4/3 binary64) eps) |
(+.f64 (+.f64 eps x) x) |
| Outputs |
|---|
(*.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (+.f64 (cos.f64 eps) (cos.f64 (fma.f64 #s(literal 2 binary64) x eps)))) #s(literal 2 binary64)) |
(*.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (pow.f64 (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 x) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 (+.f64 eps x)))) |
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 eps x))) (pow.f64 (pow.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (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 eps x))) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))) |
(*.f64 (neg.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))) (pow.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
(*.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 eps x)))) |
(pow.f64 (/.f64 (cos.f64 x) (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 (+.f64 eps x)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)))) #s(literal -1 binary64)) |
(/.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x))) |
(/.f64 (*.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) #s(literal 1 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 (neg.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 (+.f64 eps x)))) (neg.f64 (cos.f64 x))) |
(/.f64 (neg.f64 (neg.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)))) (neg.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x))))) |
(/.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x)) |
(/.f64 (neg.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 (+.f64 eps x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(neg.f64 (/.f64 (neg.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))) |
(neg.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))))) #s(literal -1 binary64))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) |
(*.f64 (*.f64 (sin.f64 eps) (fma.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x))))) (pow.f64 (fma.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x)))) #s(literal -1 binary64))) |
(*.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 3 binary64))) (pow.f64 (fma.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (fma.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x)))) (*.f64 (sin.f64 eps) (fma.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x)))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 3 binary64)))) #s(literal -1 binary64)) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64)) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x))))) |
(/.f64 (neg.f64 (*.f64 (sin.f64 eps) (fma.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x)))))) (neg.f64 (fma.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x)))))) |
(/.f64 (neg.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal 2 binary64))))) |
(/.f64 (*.f64 (sin.f64 eps) (fma.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x))))) (fma.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x))))) |
(/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) (*.f64 (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x)))))))) |
(/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x)))) (*.f64 (sin.f64 eps) (fma.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 (+.f64 eps x))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 3 binary64))))) |
(neg.f64 (sin.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal -1 binary64))))) |
(fma.f64 (sin.f64 (*.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -1 binary64)))) (cos.f64 eps) (*.f64 (cos.f64 (*.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -1 binary64)))) (sin.f64 eps))) |
(fma.f64 (sin.f64 (*.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -1 binary64)) #s(literal 0 binary64))) (cos.f64 eps) (*.f64 (cos.f64 (*.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -1 binary64)) #s(literal 0 binary64))) (sin.f64 eps))) |
(fma.f64 (*.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x)))) |
(fma.f64 #s(literal -1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x)))) |
(fma.f64 (+.f64 (sin.f64 (fma.f64 #s(literal 2 binary64) x eps)) (sin.f64 eps)) #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) |
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(fma.f64 eps #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x)) |
(fma.f64 x #s(literal 2 binary64) eps) |
(-.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 (*.f64 x x) eps)) |
(+.f64 (*.f64 #s(literal 2 binary64) x) eps) |
(+.f64 #s(literal 0 binary64) (fma.f64 #s(literal 2 binary64) x eps)) |
(+.f64 (+.f64 eps x) x) |
(+.f64 eps (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) x))) |
(+.f64 eps (*.f64 #s(literal 2 binary64) x)) |
(+.f64 x (+.f64 eps x)) |
Compiled 46 131 to 4 146 computations (91% saved)
27 alts after pruning (23 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 856 | 18 | 874 |
| Fresh | 8 | 5 | 13 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 1 | 1 |
| Total | 866 | 27 | 893 |
| Status | Accuracy | Program |
|---|---|---|
| 99.9% | (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))) | |
| 99.8% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| ▶ | 100.0% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x))) |
| ✓ | 99.9% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
| 99.2% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (+.f64 (cos.f64 eps) (cos.f64 (fma.f64 #s(literal 2 binary64) x eps))) #s(literal 1/2 binary64))) | |
| ✓ | 99.2% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
| ▶ | 99.3% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x))) |
| 98.7% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) | |
| 98.0% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (cos.f64 eps))) | |
| 59.0% | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x)) (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))))))) | |
| 90.8% | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))))) | |
| 99.3% | (/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (fma.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps) #s(literal -1/3 binary64) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))) | |
| ✓ | 62.5% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 99.2% | (*.f64 (neg.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps)) (pow.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal -1 binary64))) | |
| 90.8% | (exp.f64 (*.f64 (log.f64 (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))))) #s(literal -1 binary64))) | |
| 99.3% | #s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) | |
| 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) | |
| ▶ | 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
| 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) | |
| 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) | |
| ▶ | 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
| 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 (*.f64 eps x) eps) #s(literal 4/3 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) | |
| 98.1% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 x x) (fma.f64 #s(literal 4/3 binary64) (+.f64 eps (/.f64 (*.f64 eps eps) x)) (/.f64 #s(literal 1 binary64) x)))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) | |
| 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) | |
| 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) | |
| ▶ | 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) |
| ✓ | 5.3% | #s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
Compiled 2 601 to 1 370 computations (47.3% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) | |
| cost-diff | 0 | (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x)) | |
| cost-diff | 0 | #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) | |
| cost-diff | 0 | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x))) | |
| cost-diff | 0 | (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) | |
| cost-diff | 0 | #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) | |
| cost-diff | 3 | (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) | |
| cost-diff | 0 | (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) | |
| cost-diff | 0 | #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) | |
| cost-diff | 0 | (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps) | |
| cost-diff | 0 | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) | |
| cost-diff | 0 | (*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x)) | |
| cost-diff | 0 | (sin.f64 eps) | |
| cost-diff | 0 | #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) | |
| cost-diff | 0 | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 79 | 986 |
| 0 | 123 | 986 |
| 1 | 222 | 982 |
| 2 | 438 | 978 |
| 3 | 1192 | 978 |
| 4 | 3770 | 902 |
| 5 | 5450 | 902 |
| 0 | 8114 | 858 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) |
(sin.f64 eps) |
eps |
(*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x)) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) |
(cos.f64 x) |
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)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(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 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) |
(fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
