
Time bar (total: 11.2s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 0 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 1 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 2 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 3 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 4 |
| 0% | 0% | 19% | 49.4% | 0% | 31.6% | 0% | 5 |
| 0% | 0% | 15.8% | 49.4% | 0% | 34.8% | 0% | 6 |
| 0% | 0% | 11.1% | 49.4% | 0% | 39.5% | 0% | 7 |
| 0% | 0% | 8.7% | 49.4% | 0% | 41.9% | 0% | 8 |
| 0% | 0% | 5.9% | 49.4% | 0% | 44.6% | 0% | 9 |
| 0% | 0% | 4.5% | 49.4% | 0% | 46% | 0% | 10 |
| 0% | 0% | 3.1% | 49.4% | 0% | 47.5% | 0% | 11 |
| 0% | 0% | 2.7% | 49.4% | 0% | 47.9% | 0% | 12 |
Compiled 27 to 19 computations (29.6% saved)
| 4.0s | 26 171× | 0 | invalid |
| 787.0ms | 5 443× | 0 | valid |
| 523.0ms | 2 813× | 1 | valid |
ival-sin: 1.0s (27.3% of total)const: 938.0ms (25.2% of total)ival-add: 339.0ms (9.1% of total)ival-<: 297.0ms (8% of total)ival-<=: 249.0ms (6.7% of total)ival-mult: 247.0ms (6.6% of total)ival-sub: 204.0ms (5.5% of total)ival-fabs: 201.0ms (5.4% of total)ival-and: 100.0ms (2.7% of total)adjust: 75.0ms (2% of total)exact: 42.0ms (1.1% of total)ival-assert: 14.0ms (0.4% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 225 | 0 | - | 7 | (2.856233422121792e-26 2.893370470922743e-28) | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 0 | 0 | - | 0 | - | (sin.f64 (+.f64 x eps)) |
| 0 | 0 | - | 0 | - | eps |
| 0 | 0 | - | 0 | - | (+.f64 x eps) |
| 0 | 0 | - | 0 | - | (sin.f64 x) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) | cancellation | 218 | 15 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 218 | 7 |
| - | 0 | 31 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 218 | 7 | 0 |
| - | 0 | 8 | 23 |
| number | freq |
|---|---|
| 0 | 38 |
| 1 | 218 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 18.0ms | 172× | 1 | valid |
| 15.0ms | 336× | 0 | valid |
| 2.0ms | 4× | 3 | valid |
Compiled 47 to 22 computations (53.2% saved)
ival-sin: 10.0ms (47.7% of total)adjust: 4.0ms (19.1% of total)ival-sub: 4.0ms (19.1% of total)ival-add: 3.0ms (14.3% 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 | 43 |
| 1 | 22 | 43 |
| 2 | 29 | 43 |
| 3 | 37 | 43 |
| 4 | 49 | 43 |
| 5 | 71 | 43 |
| 6 | 93 | 43 |
| 7 | 147 | 43 |
| 8 | 231 | 43 |
| 9 | 385 | 43 |
| 10 | 1010 | 43 |
| 11 | 4371 | 43 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 11 | 7 |
| 0 | 11 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Outputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 63.4% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.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 | (sin.f64 x) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (sin.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 0 | 10 | 18 |
| 1 | 11 | 18 |
| 0 | 11 | 18 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(sin.f64 x) |
| Outputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(sin.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
(sin.f64 x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0 | (+.f64 x eps) | |
| accuracy | 0.0 | (sin.f64 x) | |
| accuracy | 0.015625 | (sin.f64 (+.f64 x eps)) | |
| accuracy | 23.436072649282334 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 11.0ms | 168× | 0 | valid |
| 8.0ms | 86× | 1 | valid |
| 1.0ms | 2× | 3 | valid |
Compiled 20 to 8 computations (60% saved)
ival-sin: 8.0ms (59.6% of total)adjust: 2.0ms (14.9% of total)ival-add: 2.0ms (14.9% of total)ival-sub: 1.0ms (7.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(sin.f64 x) |
| Outputs |
|---|
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
eps |
(+ eps x) |
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)))) |
(- (sin (+ eps x)) (sin x)) |
(sin (+ eps x)) |
(* x (+ 1 (/ eps x))) |
(sin x) |
(- (sin (- eps (* -1 x))) (sin x)) |
(sin (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(* eps (+ 1 (/ x eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(sin (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | 0 | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 1.0ms | eps | @ | inf | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 1.0ms | eps | @ | 0 | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 1.0ms | eps | @ | -inf | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 0.0ms | x | @ | inf | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 107 | 303 |
| 1 | 366 | 303 |
| 2 | 1224 | 296 |
| 3 | 4149 | 296 |
| 4 | 7986 | 296 |
| 0 | 8046 | 267 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
eps |
(+ eps x) |
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)))) |
(- (sin (+ eps x)) (sin x)) |
(sin (+ eps x)) |
(* x (+ 1 (/ eps x))) |
(sin x) |
(- (sin (- eps (* -1 x))) (sin x)) |
(sin (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(* eps (+ 1 (/ x eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(sin (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
| Outputs |
|---|
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(+ (sin eps) (* x (cos eps))) |
(fma.f64 (cos.f64 eps) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (cos.f64 eps)) x (sin.f64 eps)) |
eps |
(+ eps x) |
(+.f64 eps x) |
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)) (-.f64 (*.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 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/5040 binary64) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64))) x) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
(sin x) |
(sin.f64 x) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))) |
(* eps (cos x)) |
(*.f64 (cos.f64 x) eps) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps) |
(+ (sin x) (* eps (cos x))) |
(fma.f64 (cos.f64 x) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps (sin.f64 x)) |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 51 | 16 |
| 2 | 365 | 16 |
| 3 | 4452 | 16 |
| 0 | 8177 | 16 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(sin.f64 x) |
| Outputs |
|---|
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (-.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) |
(*.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (*.f64 (cos.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (/.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) |
(*.f64 (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (/.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #s(literal 2 binary64))) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (+.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))) |
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(/.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))) |
(neg.f64 (/.f64 (*.f64 (neg.f64 (+.f64 eps x)) (-.f64 x eps)) (-.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 (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 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 (/.f64 (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 (pow.f64 eps #s(literal 3 binary64)) (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)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(fma.f64 (/.f64 (pow.f64 eps #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 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 (/.f64 (pow.f64 eps #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 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 (pow.f64 eps #s(literal 3/2 binary64)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 (fabs.f64 x) (/.f64 (fabs.f64 x) (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(fma.f64 (neg.f64 x) (/.f64 (neg.f64 x) (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(fma.f64 (*.f64 eps eps) (/.f64 eps (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 eps (/.f64 (*.f64 eps eps) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) 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 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(+.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(+.f64 eps x) |
(+.f64 x eps) |
(sin.f64 x) |
Compiled 5 510 to 734 computations (86.7% saved)
7 alts after pruning (6 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 171 | 6 | 177 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 171 | 7 | 178 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 33.8% | (-.f64 (sin.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) (sin.f64 x)) |
| ✓ | 63.4% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| ▶ | 100.0% | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) | |
| ▶ | 99.6% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| ▶ | 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| ▶ | 98.9% | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
Compiled 217 to 150 computations (30.9% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) | |
| cost-diff | 0 | (sin.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) | |
| cost-diff | 0 | (-.f64 (sin.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) (sin.f64 x)) | |
| cost-diff | 12 | (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) | |
| cost-diff | 0 | (*.f64 (sin.f64 x) eps) | |
| cost-diff | 0 | (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) | |
| cost-diff | 0 | (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| cost-diff | 0 | (cos.f64 x) | |
| cost-diff | 0 | (*.f64 (cos.f64 x) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) | |
| cost-diff | 0 | (sin.f64 eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) | |
| cost-diff | 0 | (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| cost-diff | 1 | (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) | |
| cost-diff | 2 | (+.f64 #s(literal 0 binary64) eps) |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 39 | 259 |
| 0 | 68 | 249 |
| 1 | 136 | 249 |
| 2 | 423 | 222 |
| 3 | 1948 | 210 |
| 4 | 7959 | 210 |
| 0 | 8019 | 210 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) |
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) |
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
#s(literal 0 binary64) |
eps |
#s(literal 2 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(fma.f64 #s(literal 2 binary64) x eps) |
x |
#s(literal -2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(sin.f64 eps) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
x |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 (sin.f64 x) eps) |
(sin.f64 x) |
x |
eps |
#s(literal -1/2 binary64) |
(cos.f64 x) |
(-.f64 (sin.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) (sin.f64 x)) |
(sin.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) |
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) |
(*.f64 x x) |
x |
(*.f64 (-.f64 x eps) (+.f64 eps x)) |
(-.f64 x eps) |
eps |
(+.f64 eps x) |
(/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)) |
(*.f64 (neg.f64 eps) eps) |
(neg.f64 eps) |
(sin.f64 x) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (cos.f64 (+.f64 x (/.f64 eps #s(literal 2 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64))) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) |
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) |
(sin.f64 (/.f64 eps #s(literal 2 binary64))) |
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)) |
(/.f64 eps #s(literal 2 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
eps |
#s(literal 0 binary64) |
eps |
#s(literal 2 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(cos.f64 (+.f64 x (/.f64 eps #s(literal 2 binary64)))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(-.f64 (/.f64 eps #s(literal -2 binary64)) x) |
(fma.f64 #s(literal 2 binary64) x eps) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal -2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(sin.f64 eps) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
x |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) |
(*.f64 (sin.f64 x) eps) |
(sin.f64 x) |
x |
eps |
#s(literal -1/2 binary64) |
(cos.f64 x) |
(-.f64 (sin.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) (sin.f64 x)) |
(-.f64 (sin.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (sin.f64 x)) |
(sin.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) |
(sin.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) |
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps)) |
(/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) |
(*.f64 (/.f64 x (+.f64 x eps)) (/.f64 x (-.f64 x eps))) |
(*.f64 x x) |
x |
(*.f64 (-.f64 x eps) (+.f64 eps x)) |
(*.f64 (+.f64 x eps) (-.f64 x eps)) |
(-.f64 x eps) |
eps |
(+.f64 eps x) |
(+.f64 x eps) |
(/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)) |
(*.f64 (/.f64 eps (-.f64 x eps)) (neg.f64 eps)) |
(*.f64 (neg.f64 eps) eps) |
(neg.f64 eps) |
(sin.f64 x) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.19921875 | (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) | |
| accuracy | 23.40909260789324 | (-.f64 (sin.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) (sin.f64 x)) | |
| accuracy | 28.210503450742433 | (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) | |
| accuracy | 29.099719672916414 | (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)) | |
| accuracy | 0.00390625 | (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) | |
| accuracy | 0.00390625 | (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) | |
| accuracy | 0.0078125 | (*.f64 (sin.f64 x) eps) | |
| accuracy | 0.06986876995342235 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| accuracy | 0.0 | (cos.f64 x) | |
| accuracy | 0.0078125 | (*.f64 (cos.f64 x) eps) | |
| accuracy | 0.14187710377844137 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) | |
| accuracy | 0.0 | (sin.f64 eps) | |
| accuracy | 0.5255923811614924 | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) | |
| accuracy | 0.0 | (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) | |
| accuracy | 0.0 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) | |