(*.f64 eps eps) |
eps |
#s(literal 4/3 binary64) |
#s(literal 1 binary64) |
x |
(fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) |
#s(literal 1/3 binary64) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) |
#s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) |
(*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) |
(fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
(*.f64 eps (+.f64 eps x)) |
eps |
(+.f64 eps x) |
x |
#s(literal 4/3 binary64) |
#s(literal 1 binary64) |
(*.f64 eps eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) |
(pow.f64 eps #s(literal 3 binary64)) |
#s(literal 3 binary64) |
#s(literal 1/3 binary64) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) |
eps |
(*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x)) |
#s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) |
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)) |
(neg.f64 eps) |
(sin.f64 x) |
x |
(cos.f64 x) |
| Outputs |
|---|
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x))) |
(/.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 x)) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) |
(sin.f64 eps) |
eps |
(*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x)) |
(*.f64 (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 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 (neg.f64 (sin.f64 eps)) (sin.f64 x))) |
(cos.f64 x) |
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)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) |
(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 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) |
(fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) |
(fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
(fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) |
(*.f64 eps eps) |
eps |
#s(literal 4/3 binary64) |
#s(literal 1 binary64) |
x |
(fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) |
#s(literal 1/3 binary64) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) eps #s(literal 1 binary64)) (*.f64 (+.f64 eps x) eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) |
#s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))) |
#s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) eps #s(literal 1 binary64)) (*.f64 (+.f64 eps x) eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(fma.f64 (*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) eps #s(literal 1 binary64)) (*.f64 (+.f64 eps x) eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) |
(*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) eps #s(literal 1 binary64)) (*.f64 (+.f64 eps x) eps)) |
(*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) |
(*.f64 (fma.f64 (*.f64 (+.f64 eps x) eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) |
(fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
(fma.f64 (*.f64 (+.f64 eps x) eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) |
(*.f64 eps (+.f64 eps x)) |
(*.f64 (+.f64 eps x) eps) |
eps |
(+.f64 eps x) |
x |
#s(literal 4/3 binary64) |
#s(literal 1 binary64) |
(*.f64 eps eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) |
(pow.f64 eps #s(literal 3 binary64)) |
#s(literal 3 binary64) |
#s(literal 1/3 binary64) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) |
eps |
(*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x)) |
#s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) |
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)) |
(neg.f64 eps) |
(sin.f64 x) |
x |
(cos.f64 x) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x)) | |
| accuracy | 0.01953125 | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x))) | |
| accuracy | 0.43705820201513584 | #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) | |
| accuracy | 0.47037291501413686 | #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) | |
| accuracy | 0.024695031620653757 | (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) | |
| accuracy | 0.15625 | (*.f64 eps (+.f64 eps x)) | |
| accuracy | 0.20834789826985745 | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) | |
| accuracy | 1.0793044574933466 | #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))) | |
| accuracy | 0.0078125 | (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps) | |
| accuracy | 0.01953125 | (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) | |
| accuracy | 0.20834789826985745 | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) | |
| accuracy | 1.0780424750196158 | #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) | |
| accuracy | 0.0 | (*.f64 eps eps) | |
| accuracy | 0.0078125 | (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps) | |
| accuracy | 0.20834789826985745 | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) | |
| accuracy | 1.245555201181097 | #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 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 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x)) | |
| accuracy | 0.0078125 | (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) | |
| accuracy | 0.01953125 | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x))) |
| 188.0ms | 167× | 0 | valid |
| 140.0ms | 86× | 1 | valid |
| 4.0ms | 2× | 2 | valid |
| 3.0ms | 1× | 3 | valid |
Compiled 658 to 77 computations (88.3% saved)
ival-neg: 102.0ms (34.6% of total)ival-mult: 80.0ms (27.1% of total)ival-add: 29.0ms (9.8% of total)ival-div: 16.0ms (5.4% of total)adjust: 16.0ms (5.4% of total)const: 16.0ms (5.4% of total)ival-pow: 8.0ms (2.7% of total)ival-cos: 7.0ms (2.4% of total)ival-sin: 7.0ms (2.4% of total)ival-tan: 5.0ms (1.7% of total)ival-pow2: 4.0ms (1.4% of total)ival-sub: 3.0ms (1% of total)exact: 1.0ms (0.3% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) |
(sin.f64 eps) |
(*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) |
(fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) |
#s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) |
(*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x)) |
#s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) |
(*.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 eps eps) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) |
(*.f64 eps (+.f64 eps x)) |
| Outputs |
|---|
(/ (sin eps) (cos eps)) |
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2))) |
(+ (* x (- (* x (- (/ (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 (- (+ (* x (- (* -1 (/ (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))) (cos eps))) (+ 2/3 (+ (* -1 (/ (* (sin eps) (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))))))) (/ (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) (* x (+ (cos eps) (* -1 (cos eps))))) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (sin eps)))))))) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (+ (* -1 (sin eps)) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (+ (* -1/2 (cos eps)) (* -1/6 (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 (* (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 (+ 1 (* 1/3 (pow eps 2)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x)) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))) |
(+ 1 (* 1/3 (pow eps 2))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps x))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))))) |
(pow eps 2) |
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)) |
(+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)) |
(+ eps (* 1/3 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(+ (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 (* 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)))))))) |
eps |
(+ eps (* x (+ 1 (* 4/3 (pow eps 2))))) |
(+ (* eps x) (pow eps 2)) |
(/ (+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))))) |
(+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) |
(* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x)))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(* eps (+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x)))) |
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (+ (/ 1 (pow x 2)) (/ eps x)))))) |
(* 4/3 (* (pow eps 2) (pow x 2))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (+ (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x) (/ (pow eps 2) (pow x 2))))) |
(* 4/3 (* (pow eps 2) (pow x 3))) |
(* (pow x 3) (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))) |
(* (pow x 3) (+ (* 4/3 (pow eps 2)) (+ (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x) (/ (pow eps 2) (pow x 2))))) |
(* (pow x 3) (+ (* 1/3 (/ (pow eps 3) (pow x 3))) (+ (* 4/3 (pow eps 2)) (+ (/ eps (pow x 3)) (+ (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x) (/ (pow eps 2) (pow x 2))))))) |
(/ (+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) (* (cos x) (cos (+ eps x)))) |
(* (cos x) (cos (+ eps x))) |
(cos (+ eps x)) |
(* -1 (* (sin eps) (sin x))) |
(+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))) |
(* x (+ 1 (* 4/3 (pow eps 2)))) |
(* x (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x)))) |
(* eps x) |
(* x (+ eps (/ (pow eps 2) x))) |
(/ (+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))))) |
(+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1 (/ (+ 1 (* 1/3 (pow eps 2))) x))) x)) (* 4/3 (pow eps 2))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))) |
(* -1 (* (pow x 3) (+ (* -4/3 (pow eps 2)) (* -1 (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))))) |
(* -1 (* (pow x 3) (+ (* -4/3 (pow eps 2)) (* -1 (/ (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x)) x))))) |
(* -1 (* (pow x 3) (+ (* -4/3 (pow eps 2)) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x)) (* -1 (pow eps 2))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))) x))))) |
(/ (+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) (* (cos x) (cos (- eps (* -1 x))))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(cos (- eps (* -1 x))) |
(* -1 (* x (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))))) |
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x))))) |
(/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (+ (* 1/2 (/ (sin x) (cos x))) (* eps (- (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/6 (+ (* -1 (/ (* (sin x) (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (* 1/6 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3)))))))))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (pow (cos x) 2) (pow (sin x) 2))) (* (cos x) (sin x)))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x)))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x)))) |
(* 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)))) |
(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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
1 |
(+ 1 (pow x 2)) |
(+ 1 (+ (* eps x) (pow x 2))) |
(+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))) |
(* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) |
(* eps (+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (pow x 2)))) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))) (pow 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 (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) (* 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)))))))) |
x |
(+ eps x) |
(+ x (* eps (+ 1 (* 4/3 (* eps x))))) |
(* eps (+ eps x)) |
(* (pow eps 3) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* 1/3 (pow eps 2)) |
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2)))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) |
(* 4/3 (* (pow eps 3) x)) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2)))))) |
(* (pow eps 3) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps)))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps) (/ (pow x 2) (pow eps 2))))))) |
(* 4/3 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* 4/3 x) (/ 1 eps))) |
(* (pow eps 2) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2))))) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(/ (+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))))) |
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps))))) |
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (+ 1 (pow x 2)) eps))) eps)) (* 4/3 (pow x 2))))) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (* 4/3 (pow x 2))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps))) eps))))) |
(* -1 (* (pow eps 3) (- (* -4/3 (pow x 2)) 1/3))) |
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps))) 1/3))) |
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ (* -1 (/ (- (* -1 (pow x 2)) 1) eps)) (* x (+ 1 (* 4/3 (pow x 2))))) eps))) 1/3))) |
(/ (+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) (* (cos x) (cos (- x (* -1 eps))))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(cos (- x (* -1 eps))) |
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 22.0ms | eps | @ | -inf | ((/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin eps) (* (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (cos x)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (+ (* (* (+ (* (* eps (+ eps x)) 4/3) 1) eps) x) (* eps eps)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (+ (* (* (+ (* (* eps (+ eps x)) 4/3) 1) eps) x) (* eps eps)) x) (+ (* (pow eps 3) 1/3) eps)) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* eps eps) (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (* eps (+ eps x))) |
| 14.0ms | x | @ | inf | ((/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin eps) (* (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (cos x)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (+ (* (* (+ (* (* eps (+ eps x)) 4/3) 1) eps) x) (* eps eps)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (+ (* (* (+ (* (* eps (+ eps x)) 4/3) 1) eps) x) (* eps eps)) x) (+ (* (pow eps 3) 1/3) eps)) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* eps eps) (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (* eps (+ eps x))) |
| 10.0ms | x | @ | -inf | ((/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin eps) (* (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (cos x)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (+ (* (* (+ (* (* eps (+ eps x)) 4/3) 1) eps) x) (* eps eps)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (+ (* (* (+ (* (* eps (+ eps x)) 4/3) 1) eps) x) (* eps eps)) x) (+ (* (pow eps 3) 1/3) eps)) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* eps eps) (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (* eps (+ eps x))) |
| 7.0ms | eps | @ | inf | ((/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin eps) (* (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (cos x)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (+ (* (* (+ (* (* eps (+ eps x)) 4/3) 1) eps) x) (* eps eps)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (+ (* (* (+ (* (* eps (+ eps x)) 4/3) 1) eps) x) (* eps eps)) x) (+ (* (pow eps 3) 1/3) eps)) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* eps eps) (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (* eps (+ eps x))) |
| 4.0ms | eps | @ | 0 | ((/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin eps) (* (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (cos x)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (* eps eps) 1/3) 1) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (+ (* (* (+ (* (* eps (+ eps x)) 4/3) 1) eps) x) (* eps eps)) (- (tan (+ x eps)) (tan x)) (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (+ (* (+ (* (* (+ (* (* eps (+ eps x)) 4/3) 1) eps) x) (* eps eps)) x) (+ (* (pow eps 3) 1/3) eps)) (/ (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x))) (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (* (neg (sin eps)) (sin x)) (+ (* (cos x) (cos eps)) (* (neg (sin eps)) (sin x))) (* eps eps) (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (* eps (+ eps x))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 714 | 4132 |
| 1 | 2433 | 3678 |
| 0 | 8473 | 3445 |
| 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) (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 (- (+ (* x (- (* -1 (/ (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))) (cos eps))) (+ 2/3 (+ (* -1 (/ (* (sin eps) (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))))))) (/ (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) (* x (+ (cos eps) (* -1 (cos eps))))) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (sin eps)))))))) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (+ (* -1 (sin eps)) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (+ (* -1/2 (cos eps)) (* -1/6 (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 (* (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 (+ 1 (* 1/3 (pow eps 2)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x)) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))) |
(+ 1 (* 1/3 (pow eps 2))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps x))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))))))))) |
(pow eps 2) |
(+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)) |
(+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)) |
(+ eps (* 1/3 (pow eps 3))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* (pow eps 2) x))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2))))) |
(+ eps (+ (* 1/3 (pow eps 3)) (* x (+ (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2))))) |
(+ (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 (* 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)))))))) |
eps |
(+ eps (* x (+ 1 (* 4/3 (pow eps 2))))) |
(+ (* eps x) (pow eps 2)) |
(/ (+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))))) |
(+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) |
(* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x)))) |
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x))) |
(* eps (+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) |
(+ (* (+ 1 (/ (* eps (sin x)) (cos x))) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))))) |
(* (pow x 2) (+ 1 (* 4/3 (pow eps 2)))) |
(* (pow x 2) (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x)))) |
(* (pow x 2) (+ 1 (+ (* 1/3 (/ (pow eps 2) (pow x 2))) (+ (* 4/3 (pow eps 2)) (+ (/ 1 (pow x 2)) (/ eps x)))))) |
(* 4/3 (* (pow eps 2) (pow x 2))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))) |
(* (pow x 2) (+ (* 4/3 (pow eps 2)) (+ (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x) (/ (pow eps 2) (pow x 2))))) |
(* 4/3 (* (pow eps 2) (pow x 3))) |
(* (pow x 3) (+ (* 4/3 (pow eps 2)) (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))) |
(* (pow x 3) (+ (* 4/3 (pow eps 2)) (+ (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x) (/ (pow eps 2) (pow x 2))))) |