| accuracy | 0.00390625 | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| accuracy | 0.00390625 | (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) |
| 41.0ms | 87× | 1 | valid |
| 37.0ms | 163× | 0 | valid |
| 9.0ms | 6× | 5 | exit |
Compiled 251 to 40 computations (84.1% saved)
ival-mult: 18.0ms (29% of total)ival-sin: 12.0ms (19.3% of total)adjust: 9.0ms (14.5% of total)ival-div: 7.0ms (11.3% of total)ival-add: 7.0ms (11.3% of total)ival-sub: 4.0ms (6.4% of total)ival-cos: 4.0ms (6.4% of total)ival-neg: 1.0ms (1.6% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(+.f64 #s(literal 0 binary64) eps) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(sin.f64 eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 (sin.f64 x) eps) |
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(-.f64 (sin.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) (sin.f64 x)) |
(sin.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) |
(/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) |
(/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)) |
| Outputs |
|---|
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(* eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
(+ eps x) |
(+ (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 (/ (pow x 2) (pow eps 2))) |
(* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 4))) (/ 1 (pow eps 2)))) |
(* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 6))) (/ 1 (pow eps 4)))) (/ 1 (pow eps 2)))) |
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 8))) (/ 1 (pow eps 6)))) (/ 1 (pow eps 4)))) (/ 1 (pow eps 2)))) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(+ eps (* x (+ 1 (/ x eps)))) |
(+ eps (* x (+ 1 (* x (+ (/ 1 eps) (/ x (pow eps 2))))))) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(cos x) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* eps (sin x)) |
x |
(* x (+ 1 (/ eps x))) |
(- (sin (+ (* -1 (/ (pow eps 2) (- x eps))) (/ (pow x 2) (- x eps)))) (sin x)) |
(sin (+ (* -1 (/ (pow eps 2) (- x eps))) (/ (pow x 2) (- x eps)))) |
(+ 1 (* -1 (/ (+ eps (* -1 eps)) x))) |
(- (+ 1 (* -1 (/ (+ (* -1 (pow eps 2)) (* -1 (pow (+ eps (* -1 eps)) 2))) (pow x 2)))) (+ (* -1 (/ eps x)) (/ eps x))) |
(- (+ 1 (* -1 (/ (+ (* -1 (* (+ eps (* -1 eps)) (+ (* -1 (pow eps 2)) (* -1 (pow (+ eps (* -1 eps)) 2))))) (* (pow eps 2) (+ eps (* -1 eps)))) (pow x 3)))) (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (+ (* -1 (/ (pow (+ eps (* -1 eps)) 2) (pow x 2))) (/ eps x))))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* -1 (/ (pow eps 2) x)) |
(/ (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2))) x) |
(/ (+ (* -1 (/ (pow eps 3) x)) (+ (* -1 (/ (pow eps 4) (pow x 2))) (* -1 (pow eps 2)))) x) |
(/ (+ (* -1 (/ (pow eps 3) x)) (+ (* -1 (/ (pow eps 4) (pow x 2))) (+ (* -1 (/ (pow eps 5) (pow x 3))) (* -1 (pow eps 2))))) x) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ (+ eps (* -1 (/ (+ (* -1 (pow eps 2)) (pow eps 2)) x))) x)) 1))) |
(- (sin (- (/ (pow eps 2) (+ eps (* -1 x))) (/ (pow x 2) (+ eps (* -1 x))))) (sin x)) |
(sin (- (/ (pow eps 2) (+ eps (* -1 x))) (/ (pow x 2) (+ eps (* -1 x))))) |
(+ 1 (* -1 (/ (- (+ (* -1 (/ (pow eps 2) x)) (* -1 (/ (pow (+ eps (* -1 eps)) 2) x))) (* -1 (+ eps (* -1 eps)))) x))) |
(+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (pow eps 2) (+ eps (* -1 eps))) x)) (/ (* (+ eps (* -1 eps)) (+ (* -1 (pow eps 2)) (* -1 (pow (+ eps (* -1 eps)) 2)))) x)) (+ (* -1 (pow eps 2)) (* -1 (pow (+ eps (* -1 eps)) 2)))) x)) (* -1 (+ eps (* -1 eps)))) x))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(* -1 (/ (+ (/ (pow eps 3) x) (pow eps 2)) x)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow eps 4) x)) (pow eps 3)) x)) (pow eps 2)) x)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (/ (pow eps 5) x) (* -1 (pow eps 4))) x)) (pow eps 3)) x)) (pow eps 2)) x)) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (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)))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(+ 1 (/ (pow eps 2) (pow x 2))) |
(+ 1 (* (pow eps 2) (+ (/ 1 (pow x 2)) (/ (pow eps 2) (pow x 4))))) |
(+ 1 (* (pow eps 2) (+ (* (pow eps 2) (+ (/ 1 (pow x 4)) (/ (pow eps 2) (pow x 6)))) (/ 1 (pow x 2))))) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* (pow eps 2) (- (* -1 (/ eps (pow x 2))) (/ 1 x))) |
(* (pow eps 2) (- (* eps (- (* -1 (/ eps (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))) |
(* (pow eps 2) (- (* eps (- (* eps (- (* -1 (/ eps (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* 2 (sin (* 1/2 eps))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))) |
(- (sin (- (/ (pow x 2) (- x eps)) (/ (pow eps 2) (- x eps)))) (sin x)) |
(sin (- (/ (pow x 2) (- x eps)) (/ (pow eps 2) (- x eps)))) |
(/ (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) eps)) (* -1 (pow x 2))) (pow eps 2)) |
(/ (- (+ (* -1 (/ (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4)) (pow eps 2))) (* -1 (pow x 2))) (/ (* (pow x 2) (+ x (* -1 x))) eps)) (pow eps 2)) |
(/ (- (+ (* -1 (/ (+ (* (+ x (* -1 x)) (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4))) (* (pow x 4) (+ x (* -1 x)))) (pow eps 3))) (* -1 (pow x 2))) (+ (/ (* (pow x 2) (+ x (* -1 x))) eps) (+ (/ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow eps 2)) (/ (pow x 4) (pow eps 2))))) (pow eps 2)) |
(sin (* 1/2 eps)) |
(* eps (- (+ 1 (/ (pow x 2) (pow eps 2))) (* -1 (/ x eps)))) |
(* eps (- (+ 1 (/ (pow x 3) (pow eps 3))) (+ (* -1 (/ x eps)) (* -1 (/ (pow x 2) (pow eps 2)))))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps)) 1))) |
(- (sin (- (/ (pow x 2) (+ x (* -1 eps))) (/ (pow eps 2) (+ x (* -1 eps))))) (sin x)) |
(sin (- (/ (pow x 2) (+ x (* -1 eps))) (/ (pow eps 2) (+ x (* -1 eps))))) |
(/ (+ (* -1 (pow x 2)) (/ (* (pow x 2) (+ x (* -1 x))) eps)) (pow eps 2)) |
(/ (+ (* -1 (/ (- (+ (/ (* (pow x 2) (pow (+ x (* -1 x)) 2)) eps) (/ (pow x 4) eps)) (* (pow x 2) (+ x (* -1 x)))) eps)) (* -1 (pow x 2))) (pow eps 2)) |
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (/ (* (+ x (* -1 x)) (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4))) eps) (/ (* (pow x 4) (+ x (* -1 x))) eps)) (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4))) eps)) (* (pow x 2) (+ x (* -1 x)))) eps)) (* -1 (pow x 2))) (pow eps 2)) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(* -1 (* eps (- (* -1 (/ (- (/ (pow x 2) eps) (* -1 x)) eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow x 3) eps)) (pow x 2)) eps)) (* -1 x)) eps)) 1))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 13.0ms | eps | @ | 0 | ((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps))) (- (sin (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps)))) (sin x)) (sin (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps)))) (/ (* x x) (* (- x eps) (+ eps x))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (/ (* (neg eps) eps) (- x eps))) |
| 6.0ms | x | @ | -inf | ((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps))) (- (sin (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps)))) (sin x)) (sin (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps)))) (/ (* x x) (* (- x eps) (+ eps x))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (/ (* (neg eps) eps) (- x eps))) |
| 6.0ms | x | @ | inf | ((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps))) (- (sin (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps)))) (sin x)) (sin (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps)))) (/ (* x x) (* (- x eps) (+ eps x))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (/ (* (neg eps) eps) (- x eps))) |
| 5.0ms | x | @ | 0 | ((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps))) (- (sin (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps)))) (sin x)) (sin (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps)))) (/ (* x x) (* (- x eps) (+ eps x))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (/ (* (neg eps) eps) (- x eps))) |
| 5.0ms | eps | @ | inf | ((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps))) (- (sin (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps)))) (sin x)) (sin (+ (* (/ (* x x) (* (- x eps) (+ eps x))) (+ eps x)) (/ (* (neg eps) eps) (- x eps)))) (/ (* x x) (* (- x eps) (+ eps x))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (/ (* (neg eps) eps) (- x eps))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 621 | 2119 |
| 1 | 2146 | 1864 |
| 0 | 8334 | 1737 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(* eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
(+ eps x) |
(+ (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 (/ (pow x 2) (pow eps 2))) |
(* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 4))) (/ 1 (pow eps 2)))) |
(* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 6))) (/ 1 (pow eps 4)))) (/ 1 (pow eps 2)))) |
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 8))) (/ 1 (pow eps 6)))) (/ 1 (pow eps 4)))) (/ 1 (pow eps 2)))) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(+ eps (* x (+ 1 (/ x eps)))) |
(+ eps (* x (+ 1 (* x (+ (/ 1 eps) (/ x (pow eps 2))))))) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(cos x) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* eps (sin x)) |
x |
(* x (+ 1 (/ eps x))) |
(- (sin (+ (* -1 (/ (pow eps 2) (- x eps))) (/ (pow x 2) (- x eps)))) (sin x)) |
(sin (+ (* -1 (/ (pow eps 2) (- x eps))) (/ (pow x 2) (- x eps)))) |
(+ 1 (* -1 (/ (+ eps (* -1 eps)) x))) |
(- (+ 1 (* -1 (/ (+ (* -1 (pow eps 2)) (* -1 (pow (+ eps (* -1 eps)) 2))) (pow x 2)))) (+ (* -1 (/ eps x)) (/ eps x))) |
(- (+ 1 (* -1 (/ (+ (* -1 (* (+ eps (* -1 eps)) (+ (* -1 (pow eps 2)) (* -1 (pow (+ eps (* -1 eps)) 2))))) (* (pow eps 2) (+ eps (* -1 eps)))) (pow x 3)))) (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (+ (* -1 (/ (pow (+ eps (* -1 eps)) 2) (pow x 2))) (/ eps x))))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* -1 (/ (pow eps 2) x)) |
(/ (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2))) x) |
(/ (+ (* -1 (/ (pow eps 3) x)) (+ (* -1 (/ (pow eps 4) (pow x 2))) (* -1 (pow eps 2)))) x) |
(/ (+ (* -1 (/ (pow eps 3) x)) (+ (* -1 (/ (pow eps 4) (pow x 2))) (+ (* -1 (/ (pow eps 5) (pow x 3))) (* -1 (pow eps 2))))) x) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ (+ eps (* -1 (/ (+ (* -1 (pow eps 2)) (pow eps 2)) x))) x)) 1))) |
(- (sin (- (/ (pow eps 2) (+ eps (* -1 x))) (/ (pow x 2) (+ eps (* -1 x))))) (sin x)) |
(sin (- (/ (pow eps 2) (+ eps (* -1 x))) (/ (pow x 2) (+ eps (* -1 x))))) |
(+ 1 (* -1 (/ (- (+ (* -1 (/ (pow eps 2) x)) (* -1 (/ (pow (+ eps (* -1 eps)) 2) x))) (* -1 (+ eps (* -1 eps)))) x))) |
(+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (pow eps 2) (+ eps (* -1 eps))) x)) (/ (* (+ eps (* -1 eps)) (+ (* -1 (pow eps 2)) (* -1 (pow (+ eps (* -1 eps)) 2)))) x)) (+ (* -1 (pow eps 2)) (* -1 (pow (+ eps (* -1 eps)) 2)))) x)) (* -1 (+ eps (* -1 eps)))) x))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(* -1 (/ (+ (/ (pow eps 3) x) (pow eps 2)) x)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow eps 4) x)) (pow eps 3)) x)) (pow eps 2)) x)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (/ (pow eps 5) x) (* -1 (pow eps 4))) x)) (pow eps 3)) x)) (pow eps 2)) x)) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (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)))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(+ 1 (/ (pow eps 2) (pow x 2))) |
(+ 1 (* (pow eps 2) (+ (/ 1 (pow x 2)) (/ (pow eps 2) (pow x 4))))) |
(+ 1 (* (pow eps 2) (+ (* (pow eps 2) (+ (/ 1 (pow x 4)) (/ (pow eps 2) (pow x 6)))) (/ 1 (pow x 2))))) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* (pow eps 2) (- (* -1 (/ eps (pow x 2))) (/ 1 x))) |
(* (pow eps 2) (- (* eps (- (* -1 (/ eps (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))) |
(* (pow eps 2) (- (* eps (- (* eps (- (* -1 (/ eps (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* 2 (sin (* 1/2 eps))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))) |
(- (sin (- (/ (pow x 2) (- x eps)) (/ (pow eps 2) (- x eps)))) (sin x)) |
(sin (- (/ (pow x 2) (- x eps)) (/ (pow eps 2) (- x eps)))) |
(/ (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) eps)) (* -1 (pow x 2))) (pow eps 2)) |
(/ (- (+ (* -1 (/ (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4)) (pow eps 2))) (* -1 (pow x 2))) (/ (* (pow x 2) (+ x (* -1 x))) eps)) (pow eps 2)) |
(/ (- (+ (* -1 (/ (+ (* (+ x (* -1 x)) (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4))) (* (pow x 4) (+ x (* -1 x)))) (pow eps 3))) (* -1 (pow x 2))) (+ (/ (* (pow x 2) (+ x (* -1 x))) eps) (+ (/ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow eps 2)) (/ (pow x 4) (pow eps 2))))) (pow eps 2)) |
(sin (* 1/2 eps)) |
(* eps (- (+ 1 (/ (pow x 2) (pow eps 2))) (* -1 (/ x eps)))) |
(* eps (- (+ 1 (/ (pow x 3) (pow eps 3))) (+ (* -1 (/ x eps)) (* -1 (/ (pow x 2) (pow eps 2)))))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps)) 1))) |
(- (sin (- (/ (pow x 2) (+ x (* -1 eps))) (/ (pow eps 2) (+ x (* -1 eps))))) (sin x)) |
(sin (- (/ (pow x 2) (+ x (* -1 eps))) (/ (pow eps 2) (+ x (* -1 eps))))) |
(/ (+ (* -1 (pow x 2)) (/ (* (pow x 2) (+ x (* -1 x))) eps)) (pow eps 2)) |
(/ (+ (* -1 (/ (- (+ (/ (* (pow x 2) (pow (+ x (* -1 x)) 2)) eps) (/ (pow x 4) eps)) (* (pow x 2) (+ x (* -1 x)))) eps)) (* -1 (pow x 2))) (pow eps 2)) |
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (/ (* (+ x (* -1 x)) (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4))) eps) (/ (* (pow x 4) (+ x (* -1 x))) eps)) (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4))) eps)) (* (pow x 2) (+ x (* -1 x)))) eps)) (* -1 (pow x 2))) (pow eps 2)) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(* -1 (* eps (- (* -1 (/ (- (/ (pow x 2) eps) (* -1 x)) eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow x 3) eps)) (pow x 2)) eps)) (* -1 x)) eps)) 1))) |
| Outputs |
|---|
(* -1/2 eps) |