(* (pow x 3) (+ (* 1/3 (/ (pow eps 3) (pow x 3))) (+ (* 4/3 (pow eps 2)) (+ (/ eps (pow x 3)) (+ (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x) (/ (pow eps 2) (pow x 2))))))) |
(/ (+ (* -1 (* (cos (+ eps x)) (sin x))) (* (cos x) (sin (+ eps x)))) (* (cos x) (cos (+ eps x)))) |
(* (cos x) (cos (+ eps x))) |
(cos (+ eps x)) |
(* -1 (* (sin eps) (sin x))) |
(+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))) |
(* x (+ 1 (* 4/3 (pow eps 2)))) |
(* x (+ 1 (+ (* 4/3 (pow eps 2)) (/ eps x)))) |
(* eps x) |
(* x (+ eps (/ (pow eps 2) x))) |
(/ (+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))))) |
(+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) |
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x))) |
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ (* -1 eps) (* -1 (/ (+ 1 (* 1/3 (pow eps 2))) x))) x)) (* 4/3 (pow eps 2))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* eps (+ 1 (* 4/3 (pow eps 2))))) (* -1 (/ (pow eps 2) x))) x)) (* 4/3 (pow eps 2)))) |
(* -1 (* (pow x 3) (+ (* -4/3 (pow eps 2)) (* -1 (/ (* eps (+ 1 (* 4/3 (pow eps 2)))) x))))) |
(* -1 (* (pow x 3) (+ (* -4/3 (pow eps 2)) (* -1 (/ (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (/ (pow eps 2) x)) x))))) |
(* -1 (* (pow x 3) (+ (* -4/3 (pow eps 2)) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/3 (pow eps 3))) x)) (* -1 (pow eps 2))) x)) (* eps (+ 1 (* 4/3 (pow eps 2))))) x))))) |
(/ (+ (* -1 (* (cos (- eps (* -1 x))) (sin x))) (* (cos x) (sin (- eps (* -1 x))))) (* (cos x) (cos (- eps (* -1 x))))) |
(* (cos x) (cos (- eps (* -1 x)))) |
(cos (- eps (* -1 x))) |
(* -1 (* x (+ (* -1 (+ 1 (* 4/3 (pow eps 2)))) (* -1 (/ eps x))))) |
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x))))) |
(/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (/ (sin x) (cos x))) (+ (* eps (- (+ 1 (+ (* eps (- (+ (* -1/2 (/ (sin x) (cos x))) (+ (* 1/2 (/ (sin x) (cos x))) (* eps (- (* -1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/6 (+ (* -1 (/ (* (sin x) (- (+ (* -1/2 (/ (sin x) (cos x))) (* 1/2 (/ (sin x) (cos x)))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (* 1/6 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3)))))))))) (+ (* -1 (/ (* (sin x) (- (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (cos x))) (* -1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) (pow (cos x) 2)))))) (/ (pow (sin x) 2) (pow (cos x) 2)))) (* -1 (/ (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x)))) (pow (cos x) 3))))) (/ (sin x) (cos x)))) |
(+ (* -1 (* (cos x) (sin x))) (* (cos x) (sin x))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (pow (cos x) 2) (pow (sin x) 2))) (* (cos x) (sin x)))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (* 1/2 (* (cos x) (sin x))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x)))) |
(+ (* -1 (* (cos x) (sin x))) (+ (* eps (+ (* eps (+ (* -1/2 (* (cos x) (sin x))) (+ (* 1/2 (* (cos x) (sin x))) (* eps (+ (* -1/6 (pow (cos x) 2)) (* -1/6 (pow (sin x) 2))))))) (+ (pow (cos x) 2) (pow (sin x) 2)))) (* (cos x) (sin x)))) |
(* 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)))) |
(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 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(* eps (+ 1 (+ (* eps (+ (* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
(+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
(+ 1 (+ (* eps (+ (* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))) |
1 |
(+ 1 (pow x 2)) |
(+ 1 (+ (* eps x) (pow x 2))) |
(+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))) |
(* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) |
(* eps (+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))) |
(* eps (+ 1 (pow x 2))) |
(* eps (+ 1 (+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (pow x 2)))) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))) (pow 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 (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) (* 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)))))))) |
x |
(+ eps x) |
(+ x (* eps (+ 1 (* 4/3 (* eps x))))) |
(* eps (+ eps x)) |
(* (pow eps 3) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 3) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* 1/3 (pow eps 2)) |
(* (pow eps 2) (+ 1/3 (/ 1 (pow eps 2)))) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) |
(* 4/3 (* (pow eps 3) x)) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2)))))) |
(* (pow eps 3) (+ 1/3 (* 4/3 (pow x 2)))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps)))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps) (/ (pow x 2) (pow eps 2))))))) |
(* 4/3 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* 4/3 x) (/ 1 eps))) |
(* (pow eps 2) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2))))) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(/ (+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))))) |
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) |
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps))))) |
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (+ 1 (pow x 2)) eps))) eps)) (* 4/3 (pow x 2))))) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (* 4/3 (pow x 2))) eps))))) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps))) eps))))) |
(* -1 (* (pow eps 3) (- (* -4/3 (pow x 2)) 1/3))) |
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps))) 1/3))) |
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ (* -1 (/ (- (* -1 (pow x 2)) 1) eps)) (* x (+ 1 (* 4/3 (pow x 2))))) eps))) 1/3))) |
(/ (+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) (* (cos x) (cos (- x (* -1 eps))))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(cos (- x (* -1 eps))) |
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x))) |
| 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 (- (* x (- (/ (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 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (* x (- (+ (* x (- (* -1 (/ (+ (* -1/2 (cos eps)) (* -1/6 (cos eps))) (cos eps))) (+ 2/3 (+ (* -1 (/ (* (sin eps) (- (/ (sin eps) (cos eps)) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2))))))) (/ (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 (-.f64 (-.f64 (/.f64 (*.f64 (cos.f64 eps) #s(literal 2/3 binary64)) (cos.f64 eps)) #s(literal 2/3 binary64)) (fma.f64 #s(literal -1 binary64) (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (/.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)))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 2/3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) x (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (+ (cos eps) (* -1 (cos eps))))) |
(fma.f64 #s(literal 0 binary64) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (* -1 (sin eps)))))))) |
(fma.f64 (fma.f64 #s(literal 0 binary64) x #s(literal 0 binary64)) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (+ (* -1 (cos eps)) (* x (+ (sin eps) (+ (* -1 (sin eps)) (* x (+ (* -1 (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))) (+ (* -1/2 (cos eps)) (* -1/6 (cos eps)))))))))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 0 binary64) x #s(literal 0 binary64)) x #s(literal 0 binary64)) x (sin.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 x) (fma.f64 (cos.f64 eps) x (sin.f64 eps)) (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 (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (/.f64 x (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (/.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (+.f64 (fma.f64 (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))) (*.f64 (fma.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) (cos.f64 eps)))) x (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) x (/.f64 (sin.f64 eps) (cos.f64 eps))) |
(* eps (+ 1 (* 1/3 (pow eps 2)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) x)) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) (fma.f64 (*.f64 eps x) eps eps)) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (pow eps 2)))) |
(fma.f64 (*.f64 eps (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (* x (- (+ eps (* -1/6 eps)) (* -1/2 eps)))) (* eps (+ 1 (* 4/3 (pow eps 2)))))) (pow eps 2)))) |
(fma.f64 (fma.f64 (*.f64 eps (fma.f64 (*.f64 eps x) #s(literal 4/3 binary64) (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(+ 1 (* 1/3 (pow eps 2))) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* eps x))) |
(fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ eps (* x (+ 1 (* 4/3 (pow eps 2)))))))) |
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#s(literal 0 binary64) |
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(pow (cos x) 2) |
(pow.f64 (cos.f64 x) #s(literal 2 binary64)) |
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(* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) |
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(* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(* eps (+ 1 (+ (* eps (+ (* eps (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2))))) |
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(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) |
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1 |
#s(literal 1 binary64) |
(+ 1 (pow x 2)) |
(fma.f64 x x #s(literal 1 binary64)) |
(+ 1 (+ (* eps x) (pow x 2))) |