(*.f64 #s(literal -1/2 binary64) eps) |
(+ (* -1 x) (* -1/2 eps)) |
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(fma.f64 (neg.f64 x) (*.f64 (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64) (*.f64 (*.f64 x x) (fma.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (*.f64 #s(literal -1/3 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(fma.f64 (-.f64 (*.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 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(fma.f64 (fma.f64 (*.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) x)) x)) x eps) |
(+ 1 (* -1/2 (* eps x))) |
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)) |
(* eps x) |
(*.f64 x eps) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/120 binary64) eps)) x) x (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x eps)) |
(+ eps x) |
(+.f64 x eps) |
(+ (sin eps) (* x (cos eps))) |
(fma.f64 (cos.f64 eps) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) x (sin.f64 eps)) |
(* -1 (/ (pow x 2) (pow eps 2))) |
(/.f64 (/.f64 (*.f64 (neg.f64 x) x) eps) eps) |
(* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 4))) (/ 1 (pow eps 2)))) |
(*.f64 (-.f64 (/.f64 (*.f64 (neg.f64 x) x) (pow.f64 eps #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 x x)) |
(* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 6))) (/ 1 (pow eps 4)))) (/ 1 (pow eps 2)))) |
(*.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 (neg.f64 x) x) (pow.f64 eps #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 4 binary64)))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 x x)) |
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 8))) (/ 1 (pow eps 6)))) (/ 1 (pow eps 4)))) (/ 1 (pow eps 2)))) |
(*.f64 (-.f64 (*.f64 (-.f64 (*.f64 (-.f64 (/.f64 (*.f64 (neg.f64 x) x) (pow.f64 eps #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 6 binary64)))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 4 binary64)))) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 x x)) |
(cos (* -1/2 eps)) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ eps (* x (+ 1 (/ x eps)))) |
(fma.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) x eps) |
(+ eps (* x (+ 1 (* x (+ (/ 1 eps) (/ x (pow eps 2))))))) |
(+.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 x eps) x x) eps) x x) eps) |
(* -1 x) |
(neg.f64 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(*.f64 (-.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* eps (cos x)) |
(*.f64 (cos.f64 x) eps) |
(cos x) |
(cos.f64 x) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) |
(* eps (sin x)) |
(*.f64 (sin.f64 x) eps) |
x |
(* x (+ 1 (/ eps x))) |
(fma.f64 (/.f64 eps x) x x) |
(- (sin (+ (* -1 (/ (pow eps 2) (- x eps))) (/ (pow x 2) (- x eps)))) (sin x)) |
(-.f64 (sin.f64 (/.f64 (fma.f64 (neg.f64 eps) eps (*.f64 x x)) (-.f64 x eps))) (sin.f64 x)) |
(sin (+ (* -1 (/ (pow eps 2) (- x eps))) (/ (pow x 2) (- x eps)))) |
(sin.f64 (/.f64 (fma.f64 (neg.f64 eps) eps (*.f64 x x)) (-.f64 x eps))) |
(+ 1 (* -1 (/ (+ eps (* -1 eps)) x))) |
#s(literal 1 binary64) |
(- (+ 1 (* -1 (/ (+ (* -1 (pow eps 2)) (* -1 (pow (+ eps (* -1 eps)) 2))) (pow x 2)))) (+ (* -1 (/ eps x)) (/ eps x))) |
(+.f64 (/.f64 (fma.f64 eps eps #s(literal 0 binary64)) (*.f64 x x)) #s(literal 1 binary64)) |
(- (+ 1 (* -1 (/ (+ (* -1 (* (+ eps (* -1 eps)) (+ (* -1 (pow eps 2)) (* -1 (pow (+ eps (* -1 eps)) 2))))) (* (pow eps 2) (+ eps (* -1 eps)))) (pow x 3)))) (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (+ (* -1 (/ (pow (+ eps (* -1 eps)) 2) (pow x 2))) (/ eps x))))) |
(+.f64 (/.f64 (fma.f64 eps eps #s(literal 0 binary64)) (*.f64 x x)) #s(literal 1 binary64)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* -1 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (neg.f64 eps) eps) x) |
(/ (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2))) x) |
(/.f64 (fma.f64 eps eps (/.f64 (pow.f64 eps #s(literal 3 binary64)) x)) (neg.f64 x)) |
(/ (+ (* -1 (/ (pow eps 3) x)) (+ (* -1 (/ (pow eps 4) (pow x 2))) (* -1 (pow eps 2)))) x) |
(/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (pow.f64 eps #s(literal 4 binary64)) x) (neg.f64 (fma.f64 eps eps (/.f64 (pow.f64 eps #s(literal 3 binary64)) x)))) x) |
(/ (+ (* -1 (/ (pow eps 3) x)) (+ (* -1 (/ (pow eps 4) (pow x 2))) (+ (* -1 (/ (pow eps 5) (pow x 3))) (* -1 (pow eps 2))))) x) |
(/.f64 (fma.f64 (fma.f64 eps eps (/.f64 (pow.f64 eps #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64) (neg.f64 (+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) (/.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) x) x)))) x) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))) |
(* -1 (* x (- (* -1 (/ (+ eps (* -1 (/ (+ (* -1 (pow eps 2)) (pow eps 2)) x))) x)) 1))) |
(*.f64 (neg.f64 x) (-.f64 (fma.f64 (/.f64 eps x) #s(literal -1 binary64) #s(literal 0 binary64)) #s(literal 1 binary64))) |
(- (sin (- (/ (pow eps 2) (+ eps (* -1 x))) (/ (pow x 2) (+ eps (* -1 x))))) (sin x)) |
(-.f64 (sin.f64 (-.f64 (*.f64 eps (/.f64 eps (-.f64 eps x))) (*.f64 x (/.f64 x (-.f64 eps x))))) (sin.f64 x)) |
(sin (- (/ (pow eps 2) (+ eps (* -1 x))) (/ (pow x 2) (+ eps (* -1 x))))) |
(sin.f64 (-.f64 (*.f64 eps (/.f64 eps (-.f64 eps x))) (*.f64 x (/.f64 x (-.f64 eps x))))) |
(+ 1 (* -1 (/ (- (+ (* -1 (/ (pow eps 2) x)) (* -1 (/ (pow (+ eps (* -1 eps)) 2) x))) (* -1 (+ eps (* -1 eps)))) x))) |
(+.f64 (/.f64 (fma.f64 eps eps #s(literal 0 binary64)) (*.f64 x x)) #s(literal 1 binary64)) |
(+ 1 (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (pow eps 2) (+ eps (* -1 eps))) x)) (/ (* (+ eps (* -1 eps)) (+ (* -1 (pow eps 2)) (* -1 (pow (+ eps (* -1 eps)) 2)))) x)) (+ (* -1 (pow eps 2)) (* -1 (pow (+ eps (* -1 eps)) 2)))) x)) (* -1 (+ eps (* -1 eps)))) x))) |
(+.f64 (/.f64 (fma.f64 eps eps #s(literal 0 binary64)) (*.f64 x x)) #s(literal 1 binary64)) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* -1 (/ (+ (/ (pow eps 3) x) (pow eps 2)) x)) |
(/.f64 (fma.f64 eps eps (/.f64 (pow.f64 eps #s(literal 3 binary64)) x)) (neg.f64 x)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow eps 4) x)) (pow eps 3)) x)) (pow eps 2)) x)) |
(/.f64 (fma.f64 eps eps (/.f64 (-.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (neg.f64 x)) (pow.f64 eps #s(literal 3 binary64))) (neg.f64 x))) (neg.f64 x)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (/ (pow eps 5) x) (* -1 (pow eps 4))) x)) (pow eps 3)) x)) (pow eps 2)) x)) |
(/.f64 (fma.f64 eps eps (/.f64 (-.f64 (/.f64 (+.f64 (/.f64 (pow.f64 eps #s(literal 5 binary64)) x) (pow.f64 eps #s(literal 4 binary64))) (neg.f64 x)) (pow.f64 eps #s(literal 3 binary64))) (neg.f64 x))) (neg.f64 x)) |
(* eps (cos (* -1 x))) |
(*.f64 (cos.f64 x) eps) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(*.f64 (fma.f64 (neg.f64 (sin.f64 x)) (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 x)) eps) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 (neg.f64 (sin.f64 x)) #s(literal 1/2 binary64))) eps (cos.f64 x)) eps) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(fma.f64 #s(literal -1/24 binary64) (pow.f64 eps #s(literal 3 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/120 binary64) eps) eps) #s(literal 1/6 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)) (pow.f64 eps #s(literal 3 binary64)) eps) |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* eps (cos x))) |
(fma.f64 (cos.f64 x) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (sin.f64 x)) |
(+ 1 (/ (pow eps 2) (pow x 2))) |
(fma.f64 (/.f64 eps x) (/.f64 eps x) #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (+ (/ 1 (pow x 2)) (/ (pow eps 2) (pow x 4))))) |
(fma.f64 (fma.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 eps eps) #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (+ (* (pow eps 2) (+ (/ 1 (pow x 4)) (/ (pow eps 2) (pow x 6)))) (/ 1 (pow x 2))))) |
(fma.f64 (fma.f64 (fma.f64 eps (/.f64 eps (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 eps eps) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 eps eps) #s(literal 1 binary64)) |
(cos (* -1 x)) |
(cos.f64 x) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(fma.f64 (neg.f64 (sin.f64 x)) (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 x)) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (neg.f64 (sin.f64 x)) #s(literal 1/2 binary64))) eps (cos.f64 x)) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 #s(literal -1/8 binary64) (cos.f64 x))) eps (*.f64 (neg.f64 (sin.f64 x)) #s(literal 1/2 binary64))) eps (cos.f64 x)) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (pow.f64 eps #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) eps)) |
(* (pow eps 2) (- (* -1 (/ eps (pow x 2))) (/ 1 x))) |
(*.f64 (-.f64 (/.f64 (neg.f64 eps) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x)) (*.f64 eps eps)) |
(* (pow eps 2) (- (* eps (- (* -1 (/ eps (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))) |
(*.f64 (-.f64 (*.f64 (-.f64 (/.f64 (neg.f64 eps) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x))) eps) (/.f64 #s(literal 1 binary64) x)) (*.f64 eps eps)) |
(* (pow eps 2) (- (* eps (- (* eps (- (* -1 (/ eps (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))) |
(*.f64 (-.f64 (*.f64 (-.f64 (*.f64 (-.f64 (/.f64 (neg.f64 eps) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) (/.f64 #s(literal 1 binary64) (*.f64 x x))) eps) (/.f64 #s(literal 1 binary64) x)) (*.f64 eps eps)) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps) |
(* 2 (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (*.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal -1/2 binary64)) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 (/.f64 x eps) eps eps) |
(* eps (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))) |
(fma.f64 (-.f64 (/.f64 (fma.f64 (/.f64 x eps) x x) eps) (*.f64 (/.f64 (/.f64 x eps) eps) x)) eps eps) |
(- (sin (- (/ (pow x 2) (- x eps)) (/ (pow eps 2) (- x eps)))) (sin x)) |
(-.f64 (sin.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (sin.f64 x)) |
(sin (- (/ (pow x 2) (- x eps)) (/ (pow eps 2) (- x eps)))) |
(sin.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(/ (+ (* -1 (/ (* (pow x 2) (+ x (* -1 x))) eps)) (* -1 (pow x 2))) (pow eps 2)) |
(/.f64 (neg.f64 (fma.f64 x x (/.f64 #s(literal 0 binary64) eps))) (*.f64 eps eps)) |
(/ (- (+ (* -1 (/ (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4)) (pow eps 2))) (* -1 (pow x 2))) (/ (* (pow x 2) (+ x (* -1 x))) eps)) (pow eps 2)) |
(/.f64 (-.f64 (/.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64) #s(literal 0 binary64)) eps) eps) (fma.f64 x x (/.f64 #s(literal 0 binary64) eps))) (*.f64 eps eps)) |
(/ (- (+ (* -1 (/ (+ (* (+ x (* -1 x)) (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4))) (* (pow x 4) (+ x (* -1 x)))) (pow eps 3))) (* -1 (pow x 2))) (+ (/ (* (pow x 2) (+ x (* -1 x))) eps) (+ (/ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow eps 2)) (/ (pow x 4) (pow eps 2))))) (pow eps 2)) |
(/.f64 (-.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64) #s(literal 0 binary64)))) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 x x (/.f64 (-.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) eps) #s(literal 0 binary64)) eps))) (*.f64 eps eps)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(* eps (- (+ 1 (/ (pow x 2) (pow eps 2))) (* -1 (/ x eps)))) |
(*.f64 (+.f64 (/.f64 (fma.f64 (/.f64 x eps) x x) eps) #s(literal 1 binary64)) eps) |
(* eps (- (+ 1 (/ (pow x 3) (pow eps 3))) (+ (* -1 (/ x eps)) (* -1 (/ (pow x 2) (pow eps 2)))))) |
(*.f64 (+.f64 (pow.f64 (/.f64 x eps) #s(literal 3 binary64)) (+.f64 (/.f64 (fma.f64 (/.f64 x eps) x x) eps) #s(literal 1 binary64))) eps) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps)))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps)) 1))) |
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (-.f64 x (/.f64 #s(literal 0 binary64) eps)) (neg.f64 eps)) #s(literal 1 binary64))) |
(- (sin (- (/ (pow x 2) (+ x (* -1 eps))) (/ (pow eps 2) (+ x (* -1 eps))))) (sin x)) |
(-.f64 (sin.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) (sin.f64 x)) |
(sin (- (/ (pow x 2) (+ x (* -1 eps))) (/ (pow eps 2) (+ x (* -1 eps))))) |
(sin.f64 (-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(/ (+ (* -1 (pow x 2)) (/ (* (pow x 2) (+ x (* -1 x))) eps)) (pow eps 2)) |
(/.f64 (neg.f64 (fma.f64 x x (/.f64 #s(literal 0 binary64) eps))) (*.f64 eps eps)) |
(/ (+ (* -1 (/ (- (+ (/ (* (pow x 2) (pow (+ x (* -1 x)) 2)) eps) (/ (pow x 4) eps)) (* (pow x 2) (+ x (* -1 x)))) eps)) (* -1 (pow x 2))) (pow eps 2)) |
(/.f64 (neg.f64 (fma.f64 x x (/.f64 (-.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64)) eps) #s(literal 0 binary64)) eps))) (*.f64 eps eps)) |
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (/ (* (+ x (* -1 x)) (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4))) eps) (/ (* (pow x 4) (+ x (* -1 x))) eps)) (+ (* (pow x 2) (pow (+ x (* -1 x)) 2)) (pow x 4))) eps)) (* (pow x 2) (+ x (* -1 x)))) eps)) (* -1 (pow x 2))) (pow eps 2)) |
(/.f64 (neg.f64 (fma.f64 x x (/.f64 (fma.f64 (/.f64 (-.f64 (-.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64) #s(literal 0 binary64))) eps) #s(literal 0 binary64)) (pow.f64 x #s(literal 4 binary64))) eps) #s(literal -1 binary64) #s(literal 0 binary64)) eps))) (*.f64 eps eps)) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* -1 (* eps (- (* -1 (/ (- (/ (pow x 2) eps) (* -1 x)) eps)) 1))) |
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (fma.f64 (/.f64 x eps) x x) (neg.f64 eps)) #s(literal 1 binary64))) |
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow x 3) eps)) (pow x 2)) eps)) (* -1 x)) eps)) 1))) |
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 eps)) (*.f64 x x)) eps) #s(literal -1 binary64) x) (neg.f64 eps)) #s(literal 1 binary64))) |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 39 | 209 |
| 0 | 68 | 201 |
| 1 | 270 | 177 |
| 2 | 2628 | 141 |
| 0 | 8334 | 141 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(+.f64 #s(literal 0 binary64) eps) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(sin.f64 eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 (sin.f64 x) eps) |
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(-.f64 (sin.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) (sin.f64 x)) |
(sin.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) |
(/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) |
(/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)) |
| Outputs |
|---|
(pow.f64 eps #s(literal 1 binary64)) |
(/.f64 (neg.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (*.f64 eps eps)) |
(/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (*.f64 (neg.f64 eps) eps)) |
(/.f64 (*.f64 (neg.f64 eps) eps) (neg.f64 (-.f64 eps #s(literal 0 binary64)))) |
(/.f64 (*.f64 (neg.f64 eps) eps) (neg.f64 (neg.f64 (neg.f64 eps)))) |
(/.f64 (*.f64 (neg.f64 eps) eps) (neg.f64 eps)) |
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps)) |
(/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64))) |
(/.f64 (*.f64 eps eps) (neg.f64 (neg.f64 eps))) |
(/.f64 (*.f64 eps eps) eps) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps)) (neg.f64 eps)) |
(-.f64 eps (/.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64)))) |
(-.f64 eps (/.f64 #s(literal 0 binary64) (neg.f64 eps))) |
(+.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) eps) |
(+.f64 eps #s(literal 0 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
eps |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64)))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64))))))) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64)) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x #s(literal 2 binary64)) #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) eps))) #s(literal -4 binary64)) |
(/.f64 (-.f64 (pow.f64 (*.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64))) (/.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64)))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps))) #s(literal -2 binary64)) |
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 eps eps))) (neg.f64 (*.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64)))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal -2 binary64)))) |
(/.f64 (fma.f64 (*.f64 x #s(literal 2 binary64)) #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) eps)) #s(literal 4 binary64)) |
(/.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 eps eps)) (*.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal -2 binary64))) |
(/.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 2 binary64)) |
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64)) |
(neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) |
(fma.f64 x #s(literal -1 binary64) (/.f64 eps #s(literal -2 binary64))) |
(fma.f64 #s(literal 2 binary64) (/.f64 x #s(literal -2 binary64)) (/.f64 eps #s(literal -2 binary64))) |
(-.f64 (/.f64 (pow.f64 (*.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (/.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64))) (/.f64 (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64)) (/.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64)))) |
(-.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64))) (/.f64 (*.f64 eps eps) (*.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64)))) |
(-.f64 (/.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) #s(literal -2 binary64)) (/.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) #s(literal -2 binary64))) |
(-.f64 (/.f64 eps #s(literal -2 binary64)) (/.f64 (*.f64 (neg.f64 x) #s(literal 2 binary64)) #s(literal -2 binary64))) |
(-.f64 (/.f64 eps #s(literal -2 binary64)) (/.f64 (*.f64 #s(literal -2 binary64) x) #s(literal -2 binary64))) |
(+.f64 (/.f64 eps #s(literal -2 binary64)) (*.f64 x #s(literal -1 binary64))) |
(+.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64))) |
(*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) |
(*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64))) |
(*.f64 (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))) |
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))))) |
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) |
(+.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(fma.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (cos.f64 eps) (*.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (sin.f64 eps))) |
(fma.f64 (sin.f64 eps) #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 0 binary64))) |
(fma.f64 #s(literal 0 binary64) (cos.f64 eps) (*.f64 #s(literal 1 binary64) (sin.f64 eps))) |
(sin.f64 eps) |
(-.f64 (*.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps))) (cos.f64 eps)) (*.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps))) (sin.f64 (neg.f64 eps)))) |
(+.f64 (*.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (cos.f64 eps)) (*.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (sin.f64 eps))) |
(+.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 eps) #s(literal 0 binary64))) |
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 eps)) (*.f64 #s(literal 1 binary64) (sin.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
(*.f64 (cos.f64 x) eps) |
(*.f64 eps (cos.f64 x)) |
(/.f64 (neg.f64 (*.f64 (*.f64 (neg.f64 eps) eps) (cos.f64 x))) (neg.f64 (neg.f64 eps))) |
(/.f64 (neg.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (cos.f64 x))) (*.f64 (neg.f64 eps) eps)) |
(/.f64 (neg.f64 (*.f64 (cos.f64 x) (*.f64 (neg.f64 eps) eps))) (neg.f64 (neg.f64 eps))) |
(/.f64 (neg.f64 (*.f64 (cos.f64 x) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (neg.f64 eps) eps)) |
(/.f64 (*.f64 (*.f64 (neg.f64 eps) eps) (cos.f64 x)) (neg.f64 eps)) |
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (cos.f64 x)) (*.f64 eps eps)) |
(/.f64 (*.f64 (cos.f64 x) (*.f64 (neg.f64 eps) eps)) (neg.f64 eps)) |
(/.f64 (*.f64 (cos.f64 x) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)) |
(fma.f64 (cos.f64 x) eps (*.f64 #s(literal 0 binary64) (cos.f64 x))) |
(fma.f64 (cos.f64 x) eps (*.f64 (cos.f64 x) #s(literal 0 binary64))) |
(fma.f64 (cos.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) eps)) |
(fma.f64 eps (cos.f64 x) (*.f64 #s(literal 0 binary64) (cos.f64 x))) |
(fma.f64 eps (cos.f64 x) (*.f64 (cos.f64 x) #s(literal 0 binary64))) |
(fma.f64 #s(literal 0 binary64) (cos.f64 x) (*.f64 (cos.f64 x) eps)) |
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 x)) (*.f64 (cos.f64 x) eps)) |
(+.f64 (*.f64 (cos.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) eps)) |
(+.f64 (*.f64 (cos.f64 x) eps) (*.f64 #s(literal 0 binary64) (cos.f64 x))) |
(+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (cos.f64 x) #s(literal 0 binary64))) |
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64))) |
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64))) |
(sin.f64 (+.f64 (neg.f64 (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) |
(cos.f64 (neg.f64 (neg.f64 (neg.f64 x)))) |
(cos.f64 (neg.f64 (neg.f64 x))) |
(cos.f64 (neg.f64 x)) |
(cos.f64 x) |
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))) |
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
(+.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) eps) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) eps)) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps))))))) |
(/.f64 (neg.f64 (*.f64 (*.f64 (neg.f64 eps) eps) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)))) (neg.f64 (neg.f64 eps))) |
(/.f64 (neg.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)))) (*.f64 (neg.f64 eps) eps)) |
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) (*.f64 (neg.f64 eps) eps))) (neg.f64 (neg.f64 eps))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (neg.f64 eps) eps)) |
(/.f64 (neg.f64 (*.f64 eps (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x)))) |
(/.f64 (neg.f64 (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps))))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (neg.f64 eps) eps))) (neg.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x)) (neg.f64 eps)))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x)) (*.f64 eps eps)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (neg.f64 eps) eps))) (neg.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps))))) (neg.f64 eps)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps))))) (*.f64 eps eps)))) |
(/.f64 (neg.f64 (*.f64 (*.f64 (neg.f64 eps) eps) (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (neg.f64 (*.f64 (neg.f64 eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x))))) |
(/.f64 (neg.f64 (*.f64 (*.f64 (neg.f64 eps) eps) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (neg.f64 (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)))))))) |
(/.f64 (neg.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (neg.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x))))) |
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(-.f64 (*.f64 (sin.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (*.f64 (neg.f64 (neg.f64 eps)) (/.f64 eps (-.f64 x eps))))) (*.f64 (cos.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (*.f64 (neg.f64 (neg.f64 eps)) (/.f64 eps (-.f64 x eps)))))) |
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps))) |
(-.f64 (*.f64 (cos.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))) (sin.f64 (*.f64 x (/.f64 x (-.f64 x eps))))) (*.f64 (cos.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))) (sin.f64 (*.f64 x (/.f64 x (-.f64 x eps))))) (*.f64 (cos.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))) (sin.f64 (*.f64 x (/.f64 x (-.f64 x eps))))) (*.f64 (cos.f64 (fma.f64 x (/.f64 x (-.f64 x eps)) (PI.f64))) (neg.f64 (sin.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))))) |
(+.f64 (*.f64 (sin.f64 (+.f64 x #s(literal 0 binary64))) (cos.f64 eps)) (*.f64 (cos.f64 (+.f64 x #s(literal 0 binary64))) (sin.f64 eps))) |
(+.f64 (*.f64 (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 x eps) x (*.f64 eps eps)))) (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x eps) x (*.f64 eps eps))))) (*.f64 (cos.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 x eps) x (*.f64 eps eps)))) (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x eps) x (*.f64 eps eps)))))) |
(+.f64 (*.f64 (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (cos.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))) (*.f64 (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))))) |
(+.f64 (*.f64 (sin.f64 (+.f64 x eps)) #s(literal 1 binary64)) (*.f64 (cos.f64 (+.f64 x eps)) #s(literal 0 binary64))) |
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 (+.f64 #s(literal 0 binary64) x))) (*.f64 (cos.f64 eps) (sin.f64 (+.f64 #s(literal 0 binary64) x)))) |
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (+.f64 x eps))) (*.f64 #s(literal 1 binary64) (sin.f64 (+.f64 x eps)))) |
(+.f64 (*.f64 (sin.f64 (fma.f64 (/.f64 eps (-.f64 x eps)) (neg.f64 eps) (*.f64 (*.f64 eps (/.f64 x (-.f64 x eps))) (/.f64 x (+.f64 x eps))))) (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 (+.f64 x eps) (-.f64 x eps))))) (*.f64 (cos.f64 (fma.f64 (/.f64 eps (-.f64 x eps)) (neg.f64 eps) (*.f64 (*.f64 eps (/.f64 x (-.f64 x eps))) (/.f64 x (+.f64 x eps))))) (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 (+.f64 x eps) (-.f64 x eps)))))) |
(+.f64 (*.f64 (sin.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 eps (-.f64 x eps)) (neg.f64 eps)) (/.f64 (-.f64 (*.f64 (neg.f64 eps) eps) (*.f64 x x)) (-.f64 x eps)) (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64))))) (cos.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 eps (-.f64 x eps)) (neg.f64 eps)) (/.f64 (-.f64 (*.f64 (neg.f64 eps) eps) (*.f64 x x)) (-.f64 x eps)) (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)))))) (*.f64 (cos.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 eps (-.f64 x eps)) (neg.f64 eps)) (/.f64 (-.f64 (*.f64 (neg.f64 eps) eps) (*.f64 x x)) (-.f64 x eps)) (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64))))) (sin.f64 (/.f64 (neg.f64 (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 eps (-.f64 x eps)) (neg.f64 eps)) (/.f64 (-.f64 (*.f64 (neg.f64 eps) eps) (*.f64 x x)) (-.f64 x eps)) (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64))))))) |
(+.f64 (*.f64 (sin.f64 (*.f64 (*.f64 eps (/.f64 x (-.f64 x eps))) (/.f64 x (+.f64 x eps)))) (cos.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (*.f64 (/.f64 eps (-.f64 x eps)) (neg.f64 eps))))) (*.f64 (cos.f64 (*.f64 (*.f64 eps (/.f64 x (-.f64 x eps))) (/.f64 x (+.f64 x eps)))) (sin.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (*.f64 (/.f64 eps (-.f64 x eps)) (neg.f64 eps)))))) |
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (sin.f64 x))) |
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(+.f64 (*.f64 (neg.f64 (sin.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) (cos.f64 (*.f64 x (/.f64 x (-.f64 x eps))))) (*.f64 (cos.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))) (sin.f64 (*.f64 x (/.f64 x (-.f64 x eps)))))) |
(+.f64 (*.f64 (cos.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))) (sin.f64 (*.f64 x (/.f64 x (-.f64 x eps))))) (*.f64 (neg.f64 (sin.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) (cos.f64 (*.f64 x (/.f64 x (-.f64 x eps)))))) |
(*.f64 (/.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (fma.f64 eps eps (*.f64 (neg.f64 x) x))) (-.f64 eps x)) |
(*.f64 (/.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 (+.f64 x eps) (-.f64 x eps))) (-.f64 x eps)) |
(*.f64 (/.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 x eps) x (*.f64 eps eps))) |
(*.f64 (/.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) |
(*.f64 (/.f64 (neg.f64 x) (+.f64 x eps)) (/.f64 (neg.f64 x) (-.f64 x eps))) |
(*.f64 (/.f64 (neg.f64 x) (-.f64 x eps)) (/.f64 (neg.f64 x) (+.f64 x eps))) |
(*.f64 (/.f64 (/.f64 x (+.f64 x eps)) (-.f64 x eps)) x) |
(*.f64 (/.f64 x (+.f64 x eps)) (/.f64 x (-.f64 x eps))) |
(*.f64 (/.f64 x (-.f64 x eps)) (/.f64 x (+.f64 x eps))) |