(fma.f64 x (+.f64 eps x) #s(literal 1 binary64)) |
(+ 1 (+ (* eps (+ x (* eps (+ 1/3 (* 4/3 (pow x 2)))))) (pow x 2))) |
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(* eps (+ x (* eps (+ 1 (* 4/3 (pow x 2)))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps x) eps) |
(* eps (+ x (* eps (+ 1 (+ (* 4/3 (* eps x)) (* 4/3 (pow x 2))))))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64)) eps x) eps) |
(* eps (+ 1 (pow x 2))) |
(*.f64 (fma.f64 x x #s(literal 1 binary64)) eps) |
(* eps (+ 1 (+ (* eps (* x (+ 1 (* 4/3 (pow x 2))))) (pow x 2)))) |
(*.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 4/3 binary64) x) eps (fma.f64 x x #s(literal 1 binary64))) eps) |
(* eps (+ 1 (+ (* eps (+ (* eps (+ 1/3 (* 4/3 (pow x 2)))) (* x (+ 1 (* 4/3 (pow x 2)))))) (pow x 2)))) |
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(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(fma.f64 (neg.f64 (sin.f64 x)) eps (cos.f64 x)) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (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 (sin x))) |
(*.f64 (neg.f64 (sin.f64 x)) eps) |
(* eps (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))) |
(*.f64 (*.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))) eps) |
(* eps (+ (* -1 (sin x)) (* (pow eps 2) (+ (* -1/120 (* (pow eps 2) (sin x))) (* 1/6 (sin x)))))) |
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(* 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))))))))) |
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(+ (cos x) (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps (cos.f64 x)) |
(+ (cos x) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps (cos.f64 x)) |
x |
(+ eps x) |
(+.f64 eps x) |
(+ x (* eps (+ 1 (* 4/3 (* eps x))))) |
(fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) |
(* eps (+ eps x)) |
(*.f64 (+.f64 eps x) eps) |
(* (pow eps 3) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64))))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64)))))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 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) #s(literal -1/3 binary64))) (*.f64 eps eps))) eps) |
(* (pow eps 2) (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64))))) (*.f64 eps eps)) |
(* (pow eps 2) (- (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64)))))) (*.f64 eps eps)) |
(* (pow eps 2) (- (+ (/ 1 (pow eps 2)) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))) (+ (/ (pow (sin x) 2) (* (pow eps 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(+.f64 #s(literal 1 binary64) (*.f64 (-.f64 (fma.f64 (/.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 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) #s(literal -1/3 binary64))) (*.f64 eps 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)) |
(* (pow eps 2) (+ 1/3 (* 4/3 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps) eps) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ x eps)))) |
(*.f64 (*.f64 (+.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) (/.f64 x eps)) #s(literal 1/3 binary64)) eps) eps) |
(* (pow eps 2) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) |
(*.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) (fma.f64 (/.f64 x eps) (/.f64 x eps) (/.f64 x eps))) (*.f64 eps eps)) |
(* 4/3 (* (pow eps 3) x)) |
(*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 4/3 binary64)) x) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (/ 1 eps)))) |
(*.f64 (fma.f64 #s(literal 4/3 binary64) (+.f64 x (*.f64 x (/.f64 x eps))) (/.f64 #s(literal 1 binary64) eps)) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (+ (* 4/3 x) (+ (* 4/3 (/ (pow x 2) eps)) (+ (/ 1 eps) (/ x (pow eps 2)))))) |
(*.f64 (fma.f64 #s(literal 4/3 binary64) (+.f64 x (*.f64 x (/.f64 x eps))) (+.f64 (/.f64 (/.f64 x eps) eps) (/.f64 #s(literal 1 binary64) eps))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (+ 1/3 (* 4/3 (pow x 2)))) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps)))) |
(*.f64 (+.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 4/3 binary64) x) eps)) #s(literal 1/3 binary64)) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (+ 1/3 (+ (* 4/3 (pow x 2)) (+ (/ 1 (pow eps 2)) (+ (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps) (/ (pow x 2) (pow eps 2))))))) |
(*.f64 (+.f64 (+.f64 #s(literal 1/3 binary64) (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) (fma.f64 x (/.f64 (/.f64 x eps) eps) (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 4/3 binary64) x) eps))) (pow.f64 eps #s(literal 3 binary64))) |
(* 4/3 (* (pow eps 2) x)) |
(*.f64 (*.f64 (*.f64 eps #s(literal 4/3 binary64)) x) eps) |
(* (pow eps 2) (+ (* 4/3 x) (/ 1 eps))) |
(*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps) eps) |
(* (pow eps 2) (+ (* 4/3 x) (+ (/ 1 eps) (/ x (pow eps 2))))) |
(*.f64 (+.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 (/.f64 x eps) eps)) (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps eps)) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(*.f64 (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps) eps) |
(/ (+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) (* (cos x) (+ (* -1 (* (sin eps) (sin x))) (* (cos eps) (cos x))))) |
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x)))) (*.f64 (fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x))) |
(+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) |
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (cos.f64 x) (sin.f64 (+.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))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) eps)) (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64)))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (- (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (+ (/ 1 eps) (+ (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))) eps))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (-.f64 (/.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (sin.f64 x) eps) (/.f64 #s(literal 1 binary64) eps))) (neg.f64 eps)) (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/3 binary64) (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64))))))) |
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps))) eps)) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) |
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/3 binary64) (-.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (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 4 binary64)))) (/.f64 (neg.f64 (fma.f64 (fma.f64 (sin.f64 x) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sin.f64 x) (cos.f64 x)) (/.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))) (*.f64 eps eps)) |
(* (pow eps 2) (+ 1/3 (+ (* -1 (/ (+ (* -1 x) (* -1 (/ (+ 1 (pow x 2)) eps))) eps)) (* 4/3 (pow x 2))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) x) x (-.f64 #s(literal 1/3 binary64) (/.f64 (neg.f64 (+.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) eps) x)) eps))) (*.f64 eps eps)) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (* 4/3 (pow x 2))) eps))))) |
(*.f64 (neg.f64 (fma.f64 #s(literal -4/3 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1 binary64)) (neg.f64 eps)))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (+ (* -4/3 x) (* -1 (/ (+ 1 (+ (* 4/3 (pow x 2)) (/ x eps))) eps))))) |
(*.f64 (neg.f64 (fma.f64 #s(literal -4/3 binary64) x (/.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) (/.f64 x eps)) #s(literal -1 binary64) #s(literal -1 binary64)) eps))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (- (* -4/3 (pow x 2)) 1/3))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 #s(literal -4/3 binary64) x) x #s(literal -1/3 binary64))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ (* x (+ 1 (* 4/3 (pow x 2)))) eps))) 1/3))) |
(*.f64 (neg.f64 (fma.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 4/3 binary64) x) eps) #s(literal -1 binary64) (fma.f64 (*.f64 #s(literal -4/3 binary64) x) x #s(literal -1/3 binary64)))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (- (+ (* -4/3 (pow x 2)) (* -1 (/ (+ (* -1 (/ (- (* -1 (pow x 2)) 1) eps)) (* x (+ 1 (* 4/3 (pow x 2))))) eps))) 1/3))) |
(*.f64 (neg.f64 (fma.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 4/3 binary64) x) (/.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64)) eps)) eps) #s(literal -1 binary64) (fma.f64 (*.f64 #s(literal -4/3 binary64) x) x #s(literal -1/3 binary64)))) (pow.f64 eps #s(literal 3 binary64))) |
(/ (+ (* -1 (* (cos (- x (* -1 eps))) (sin x))) (* (cos x) (sin (- x (* -1 eps))))) (* (cos x) (cos (- x (* -1 eps))))) |
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (cos.f64 x) (sin.f64 (+.f64 eps x)))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(* (cos x) (cos (- x (* -1 eps)))) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(* (pow eps 2) (+ (* -1 (/ (- (* -1 (/ x eps)) 1) eps)) (* 4/3 x))) |
(*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 (fma.f64 (/.f64 (neg.f64 x) eps) #s(literal -1 binary64) #s(literal 1 binary64)) eps)) eps) eps) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 79 | 898 |
| 0 | 123 | 874 |
| 1 | 539 | 701 |
| 2 | 4389 | 685 |
| 0 | 9122 | 661 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) |
(sin.f64 eps) |
(*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) |
(fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)))) |