(*.f64 (neg.f64 x) (/.f64 (neg.f64 x) (*.f64 (+.f64 x eps) (-.f64 x eps)))) |
(*.f64 x (/.f64 (/.f64 x (+.f64 x eps)) (-.f64 x eps))) |
(/.f64 (neg.f64 (*.f64 x (/.f64 x (+.f64 x eps)))) (neg.f64 (-.f64 x eps))) |
(/.f64 (neg.f64 (*.f64 (/.f64 x (-.f64 x eps)) x)) (neg.f64 (+.f64 x eps))) |
(/.f64 (neg.f64 (/.f64 (*.f64 x x) (+.f64 x eps))) (neg.f64 (-.f64 x eps))) |
(/.f64 (neg.f64 (neg.f64 (*.f64 x (/.f64 x (-.f64 x eps))))) (neg.f64 (neg.f64 (+.f64 x eps)))) |
(/.f64 (*.f64 x (/.f64 x (+.f64 x eps))) (-.f64 x eps)) |
(/.f64 (*.f64 (/.f64 x (-.f64 x eps)) x) (+.f64 x eps)) |
(/.f64 (/.f64 (*.f64 x x) (+.f64 x eps)) (-.f64 x eps)) |
(/.f64 (neg.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (neg.f64 (+.f64 x eps))) |
(/.f64 (*.f64 (neg.f64 x) x) (neg.f64 (neg.f64 (*.f64 (neg.f64 (+.f64 x eps)) (-.f64 x eps))))) |
(/.f64 (*.f64 (neg.f64 x) x) (*.f64 (neg.f64 (+.f64 x eps)) (-.f64 x eps))) |
(/.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (+.f64 x eps)) |
(/.f64 (*.f64 x x) (neg.f64 (*.f64 (neg.f64 (+.f64 x eps)) (-.f64 x eps)))) |
(/.f64 (*.f64 x x) (*.f64 (+.f64 x eps) (-.f64 x eps))) |
(neg.f64 (/.f64 (*.f64 (neg.f64 x) x) (*.f64 (+.f64 x eps) (-.f64 x eps)))) |
(-.f64 (/.f64 (*.f64 (*.f64 eps (/.f64 x (-.f64 x eps))) (/.f64 x (+.f64 x eps))) (+.f64 x eps)) (/.f64 (*.f64 (neg.f64 x) (*.f64 (/.f64 x (+.f64 x eps)) (/.f64 x (-.f64 x eps)))) (+.f64 x eps))) |
(-.f64 (/.f64 (*.f64 (*.f64 eps (/.f64 x (-.f64 x eps))) (/.f64 x (+.f64 x eps))) (+.f64 x eps)) (/.f64 (*.f64 (neg.f64 (*.f64 (/.f64 x (+.f64 x eps)) (/.f64 x (-.f64 x eps)))) x) (+.f64 x eps))) |
(fma.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 (+.f64 eps (neg.f64 (PI.f64))) #s(literal -2 binary64))) (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64))))) |
(fma.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (*.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))))) |
(fma.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(fma.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(sin.f64 (/.f64 (+.f64 (fma.f64 x #s(literal 2 binary64) eps) (PI.f64)) #s(literal 2 binary64))) |
(sin.f64 (/.f64 (+.f64 (neg.f64 (PI.f64)) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal -2 binary64))) |
(-.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x eps) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (sin.f64 (/.f64 (+.f64 x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64))))) |
(-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (*.f64 (sin.f64 (neg.f64 (*.f64 x #s(literal -1 binary64)))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (*.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64))))) |
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) |
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) |
(+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 (+.f64 eps (neg.f64 (PI.f64))) #s(literal -2 binary64)))) (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64))))) |
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))) (*.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))))) |
(+.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 0 binary64)) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(+.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) #s(literal 0 binary64)) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(neg.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64)))) |
(fma.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64) (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) #s(literal 0 binary64))) |
(fma.f64 #s(literal 0 binary64) (cos.f64 (/.f64 eps #s(literal -2 binary64))) (*.f64 #s(literal 1 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64))))) |
(sin.f64 (/.f64 eps #s(literal 2 binary64))) |
(+.f64 (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) #s(literal 0 binary64))) |
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (*.f64 #s(literal 1 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64))))) |
(*.f64 (/.f64 (*.f64 (neg.f64 eps) eps) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps)) |
(*.f64 (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 x x (*.f64 eps (+.f64 x eps)))) |
(*.f64 (/.f64 eps (-.f64 x eps)) (neg.f64 eps)) |
(*.f64 (neg.f64 eps) (/.f64 eps (-.f64 x eps))) |
(*.f64 eps (/.f64 (neg.f64 eps) (-.f64 x eps))) |
(/.f64 (*.f64 (neg.f64 eps) eps) (neg.f64 (neg.f64 (-.f64 x eps)))) |
(/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)) |
(/.f64 (*.f64 eps eps) (neg.f64 (neg.f64 (neg.f64 (-.f64 x eps))))) |
(/.f64 (*.f64 eps eps) (neg.f64 (-.f64 x eps))) |
(neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))) |
(neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (neg.f64 (-.f64 x eps)))) (/.f64 (*.f64 eps eps) (-.f64 x eps))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) |
(-.f64 (*.f64 (/.f64 eps (-.f64 x eps)) (neg.f64 eps)) (/.f64 #s(literal 0 binary64) (-.f64 x eps))) |
Compiled 16 922 to 2 492 computations (85.3% saved)
12 alts after pruning (11 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 551 | 11 | 562 |
| Fresh | 1 | 0 | 1 |
| Picked | 5 | 0 | 5 |
| Done | 0 | 1 | 1 |
| Total | 557 | 12 | 569 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 63.4% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 63.4% | (*.f64 (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| 99.9% | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| 99.8% | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| ▶ | 99.6% | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| 99.6% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| ▶ | 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
| ▶ | 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
| 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) | |
| ▶ | 98.9% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
| 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) | |
| ▶ | 100.0% | #s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
Compiled 545 to 394 computations (27.7% saved)
| 1× | egg-herbie |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) | |
| cost-diff | 0 | (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| cost-diff | 1 | (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) | |
| cost-diff | 0 | #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) | |
| cost-diff | 1 | (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) | |
| cost-diff | 0 | #s(approx (cos x) #s(literal 1 binary64)) | |
| cost-diff | 0 | (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) | |
| cost-diff | 0 | (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) | |
| cost-diff | 0 | (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) | |
| cost-diff | 0 | #s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 57 | 385 |
| 0 | 83 | 377 |
| 1 | 148 | 377 |
| 2 | 346 | 377 |
| 3 | 969 | 373 |
| 4 | 2189 | 373 |
| 5 | 5567 | 373 |
| 0 | 8185 | 361 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
#s(literal 1/2 binary64) |
eps |
x |
#s(literal 2 binary64) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) |
#s(approx (cos x) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) |
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) |
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) |
(+.f64 x eps) |
x |
eps |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)) |
(fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) |
(-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) |
#s(literal 1/12 binary64) |
(*.f64 x eps) |
x |
eps |
#s(literal 1/2 binary64) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
eps |
#s(literal 2 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(fma.f64 #s(literal 2 binary64) x eps) |
x |
#s(literal -2 binary64) |
| Outputs |
|---|
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
#s(literal 1/2 binary64) |
eps |
x |
#s(literal 2 binary64) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) |
#s(approx (cos x) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) |
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) |
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) |
(+.f64 x eps) |
x |
eps |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)) |
(fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) |
(fma.f64 (fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) |
(-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) |
(*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) |
(*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) |
#s(literal 1/12 binary64) |
(*.f64 x eps) |
x |
eps |
#s(literal 1/2 binary64) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) x)) (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
eps |
#s(literal 2 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) x)) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(-.f64 (/.f64 eps #s(literal -2 binary64)) x) |
(fma.f64 #s(literal 2 binary64) x eps) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal -2 binary64) |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) | |
| accuracy | 0.00390625 | (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) | |
| accuracy | 0.0078125 | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| accuracy | 0.21729739721033986 | #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) | |
| accuracy | 0.00390625 | (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps) | |
| accuracy | 0.19921875 | (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) | |
| accuracy | 0.2327750091963896 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) | |
| accuracy | 0.299885905967568 | #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) | |
| accuracy | 0.0 | (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) | |
| accuracy | 0.00390625 | (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps) | |
| accuracy | 0.2327750091963896 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) | |
| accuracy | 0.29538621278819543 | #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) | |
| accuracy | 0.0078125 | (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) | |
| accuracy | 0.3177879892086317 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) | |
| accuracy | 0.7257269072635404 | #s(approx (cos x) #s(literal 1 binary64)) | |
| accuracy | 0.0 | (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) | |
| accuracy | 0.0 | (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) | |
| accuracy | 0.0 | #s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) | |
| accuracy | 0.01171875 | (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
| 78.0ms | 170× | 0 | valid |
| 74.0ms | 86× | 1 | valid |
Compiled 265 to 47 computations (82.3% saved)
ival-mult: 57.0ms (59.2% of total)ival-add: 10.0ms (10.4% of total)adjust: 7.0ms (7.3% of total)ival-sin: 7.0ms (7.3% of total)ival-cos: 5.0ms (5.2% of total)const: 4.0ms (4.2% of total)ival-div: 3.0ms (3.1% of total)ival-sub: 3.0ms (3.1% of total)exact: 1.0ms (1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) |
#s(approx (cos x) #s(literal 1 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) |
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) |
(-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) |
(*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
| Outputs |
|---|
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2)))))))) |
(* 2 (cos (* 1/2 eps))) |
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps)))) |
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps))))))) |
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps))))))))) |
(cos (* 1/2 eps)) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
-1/2 |
(- (* 1/12 (* eps x)) 1/2) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1/2 eps) (* -1/2 x)) |
(* 1/12 (* eps x)) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (cos (+ x (* 1/2 eps)))) |
(cos (+ x (* 1/2 eps))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(cos x) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(* x (- (* 1/12 eps) (* 1/2 (/ 1 x)))) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* -1/2 x) |
(* x (- (* -1/2 (/ eps x)) 1/2)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(* 2 (cos (- (* 1/2 eps) (* -1 x)))) |
(cos (- (* 1/2 eps) (* -1 x))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x))))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x))))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(* 2 (cos x)) |
(+ (* -1 (* eps (sin x))) (* 2 (cos x))) |
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x)))))) |
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x)))))))) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps x)) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* eps (- (* 1/12 x) (* 1/2 (/ 1 eps)))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* 2 (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(* eps (- (* -1/2 (/ x eps)) 1/2)) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (cos (- x (* -1/2 eps)))) |
(cos (- x (* -1/2 eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps))))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps))))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 46.0ms | eps | @ | 0 | ((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (* 1/12 (* x eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (sin (* 1/2 eps)) (* (+ x eps) -1/2) (* 1/12 (* x eps)) (cos (/ (+ (* 2 x) eps) -2))) |
| 7.0ms | x | @ | inf | ((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (* 1/12 (* x eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (sin (* 1/2 eps)) (* (+ x eps) -1/2) (* 1/12 (* x eps)) (cos (/ (+ (* 2 x) eps) -2))) |
| 4.0ms | eps | @ | -inf | ((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (* 1/12 (* x eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (sin (* 1/2 eps)) (* (+ x eps) -1/2) (* 1/12 (* x eps)) (cos (/ (+ (* 2 x) eps) -2))) |
| 4.0ms | eps | @ | inf | ((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (* 1/12 (* x eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (sin (* 1/2 eps)) (* (+ x eps) -1/2) (* 1/12 (* x eps)) (cos (/ (+ (* 2 x) eps) -2))) |
| 3.0ms | x | @ | -inf | ((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* (+ x eps) -1/2) x) 1) (- (* 1/12 (* x eps)) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (sin (* 1/2 eps)) (* (+ x eps) -1/2) (* 1/12 (* x eps)) (cos (/ (+ (* 2 x) eps) -2))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 443 | 1579 |
| 1 | 1645 | 1502 |
| 2 | 5680 | 1473 |
| 0 | 8474 | 1352 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2)))))))) |
(* 2 (cos (* 1/2 eps))) |
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps)))) |
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps))))))) |
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps))))))))) |
(cos (* 1/2 eps)) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
-1/2 |
(- (* 1/12 (* eps x)) 1/2) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1/2 eps) (* -1/2 x)) |
(* 1/12 (* eps x)) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (cos (+ x (* 1/2 eps)))) |
(cos (+ x (* 1/2 eps))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(cos x) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(* x (- (* 1/12 eps) (* 1/2 (/ 1 x)))) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* -1/2 x) |
(* x (- (* -1/2 (/ eps x)) 1/2)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(* 2 (cos (- (* 1/2 eps) (* -1 x)))) |
(cos (- (* 1/2 eps) (* -1 x))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x))))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x))))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(* 2 (cos x)) |
(+ (* -1 (* eps (sin x))) (* 2 (cos x))) |
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x)))))) |
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x)))))))) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps x)) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* eps (- (* 1/12 x) (* 1/2 (/ 1 eps)))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* 2 (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(* eps (- (* -1/2 (/ x eps)) 1/2)) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (cos (- x (* -1/2 eps)))) |
(cos (- x (* -1/2 eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps))))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps))))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
| Outputs |
|---|
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(fma.f64 (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) x (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64) (*.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(*.f64 #s(literal -2 binary64) (fma.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))) |
(fma.f64 (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) x (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2)))))))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64) (*.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))))) |
(* 2 (cos (* 1/2 eps))) |
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps)))) |
(*.f64 #s(literal -2 binary64) (-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps))))))) |
(fma.f64 (fma.f64 (neg.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64))) x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (PI.f64)))) x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64))) x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(cos (* 1/2 eps)) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 x eps) eps) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps) |
1 |
#s(literal 1 binary64) |
(+ 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 (-.f64 (*.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 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps eps) eps) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(fma.f64 (fma.f64 (*.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) x)) x)) x eps) |
(+ 1 (* -1/2 (* eps x))) |
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)) |
-1/2 |
#s(literal -1/2 binary64) |
(- (* 1/12 (* eps x)) 1/2) |
(-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) |
(* -1/2 eps) |
(*.f64 #s(literal -1/2 binary64) eps) |
(+ (* -1 x) (* -1/2 eps)) |
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) |
(+ (* -1/2 eps) (* -1/2 x)) |
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) |
(* 1/12 (* eps x)) |
(*.f64 (*.f64 #s(literal 1/12 binary64) x) eps) |
(cos (* -1/2 eps)) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* 2 (cos (+ x (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(cos (+ x (* 1/2 eps))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* eps (cos x)) |
(*.f64 (cos.f64 x) eps) |
(cos x) |
(cos.f64 x) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) |
(* -1/2 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/2 binary64)) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(*.f64 (*.f64 (-.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) x) x) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (*.f64 x x)) |
(* x (- (* 1/12 eps) (* 1/2 (/ 1 x)))) |
(*.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) x) |
(* -1 x) |
(neg.f64 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(*.f64 (-.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x) |
(* -1/2 x) |
(*.f64 #s(literal -1/2 binary64) x) |
(* x (- (* -1/2 (/ eps x)) 1/2)) |
(*.f64 (-.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) x) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* 2 (cos (- (* 1/2 eps) (* -1 x)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(*.f64 (-.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1 binary64) x)) (neg.f64 x)) #s(literal 1/2 binary64)) (*.f64 x x)) |
(* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x))))) |
(*.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) x) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) x (neg.f64 x)) |
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x))))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* eps (cos (* -1 x))) |
(*.f64 (cos.f64 x) eps) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* 2 (cos x)) |
(*.f64 (cos.f64 x) #s(literal 2 binary64)) |
(+ (* -1 (* eps (sin x))) (* 2 (cos x))) |
(fma.f64 (neg.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps (*.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x)))))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (neg.f64 (sin.f64 x))) eps (*.f64 (cos.f64 x) #s(literal 2 binary64))) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/48 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/8 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (*.f64 #s(literal 1/2 binary64) eps)) |
(cos (* -1 x)) |
(cos.f64 x) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/48 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/8 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) |
(* -1/2 (* eps x)) |
(*.f64 (*.f64 x eps) #s(literal -1/2 binary64)) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) |
(* eps (- (* 1/12 x) (* 1/2 (/ 1 eps)))) |
(*.f64 (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) eps) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps) |
(* 2 (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(* eps (- (* -1/2 (/ x eps)) 1/2)) |
(*.f64 (-.f64 (*.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) eps) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* 2 (cos (- x (* -1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(cos (- x (* -1/2 eps))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) |
(* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps))))) |
(*.f64 (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) eps) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64))) |
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps))))) |
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 57 | 314 |
| 0 | 83 | 306 |
| 1 | 288 | 306 |
| 2 | 2186 | 306 |
| 0 | 8253 | 300 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) |
#s(approx (cos x) #s(literal 1 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) |
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) |
(-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) |
(*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
| Outputs |
|---|
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(/.f64 (fma.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))) (cos.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (-.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))))) (*.f64 (cos.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))))) |
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(fma.f64 (*.f64 #s(literal 1/12 binary64) eps) x (*.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64))) |
(fma.f64 (*.f64 #s(literal 1/12 binary64) x) eps (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x))) |
(fma.f64 (*.f64 #s(literal 1/12 binary64) x) eps (*.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64))) |
(fma.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64) (*.f64 (*.f64 x eps) #s(literal 1/12 binary64))) |
(fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x))) |
(fma.f64 (*.f64 x eps) #s(literal 1/12 binary64) (*.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64))) |
(fma.f64 #s(literal 1/12 binary64) (*.f64 x eps) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x))) |
(fma.f64 #s(literal 1/12 binary64) (*.f64 x eps) (*.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64))) |
(fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x))) |
(fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) (*.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64))) |
(fma.f64 eps (*.f64 #s(literal 1/12 binary64) x) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x))) |
(fma.f64 eps (*.f64 #s(literal 1/12 binary64) x) (*.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64))) |
(fma.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x) (*.f64 (*.f64 x eps) #s(literal 1/12 binary64))) |
(+.f64 (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x)) (*.f64 (*.f64 x eps) #s(literal 1/12 binary64))) |
(+.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64)) (*.f64 (*.f64 x eps) #s(literal 1/12 binary64))) |
(+.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/12 binary64) x))) |
(+.f64 (*.f64 (*.f64 x eps) #s(literal 1/12 binary64)) (*.f64 (*.f64 #s(literal 1/12 binary64) x) #s(literal 0 binary64))) |
(fma.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal 2 binary64))))) |
(fma.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(fma.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(fma.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (*.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))))) |
(sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))) |
(-.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x eps) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (sin.f64 (/.f64 (+.f64 x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64))))) |
(-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) (*.f64 (sin.f64 (neg.f64 (*.f64 x #s(literal -1 binary64)))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) (*.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64))))) |
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) |
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) |
(+.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 0 binary64)) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal 2 binary64))))) |
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))) (*.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))))) |
(+.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) #s(literal 0 binary64)) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
Compiled 14 746 to 1 919 computations (87% saved)
14 alts after pruning (9 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 379 | 3 | 382 |
| Fresh | 0 | 6 | 6 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 1 | 1 |
| Total | 380 | 14 | 394 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 63.4% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 63.4% | (*.f64 (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| ▶ | 99.9% | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| ▶ | 99.8% | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| 99.6% | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) | |
| ▶ | 99.6% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| ✓ | 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
| ✓ | 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
| ▶ | 99.2% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
| 50.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (*.f64 x x)))) eps)) | |
| 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) | |
| ✓ | 98.9% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
| ▶ | 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
| ✓ | 100.0% | #s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
Compiled 626 to 433 computations (30.8% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) | |
| cost-diff | 0 | (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| cost-diff | 1 | (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) | |
| cost-diff | 0 | #s(approx (* (sin x) eps) (*.f64 x eps)) | |
| cost-diff | 0 | (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) | |
| cost-diff | 0 | (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| cost-diff | 0 | #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) | |
| cost-diff | 5 | (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) | |
| cost-diff | 0 | (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps) | |
| cost-diff | 0 | #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps)) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) | |