#s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) eps)) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) |
(*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x)) |
#s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) |
(*.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 eps eps) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) |
(*.f64 eps (+.f64 eps x)) |
| Outputs |
|---|
(*.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal -1 binary64)) (pow.f64 (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 x) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 (+.f64 eps x)))) |
(*.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 eps x))) (pow.f64 (pow.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (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 eps x))) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))) |
(*.f64 (neg.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))) (pow.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
(*.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (/.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (cos.f64 (+.f64 eps x)))) |
(pow.f64 (/.f64 (cos.f64 x) (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 (+.f64 eps x)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)))) #s(literal -1 binary64)) |
(/.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 x)) (cos.f64 (+.f64 eps x))) |
(/.f64 (*.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) #s(literal 1 binary64)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/.f64 (neg.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 (+.f64 eps x)))) (neg.f64 (cos.f64 x))) |
(/.f64 (neg.f64 (neg.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)))) (neg.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x))))) |
(/.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 (+.f64 eps x))) (cos.f64 x)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)))))) |
(/.f64 (neg.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (cos.f64 (+.f64 eps x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(neg.f64 (/.f64 (neg.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))) (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))) |
(neg.f64 (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))))) #s(literal -1 binary64))) |
#s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) |
(sin.f64 eps) |
(*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) |
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(/.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 (+.f64 eps x) x)) (cos.f64 (+.f64 eps #s(literal 0 binary64)))) #s(literal 2 binary64)) |
(/.f64 (*.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 eps x))) (cos.f64 x)) (cos.f64 (-.f64 eps x))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64))) (cos.f64 x)) (fma.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (-.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)))) |
(/.f64 (*.f64 (cos.f64 x) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 eps x)))) (cos.f64 (-.f64 eps x))) |
(/.f64 (*.f64 (cos.f64 x) (+.f64 (pow.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (-.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x) (*.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x))) |
(fma.f64 (cos.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) |
(fma.f64 (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (*.f64 (cos.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x)))) |
(+.f64 (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x)) (*.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x))) |
(+.f64 (*.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x))) |
(+.f64 (*.f64 (cos.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) |
(+.f64 (*.f64 (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (*.f64 (cos.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps) |
(*.f64 eps #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) |
#s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) |
(*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (fma.f64 #s(literal 1/27 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.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(literal -1 binary64))) |
(pow.f64 (/.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.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)))) (fma.f64 #s(literal 1/27 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1 binary64))) #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 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 1/27 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.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 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64))) |
(/.f64 (fma.f64 #s(literal 1/27 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))) |
(/.f64 (fma.f64 #s(literal 1/27 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.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 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64)) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.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)))) (fma.f64 #s(literal 1/27 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1 binary64)))) |
(fma.f64 (*.f64 #s(literal 1/3 binary64) eps) (*.f64 eps #s(literal 1 binary64)) #s(literal 1 binary64)) |
(fma.f64 (*.f64 #s(literal 1/3 binary64) eps) eps #s(literal 1 binary64)) |
(fma.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) #s(literal 1 binary64) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) |
(fma.f64 eps (*.f64 (*.f64 #s(literal 1/3 binary64) eps) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(fma.f64 eps (*.f64 #s(literal 1/3 binary64) eps) #s(literal 1 binary64)) |
(-.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 eps #s(literal 4 binary64))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(+.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps) |
(*.f64 eps #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))))) |
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(pow.f64 (/.f64 (fma.f64 eps (-.f64 eps (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1 binary64)) |
(/.f64 (-.f64 (*.f64 eps eps) (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 2 binary64))) (-.f64 eps (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 2 binary64)) (*.f64 eps eps))) (neg.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (neg.f64 eps)))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 2 binary64)) (*.f64 eps eps)) (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (neg.f64 eps))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) eps)))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (neg.f64 eps)) (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 2 binary64)) (*.f64 eps eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (-.f64 eps (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))) |
(fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) |
(fma.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps) |
(-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (neg.f64 eps))) (/.f64 (*.f64 eps eps) (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x (neg.f64 eps)))) |
(+.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) eps) |
(+.f64 eps (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) |
(*.f64 (+.f64 eps x) eps) |
(*.f64 eps (+.f64 eps x)) |
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) eps) (-.f64 x eps)) |
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) eps) (-.f64 eps x)) |
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) eps) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) |
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) eps) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) |
(/.f64 (*.f64 eps (*.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 x eps)) |
(/.f64 (*.f64 eps (*.f64 (+.f64 eps x) (-.f64 eps x))) (-.f64 eps x)) |
(/.f64 (*.f64 eps (+.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 eps (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) |
(/.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (*.f64 eps x) #s(literal 2 binary64))) (*.f64 eps (-.f64 eps x))) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (pow.f64 (*.f64 eps x) #s(literal 2 binary64)) (*.f64 (*.f64 eps eps) (*.f64 eps x))))) |
(fma.f64 eps eps (*.f64 eps x)) |
(fma.f64 eps x (*.f64 eps eps)) |
(fma.f64 x eps (*.f64 eps eps)) |
(+.f64 (*.f64 eps x) (*.f64 eps eps)) |
(+.f64 (*.f64 eps eps) (*.f64 eps x)) |
Compiled 34 973 to 2 141 computations (93.9% saved)
29 alts after pruning (23 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 418 | 12 | 430 |
| Fresh | 7 | 11 | 18 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 4 | 4 |
| Total | 428 | 29 | 457 |
| Status | Accuracy | Program |
|---|---|---|
| 99.9% | (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))) | |
| 99.9% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x))) | |
| 99.8% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) | |
| 100.0% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (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))) (cos.f64 x))) | |
| ✓ | 99.9% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