| cost-diff | 0 | (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| cost-diff | 1 | (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) | |
| cost-diff | 1 | (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 62 | 533 |
| 0 | 95 | 521 |
| 1 | 179 | 521 |
| 2 | 565 | 521 |
| 3 | 2298 | 515 |
| 4 | 5287 | 495 |
| 0 | 8284 | 477 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) |
(-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) |
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) |
#s(literal 1/3840 binary64) |
(*.f64 eps eps) |
eps |
#s(literal 1/48 binary64) |
#s(literal 1/2 binary64) |
#s(literal 2 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(fma.f64 #s(literal 2 binary64) x eps) |
x |
#s(literal -2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
#s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps)) |
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps) |
(*.f64 (*.f64 #s(literal -1/2 binary64) x) x) |
(*.f64 #s(literal -1/2 binary64) x) |
#s(literal -1/2 binary64) |
x |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) |
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) |
(fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) |
#s(literal -1/2 binary64) |
x |
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(*.f64 x x) |
#s(literal 1 binary64) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) |
#s(approx (* (sin x) eps) (*.f64 x eps)) |
(*.f64 x eps) |
x |
eps |
#s(literal -1/2 binary64) |
(cos.f64 x) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) |
#s(literal -1/48 binary64) |
(*.f64 eps eps) |
eps |
#s(literal 1/2 binary64) |
#s(literal 2 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(fma.f64 #s(literal 2 binary64) x eps) |
x |
#s(literal -2 binary64) |
| Outputs |
|---|
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) x)) (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))) |
(*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
(*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) |
(-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) |
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) |
#s(literal 1/3840 binary64) |
(*.f64 eps eps) |
eps |
#s(literal 1/48 binary64) |
#s(literal 1/2 binary64) |
#s(literal 2 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) x)) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(-.f64 (/.f64 eps #s(literal -2 binary64)) x) |
(fma.f64 #s(literal 2 binary64) x eps) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal -2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
#s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps)) |
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps) |
(*.f64 (*.f64 #s(literal -1/2 binary64) x) x) |
(*.f64 #s(literal -1/2 binary64) x) |
#s(literal -1/2 binary64) |
x |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)))) |
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)) |
#s(approx (+ (* (* (+ x eps) -1/2) x) 1) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)) |
(fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) |
(fma.f64 (fma.f64 (/.f64 x eps) x x) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) |
#s(literal -1/2 binary64) |
x |
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(*.f64 x x) |
#s(literal 1 binary64) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) |
#s(approx (* (sin x) eps) (*.f64 x eps)) |
(*.f64 x eps) |
x |
eps |
#s(literal -1/2 binary64) |
(cos.f64 x) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) x))) |
(*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) |
#s(literal -1/48 binary64) |
(*.f64 eps eps) |
eps |
#s(literal 1/2 binary64) |
#s(literal 2 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(cos.f64 (-.f64 (/.f64 eps #s(literal -2 binary64)) x)) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(-.f64 (/.f64 eps #s(literal -2 binary64)) x) |
(fma.f64 #s(literal 2 binary64) x eps) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal -2 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) | |
| accuracy | 0.00390625 | (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) | |
| accuracy | 0.0078125 | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| accuracy | 0.10014688581320413 | #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) | |
| accuracy | 0.00390625 | (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) | |
| accuracy | 0.00390625 | (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps) | |
| accuracy | 0.2327750091963896 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| accuracy | 0.6672982103155396 | #s(approx (* (sin x) eps) (*.f64 x eps)) | |
| accuracy | 0.0078125 | (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) | |
| accuracy | 0.20703125 | (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) | |
| accuracy | 0.2327750091963896 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) | |
| accuracy | 0.29538621278819543 | #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) | |
| accuracy | 0.0 | (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) | |
| accuracy | 0.0 | (*.f64 #s(literal -1/2 binary64) x) | |
| accuracy | 0.2892473504245106 | #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps)) | |
| accuracy | 0.3177879892086317 | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) | |
| accuracy | 0.0078125 | (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) | |
| accuracy | 0.0078125 | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| accuracy | 0.04087713183724195 | #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) | |
| accuracy | 0.10546875 | (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) |
| 57.0ms | 170× | 0 | valid |
| 51.0ms | 86× | 1 | valid |
Compiled 336 to 55 computations (83.6% saved)
ival-mult: 32.0ms (39.6% of total)ival-add: 12.0ms (14.8% of total)const: 10.0ms (12.4% of total)adjust: 8.0ms (9.9% of total)ival-sin: 6.0ms (7.4% of total)ival-div: 5.0ms (6.2% of total)ival-cos: 4.0ms (4.9% of total)ival-sub: 3.0ms (3.7% of total)exact: 1.0ms (1.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
#s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps)) |
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps) |
(*.f64 (*.f64 #s(literal -1/2 binary64) x) x) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) |
#s(approx (* (sin x) eps) (*.f64 x eps)) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) |
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 #s(literal -1/2 binary64) x) |
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
| Outputs |
|---|
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
(* -1/2 (pow x 2)) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(* eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
(* -1/2 x) |
(/ 1 eps) |
(+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(* -1/2 (* eps (pow x 2))) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* eps (sin x)) |
(* -1/2 (/ (pow x 2) eps)) |
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 eps)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(cos (* -1/2 (- eps (* -2 x)))) |
-1/48 |
(- (* 1/3840 (pow eps 2)) 1/48) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(cos x) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* 1/3840 (pow eps 2)) |
(/ (+ 1 (* -1/2 (pow x 2))) eps) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* 2 (sin (* 1/2 eps))) |
(* -1/2 (* eps x)) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(sin (* 1/2 eps)) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1 (* eps (- (* 1/2 (pow x 2)) 1))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 17.0ms | eps | @ | inf | ((- (* 1/3840 (* eps eps)) 1/48) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* -1/2 x) x) eps) eps) (* (* -1/2 x) x) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* 1/3840 (* eps eps)) (sin (/ (+ 0 eps) 2)) (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps) (cos (/ (+ (* 2 x) eps) -2))) |
| 5.0ms | eps | @ | -inf | ((- (* 1/3840 (* eps eps)) 1/48) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* -1/2 x) x) eps) eps) (* (* -1/2 x) x) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* 1/3840 (* eps eps)) (sin (/ (+ 0 eps) 2)) (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps) (cos (/ (+ (* 2 x) eps) -2))) |
| 4.0ms | eps | @ | 0 | ((- (* 1/3840 (* eps eps)) 1/48) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* -1/2 x) x) eps) eps) (* (* -1/2 x) x) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* 1/3840 (* eps eps)) (sin (/ (+ 0 eps) 2)) (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps) (cos (/ (+ (* 2 x) eps) -2))) |
| 3.0ms | x | @ | inf | ((- (* 1/3840 (* eps eps)) 1/48) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* -1/2 x) x) eps) eps) (* (* -1/2 x) x) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* 1/3840 (* eps eps)) (sin (/ (+ 0 eps) 2)) (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps) (cos (/ (+ (* 2 x) eps) -2))) |
| 3.0ms | x | @ | -inf | ((- (* 1/3840 (* eps eps)) 1/48) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* -1/2 x) x) eps) eps) (* (* -1/2 x) x) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ 0 eps) 2)) (* 1/3840 (* eps eps)) (sin (/ (+ 0 eps) 2)) (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps) (cos (/ (+ (* 2 x) eps) -2))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 332 | 1128 |
| 1 | 1207 | 1084 |
| 2 | 4242 | 1064 |
| 0 | 8298 | 977 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
(* -1/2 (pow x 2)) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(* eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
(* -1/2 x) |
(/ 1 eps) |
(+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(* -1/2 (* eps (pow x 2))) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* eps (sin x)) |
(* -1/2 (/ (pow x 2) eps)) |
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 eps)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(cos (* -1/2 (- eps (* -2 x)))) |
-1/48 |
(- (* 1/3840 (pow eps 2)) 1/48) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(cos x) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* 1/3840 (pow eps 2)) |
(/ (+ 1 (* -1/2 (pow x 2))) eps) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* 2 (sin (* 1/2 eps))) |
(* -1/2 (* eps x)) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(sin (* 1/2 eps)) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1 (* eps (- (* 1/2 (pow x 2)) 1))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
| Outputs |
|---|
(* -1/2 eps) |
(*.f64 #s(literal -1/2 binary64) eps) |
(+ (* -1 x) (* -1/2 eps)) |
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(fma.f64 (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64) (*.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 #s(literal -1/3 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) eps) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps) |
(* -1/2 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/2 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (* eps x))) |
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 x eps)) eps) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(fma.f64 (fma.f64 (*.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) x)) x)) x eps) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)) |
(* eps x) |
(*.f64 x eps) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/120 binary64) eps)) x) x (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x eps)) |
(* -1/2 x) |
(*.f64 #s(literal -1/2 binary64) x) |
(/ 1 eps) |
(/.f64 #s(literal 1 binary64) eps) |
(+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)) |
(/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) eps) |
(cos (* -1/2 eps)) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* -1 x) |
(neg.f64 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(*.f64 (-.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* eps (cos x)) |
(*.f64 (cos.f64 x) eps) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 (*.f64 (*.f64 x eps) #s(literal -1/2 binary64)) x) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (/.f64 eps x) x)) x) x) |
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2)) |
(*.f64 (*.f64 (-.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) x) x) |
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2)) |
(*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (*.f64 x x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) |
(* eps (sin x)) |
(*.f64 (sin.f64 x) eps) |
(* -1/2 (/ (pow x 2) eps)) |
(*.f64 (/.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) |
(* (pow x 2) (- (/ 1 (* eps (pow x 2))) (* 1/2 (/ 1 eps)))) |
(*.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) eps) (*.f64 x x)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2)) |
(*.f64 (-.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1 binary64) x)) (neg.f64 x)) #s(literal 1/2 binary64)) (*.f64 x x)) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
-1/48 |
#s(literal -1/48 binary64) |
(- (* 1/3840 (pow eps 2)) 1/48) |
(-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) |
(* eps (cos (* -1 x))) |
(*.f64 (cos.f64 x) eps) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) eps) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) |
(cos x) |
(cos.f64 x) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (*.f64 #s(literal 1/2 binary64) eps)) |
(* 1/3840 (pow eps 2)) |
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) |
(/ (+ 1 (* -1/2 (pow x 2))) eps) |
(/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) eps) |
(cos (* -1 x)) |
(cos.f64 x) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/48 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(*.f64 (*.f64 (-.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps))) eps) eps) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps) |