| 99.2% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (+.f64 (cos.f64 eps) (cos.f64 (fma.f64 #s(literal 2 binary64) x eps))) #s(literal 1/2 binary64))) | |
| ✓ | 99.2% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
| ✓ | 99.3% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 x))) |
| 98.7% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) | |
| 98.0% | (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (cos.f64 eps))) | |
| 90.8% | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))))) | |
| ✓ | 62.5% | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 99.3% | (*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))))) | |
| 99.2% | (*.f64 (neg.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps)) (pow.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal -1 binary64))) | |
| 90.8% | (exp.f64 (*.f64 (log.f64 (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))))) #s(literal -1 binary64))) | |
| 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) | |
| 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) | |
| ✓ | 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
| 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) | |
| 98.1% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) | |
| 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (*.f64 (*.f64 eps #s(literal 4/3 binary64)) x) eps)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) | |
| 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) | |
| 98.1% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) | |
| 98.1% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) | |
| 6.5% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) x))) eps)) | |
| 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) | |
| 98.0% | #s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) | |
| 98.3% | #s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) (+.f64 eps (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x))))) | |
| ✓ | 5.3% | #s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
Compiled 4 740 to 1 283 computations (72.9% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 (*.f64 eps x) eps) #s(literal 4/3 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (*.f64 (*.f64 eps #s(literal 4/3 binary64)) x) eps)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) (+.f64 eps (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 x x) (fma.f64 #s(literal 4/3 binary64) (+.f64 eps (/.f64 (*.f64 eps eps) x)) (/.f64 #s(literal 1 binary64) x)))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) 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 (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (+.f64 (cos.f64 eps) (cos.f64 (fma.f64 #s(literal 2 binary64) x eps))) #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(-.f64 (tan.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))) (tan.f64 x)) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(*.f64 (neg.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps)) (pow.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal -1 binary64))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos 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))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 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 x)) (cos.f64 (+.f64 eps x))) |
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps 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 (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 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))))) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (neg.f64 (*.f64 (cos.f64 x) eps)) (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))))) #s(literal -1 binary64))) |
(-.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 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (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))) (cos.f64 x))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x))) |
(/.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 (+.f64 eps x)) (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (*.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x) #s(literal 1 binary64)) (+.f64 (/.f64 (*.f64 (sin.f64 x) eps) (cos.f64 x)) #s(literal 1 binary64))) eps)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (fma.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps) #s(literal -1/3 binary64) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (cos.f64 x)) (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))))))) |
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (/.f64 eps (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps eps)) |
(/.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))) (+.f64 (tan.f64 x) (tan.f64 (+.f64 eps x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (fma.f64 eps (tan.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (fma.f64 (tan.f64 x) (tan.f64 x) #s(literal 1 binary64)) (*.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))))))) eps)) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 x) (*.f64 (fma.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/24 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/18 binary64) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal 1/120 binary64)))) (*.f64 eps eps) (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) eps)) eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))) |
#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)) |
| Outputs |
|---|
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (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))) (cos.f64 x))) |
3 calls:
| 59.0ms | eps |
| 42.0ms | x |
| 19.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 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 (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 (*.f64 eps x) eps) #s(literal 4/3 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (*.f64 (*.f64 eps #s(literal 4/3 binary64)) x) eps)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) (+.f64 eps (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 x x) (fma.f64 #s(literal 4/3 binary64) (+.f64 eps (/.f64 (*.f64 eps eps) x)) (/.f64 #s(literal 1 binary64) x)))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) 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 (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (+.f64 (cos.f64 eps) (cos.f64 (fma.f64 #s(literal 2 binary64) x eps))) #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(-.f64 (tan.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))) (tan.f64 x)) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(*.f64 (neg.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps)) (pow.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal -1 binary64))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos 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))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))) (cos.f64 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 x)) (cos.f64 (+.f64 eps x))) |
(/.f64 (/.f64 (sin.f64 (+.f64 #s(literal 0 binary64) eps)) (cos.f64 x)) (cos.f64 (+.f64 eps 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 (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 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (-.f64 (+.f64 eps x) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 eps x) x) (*.f64 (+.f64 (+.f64 eps x) x) (+.f64 #s(literal 0 binary64) eps))))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps eps)) |
(*.f64 (pow.f64 (cos.f64 x) #s(literal -1 binary64)) (/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (cos (+ eps x)) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))))) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x))) (/.f64 (fma.f64 (neg.f64 (*.f64 (cos.f64 x) eps)) (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps))))) #s(literal -1 binary64))) |
(-.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 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 (exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))))) |
| Outputs |
|---|
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
3 calls:
| 16.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 15.0ms | x |
| 13.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
| 99.9% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 (*.f64 eps x) eps) #s(literal 4/3 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (*.f64 (*.f64 eps #s(literal 4/3 binary64)) x) eps)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) (+.f64 eps (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 x x) (fma.f64 #s(literal 4/3 binary64) (+.f64 eps (/.f64 (*.f64 eps eps) x)) (/.f64 #s(literal 1 binary64) x)))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) 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 (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (+.f64 (cos.f64 eps) (cos.f64 (fma.f64 #s(literal 2 binary64) x eps))) #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(-.f64 (tan.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))) (tan.f64 x)) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(*.f64 (neg.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps)) (pow.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x))) #s(literal -1 binary64))) |
| Outputs |
|---|
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
3 calls:
| 14.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 9.0ms | x |
| 9.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
| 99.8% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 (*.f64 eps x) eps) #s(literal 4/3 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (*.f64 (*.f64 eps #s(literal 4/3 binary64)) x) eps)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) (+.f64 eps (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 x x) (fma.f64 #s(literal 4/3 binary64) (+.f64 eps (/.f64 (*.f64 eps eps) x)) (/.f64 #s(literal 1 binary64) x)))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) 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 (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (+.f64 (cos.f64 eps) (cos.f64 (fma.f64 #s(literal 2 binary64) x eps))) #s(literal 1/2 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))) |
(-.f64 (tan.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))) (tan.f64 x)) |
| Outputs |
|---|
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
3 calls:
| 11.0ms | x |
| 10.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 9.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.2% | 1 | x |
| 99.2% | 1 | eps |
| 99.2% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 (*.f64 eps x) eps) #s(literal 4/3 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (*.f64 (*.f64 eps #s(literal 4/3 binary64)) x) eps)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) (+.f64 eps (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 x x) (fma.f64 #s(literal 4/3 binary64) (+.f64 eps (/.f64 (*.f64 eps eps) x)) (/.f64 #s(literal 1 binary64) x)))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) 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 (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
| Outputs |
|---|
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
3 calls:
| 8.0ms | eps |
| 8.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 8.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.7% | 1 | x |
| 98.7% | 1 | eps |
| 98.7% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 (*.f64 eps x) eps) #s(literal 4/3 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (*.f64 (*.f64 eps #s(literal 4/3 binary64)) x) eps)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) (+.f64 eps (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 x x) (fma.f64 #s(literal 4/3 binary64) (+.f64 eps (/.f64 (*.f64 eps eps) x)) (/.f64 #s(literal 1 binary64) x)))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps)) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) #s(approx (* (cos (+ eps x)) (cos x)) (cos.f64 eps))) |
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/3 binary64) 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 x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) (+.f64 eps (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x))))) |
3 calls:
| 9.0ms | eps |
| 7.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 7.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.3% | 1 | x |
| 98.3% | 1 | eps |
| 98.3% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 (*.f64 eps x) eps) #s(literal 4/3 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (*.f64 (*.f64 eps #s(literal 4/3 binary64)) x) eps)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) eps (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
3 calls:
| 5.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 5.0ms | eps |
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.3% | 1 | x |
| 98.3% | 1 | eps |
| 98.3% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 (*.f64 eps x) eps) #s(literal 4/3 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (*.f64 (*.f64 eps #s(literal 4/3 binary64)) x) eps)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
3 calls:
| 6.0ms | x |
| 5.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 5.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.3% | 1 | eps |
| 98.3% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 98.3% | 1 | x |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) x) eps) (*.f64 (*.f64 (*.f64 eps x) eps) #s(literal 4/3 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (*.f64 (*.f64 eps #s(literal 4/3 binary64)) x) eps)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
3 calls:
| 4.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 4.0ms | eps |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.3% | 1 | x |
| 98.3% | 1 | eps |
| 98.3% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (*.f64 (*.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) x) x))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) #s(literal 1 binary64)) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
3 calls:
| 3.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 3.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.3% | 1 | x |
| 98.3% | 1 | eps |
| 98.3% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 eps x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
3 calls:
| 2.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 2.0ms | x |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.1% | 1 | x |
| 98.1% | 1 | eps |
| 98.1% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
3 calls:
| 2.0ms | x |
| 2.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.1% | 1 | x |
| 98.1% | 1 | eps |
| 98.1% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
| Outputs |
|---|
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #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 |
|---|---|---|
| 98.0% | 1 | x |
| 98.0% | 1 | eps |
| 98.0% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
| Outputs |
|---|
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
3 calls:
| 1.0ms | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
| 1.0ms | eps |
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 5.3% | 1 | x |
| 5.3% | 1 | eps |
| 5.3% | 1 | (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| 1× | egg-herbie |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 156 | 955 |
| 1 | 244 | 943 |
| 2 | 438 | 938 |
| 3 | 1169 | 938 |
| 4 | 4615 | 874 |
| 5 | 7895 | 874 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (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))) (cos.f64 x))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) (+.f64 eps (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
| Outputs |
|---|
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (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))) (cos.f64 x))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (sin.f64 eps)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) eps #s(literal 0 binary64)) eps #s(literal 1 binary64)) eps #s(literal 0 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
(/.f64 #s(approx (+ (* (neg (sin x)) (cos (+ eps x))) (* (sin (+ eps x)) (cos x))) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (/ 1 (/ (* (cos (+ eps x)) (cos x)) (sin (- (+ eps x) x)))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) |
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) eps) (fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/3 binary64) eps) (+.f64 eps (*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) eps) #s(literal 4/3 binary64) #s(literal 1 binary64)) eps) x (*.f64 eps eps)) x))))) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 4/3 binary64) #s(literal 1 binary64)) x eps) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 (fma.f64 #s(approx (+ (* (* 4/3 eps) eps) (+ (* (* 4/3 eps) x) 1)) (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64))) x eps) x (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 4/3 binary64) #s(literal 1/3 binary64)) eps x) eps (fma.f64 x x #s(literal 1 binary64))))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) (+.f64 eps x)) x (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (+ (* (+ (* (* eps eps) 4/3) 1) x) eps) x) (+ (* 1/3 (* eps eps)) 1)) (fma.f64 x x #s(literal 1 binary64)))) eps)) |
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (+ (* (* (- (/ (+ (* (sin x) (sin x)) (/ (pow (sin x) 4) (pow (cos x) 2))) (pow (cos x) 2)) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) -1/3)) eps) eps) (* (+ (* (/ (sin x) (pow (cos x) 2)) (sin x)) 1) (+ (/ (* (sin x) eps) (cos x)) 1))) #s(approx (+ (* (* eps eps) 1/3) 1) #s(literal 1 binary64))) eps)) |
#s(approx (+ (* (sin x) (/ 1 (neg (cos x)))) (tan (+ eps x))) #s(literal 0 binary64)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 600 | 3604 |
| 1 | 1984 | 3149 |
| 2 | 6711 | 3092 |
| 0 | 8102 | 2938 |
| 0 | 714 | 4132 |
| 1 | 2433 | 3678 |
| 0 | 8473 | 3445 |
| 0 | 79 | 898 |
| 0 | 123 | 874 |
| 1 | 539 | 701 |
| 2 | 4389 | 685 |
| 0 | 9122 | 661 |
| 0 | 157 | 950 |
| 1 | 464 | 884 |
| 2 | 1539 | 873 |
| 3 | 6077 | 710 |
| 0 | 8335 | 686 |
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 50 | 16 |
| 2 | 402 | 16 |
| 3 | 6137 | 16 |
| 0 | 8166 | 16 |
| 0 | 73 | 481 |
| 0 | 103 | 448 |
| 1 | 512 | 310 |
| 2 | 4931 | 310 |
| 0 | 8294 | 292 |
| 0 | 741 | 3968 |
| 1 | 2302 | 3532 |
| 2 | 7176 | 3461 |
| 0 | 8166 | 3253 |
| 1× | fuel |
| 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 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 1 298 to 393 computations (69.7% saved)
Compiled 1 942 to 344 computations (82.3% saved)
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