(* 2 (sin (* 1/2 eps))) |
(*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(* -1/2 (* eps x)) |
(*.f64 (*.f64 x eps) #s(literal -1/2 binary64)) |
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) eps)) eps) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(*.f64 (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1/2 binary64)) eps) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(* -1 (* eps (- (* 1/2 (pow x 2)) 1))) |
(*.f64 (neg.f64 eps) (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64))) |
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) eps)) eps) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 62 | 395 |
| 0 | 95 | 383 |
| 1 | 351 | 383 |
| 2 | 3094 | 383 |
| 0 | 8604 | 377 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
#s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps)) |
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps) |
(*.f64 (*.f64 #s(literal -1/2 binary64) x) x) |
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) |
#s(approx (* (sin x) eps) (*.f64 x eps)) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) |
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 #s(literal -1/2 binary64) x) |
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
| Outputs |
|---|
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/14745600 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/2304 binary64))) (neg.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal 1/48 binary64)))) |
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/56623104000 binary64) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1/110592 binary64))) (neg.f64 (fma.f64 #s(literal 1/14745600 binary64) (pow.f64 eps #s(literal 4 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 1/184320 binary64) #s(literal 1/2304 binary64))))) |
(/.f64 (-.f64 (*.f64 #s(literal 1/14745600 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/2304 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal 1/48 binary64))) |
(/.f64 (-.f64 (*.f64 #s(literal 1/56623104000 binary64) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1/110592 binary64)) (fma.f64 #s(literal 1/14745600 binary64) (pow.f64 eps #s(literal 4 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 1/184320 binary64) #s(literal 1/2304 binary64)))) |
(-.f64 (/.f64 (*.f64 #s(literal 1/14745600 binary64) (pow.f64 eps #s(literal 4 binary64))) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal 1/48 binary64))) (/.f64 #s(literal 1/2304 binary64) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal 1/48 binary64)))) |
(-.f64 (/.f64 (*.f64 #s(literal 1/56623104000 binary64) (pow.f64 eps #s(literal 6 binary64))) (fma.f64 #s(literal 1/14745600 binary64) (pow.f64 eps #s(literal 4 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 1/184320 binary64) #s(literal 1/2304 binary64)))) (/.f64 #s(literal 1/110592 binary64) (fma.f64 #s(literal 1/14745600 binary64) (pow.f64 eps #s(literal 4 binary64)) (fma.f64 (*.f64 eps eps) #s(literal 1/184320 binary64) #s(literal 1/2304 binary64))))) |
(-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) #s(literal 1/48 binary64)) |
(/.f64 (fma.f64 (neg.f64 (*.f64 eps eps)) #s(literal 2 binary64) (*.f64 (*.f64 (neg.f64 eps) #s(literal -2 binary64)) (neg.f64 (*.f64 x #s(literal 2 binary64))))) (*.f64 (*.f64 (neg.f64 eps) #s(literal -2 binary64)) #s(literal 2 binary64))) |
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(fabs.f64 (neg.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))) |
(fabs.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))) |
(+.f64 (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/3840 binary64))) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))) |
(+.f64 (*.f64 (*.f64 eps #s(literal 1/3840 binary64)) #s(literal 0 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))) |
(+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/3840 binary64)))) |
(+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 (*.f64 eps #s(literal 1/3840 binary64)) #s(literal 0 binary64))) |
#s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 #s(literal -1/2 binary64) x) |
(*.f64 x #s(literal -1/2 binary64)) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps)) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps)) |
(/.f64 (fma.f64 #s(literal -1 binary64) (neg.f64 eps) (*.f64 (neg.f64 eps) (neg.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) (*.f64 eps eps)) |
(/.f64 (fma.f64 #s(literal -1 binary64) eps (*.f64 (neg.f64 eps) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (*.f64 (neg.f64 eps) eps)) |
(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 eps) (*.f64 eps (neg.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))) (*.f64 eps (neg.f64 eps))) |
(/.f64 (fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) (*.f64 eps eps)) |
(/.f64 (fma.f64 (neg.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal -1 binary64))) (*.f64 eps eps)) |
(/.f64 (fma.f64 (neg.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) eps (*.f64 (neg.f64 eps) #s(literal 1 binary64))) (*.f64 (neg.f64 eps) eps)) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 eps) (*.f64 eps #s(literal -1 binary64))) (*.f64 eps (neg.f64 eps))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps) #s(literal 2 binary64)) (pow.f64 eps #s(literal -2 binary64))) (/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps)) |
(/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (/.f64 #s(literal -1/2 binary64) eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 eps #s(literal -2 binary64)) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps) (pow.f64 eps #s(literal -1 binary64)))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (neg.f64 (neg.f64 eps))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps (*.f64 eps #s(literal 1 binary64))) (*.f64 eps eps)) |
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps)) |
(/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64) #s(literal 1 binary64)) (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps)) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (neg.f64 eps)) |
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
(neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))) |
(fma.f64 (pow.f64 (neg.f64 (*.f64 eps eps)) #s(literal -1 binary64)) (neg.f64 eps) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps)) |
(fma.f64 (pow.f64 eps #s(literal -3 binary64)) (*.f64 eps eps) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps)) |
(fma.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps) (pow.f64 eps #s(literal -1 binary64))) |
(fma.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps) (pow.f64 eps #s(literal -1 binary64))) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal -1/2 binary64) eps) (pow.f64 eps #s(literal -1 binary64))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 x eps) (pow.f64 eps #s(literal -1 binary64))) |
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) eps) (pow.f64 eps #s(literal -1 binary64))) |
(fma.f64 x (/.f64 (*.f64 #s(literal -1/2 binary64) x) eps) (pow.f64 eps #s(literal -1 binary64))) |
(+.f64 (pow.f64 eps #s(literal -1 binary64)) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps)) |
(+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps) (pow.f64 eps #s(literal -1 binary64))) |
(fma.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64))))) |
(fma.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(fma.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(fma.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (*.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))))) |
(sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))) |
(-.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x eps) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (sin.f64 (/.f64 (+.f64 x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64))))) |
(-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (*.f64 (sin.f64 (neg.f64 (*.f64 x #s(literal -1 binary64)))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))) |
(-.f64 (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (*.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64))))) |
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) |
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) |
(+.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 0 binary64)) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
(+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64))))) |
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))) (*.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))))) |
(+.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) #s(literal 0 binary64)) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64))) |
Compiled 19 920 to 2 371 computations (88.1% saved)
14 alts after pruning (6 fresh and 8 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 511 | 3 | 514 |
| Fresh | 1 | 3 | 4 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 5 | 5 |
| Total | 514 | 14 | 528 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 63.4% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 63.4% | (*.f64 (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| 99.9% | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) | |
| 99.8% | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) | |
| 99.6% | (*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) | |
| ✓ | 99.6% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| ✓ | 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
| ✓ | 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
| 99.2% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps (*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) eps)))) eps)) | |
| ✓ | 99.2% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
| 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) | |
| ✓ | 98.9% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
| ✓ | 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
| ✓ | 100.0% | #s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
Compiled 995 to 432 computations (56.6% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps (*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) eps)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) |
| Outputs |
|---|
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
3 calls:
| 6.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 6.0ms | x |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 100.0% | 1 | x |
| 100.0% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps (*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) eps)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| Outputs |
|---|
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
3 calls:
| 5.0ms | x |
| 5.0ms | eps |
| 5.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps (*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) eps)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| Outputs |
|---|
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
3 calls:
| 4.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 4.0ms | eps |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps (*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) eps)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| Outputs |
|---|
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
3 calls:
| 4.0ms | eps |
| 4.0ms | x |
| 4.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.6% | 1 | x |
| 99.6% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps (*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) eps)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
3 calls:
| 24.0ms | eps |
| 3.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.6% | 1 | x |
| 99.6% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) eps (*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) eps)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* (+ x eps) -1/2) x) 1) (*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (*.f64 x x)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
3 calls:
| 5.0ms | eps |
| 3.0ms | x |
| 3.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.5% | 1 | x |
| 99.5% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
3 calls:
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2.0ms | x |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.5% | 1 | x |
| 99.5% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
3 calls:
| 1.0ms | eps |
| 1.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.4% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.4% | 1 | x |
| 99.4% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
3 calls:
| 1.0ms | x |
| 1.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 1.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 98.9% | 1 | x |
| 98.9% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 82 | 239 |
| 1 | 120 | 239 |
| 2 | 219 | 239 |
| 3 | 520 | 239 |
| 4 | 1148 | 239 |
| 5 | 1927 | 239 |
| 6 | 2933 | 239 |
| 7 | 5344 | 239 |
| 8 | 7575 | 239 |
| 1× | node limit |
| Inputs |
|---|
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
| Outputs |
|---|
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) x) eps eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 332 | 1128 |
| 1 | 1207 | 1084 |
| 2 | 4242 | 1064 |
| 0 | 8298 | 977 |
| 0 | 621 | 2119 |
| 1 | 2146 | 1864 |
| 0 | 8334 | 1737 |
| 0 | 107 | 303 |
| 1 | 366 | 303 |
| 2 | 1224 | 296 |
| 3 | 4149 | 296 |
| 4 | 7986 | 296 |
| 0 | 8046 | 267 |
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 51 | 16 |
| 2 | 365 | 16 |
| 3 | 4452 | 16 |
| 0 | 8177 | 16 |
| 0 | 443 | 1579 |
| 1 | 1645 | 1502 |
| 2 | 5680 | 1473 |
| 0 | 8474 | 1352 |
| 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× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 461 to 263 computations (43% saved)
Compiled 538 to 206 computations (61.7% saved)
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