
Time bar (total: 16.5s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 0 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 1 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 2 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 3 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 4 |
| 0% | 0% | 19% | 49.4% | 0% | 31.6% | 0% | 5 |
| 0% | 0% | 15.8% | 49.4% | 0% | 34.8% | 0% | 6 |
| 0% | 0% | 11.1% | 49.4% | 0% | 39.5% | 0% | 7 |
| 0% | 0% | 8.7% | 49.4% | 0% | 41.9% | 0% | 8 |
| 0% | 0% | 5.9% | 49.4% | 0% | 44.6% | 0% | 9 |
| 0% | 0% | 4.5% | 49.4% | 0% | 46% | 0% | 10 |
| 0% | 0% | 3.1% | 49.4% | 0% | 47.5% | 0% | 11 |
| 0% | 0% | 2.7% | 49.4% | 0% | 47.9% | 0% | 12 |
Compiled 27 to 19 computations (29.6% saved)
| 3.9s | 26 879× | 0 | invalid |
| 3.3s | 5 692× | 2 | valid |
| 584.0ms | 2 445× | 1 | valid |
| 15.0ms | 119× | 0 | valid |
ival-cos: 2.8s (45.5% of total)const: 739.0ms (12.1% of total)ival-add: 598.0ms (9.8% of total)adjust: 380.0ms (6.2% of total)ival-mult: 356.0ms (5.8% of total)ival-<=: 335.0ms (5.5% of total)ival-<: 265.0ms (4.3% of total)ival-sub: 250.0ms (4.1% of total)ival-fabs: 228.0ms (3.7% of total)ival-and: 109.0ms (1.8% of total)exact: 48.0ms (0.8% of total)ival-assert: 14.0ms (0.2% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 125 | 0 | - | 0 | - | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 1 | 0 | - | 0 | - | (cos.f64 (+.f64 x eps)) |
| 0 | 0 | - | 0 | - | eps |
| 0 | 0 | - | 0 | - | (+.f64 x eps) |
| 0 | 0 | - | 0 | - | (cos.f64 x) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) | cancellation | 125 | 0 |
cos.f64 | (cos.f64 (+.f64 x eps)) | sensitivity | 1 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 126 | 0 |
| - | 0 | 130 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 126 | 0 | 0 |
| - | 0 | 0 | 130 |
| number | freq |
|---|---|
| 0 | 130 |
| 1 | 126 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 223.0ms | 358× | 2 | valid |
| 21.0ms | 150× | 1 | valid |
| 0.0ms | 4× | 0 | valid |
Compiled 65 to 28 computations (56.9% saved)
ival-cos: 177.0ms (81.5% of total)adjust: 20.0ms (9.2% of total)ival-sub: 16.0ms (7.4% of total)ival-add: 3.0ms (1.4% 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 | 41 |
| 1 | 38 | 37 |
| 2 | 81 | 35 |
| 3 | 152 | 35 |
| 4 | 278 | 35 |
| 5 | 370 | 35 |
| 6 | 448 | 35 |
| 7 | 485 | 35 |
| 8 | 531 | 35 |
| 9 | 546 | 35 |
| 10 | 554 | 35 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 13 | 7 |
| 2 | 18 | 7 |
| 3 | 24 | 7 |
| 4 | 32 | 7 |
| 5 | 47 | 7 |
| 6 | 80 | 7 |
| 7 | 107 | 7 |
| 8 | 151 | 7 |
| 9 | 166 | 7 |
| 10 | 174 | 7 |
| 0 | 174 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Outputs |
|---|
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 56.5% | (-.f64 (cos.f64 (+.f64 x eps)) (cos.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 | (cos.f64 x) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (cos.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 0 | 10 | 18 |
| 1 | 13 | 18 |
| 2 | 18 | 18 |
| 3 | 24 | 18 |
| 4 | 32 | 18 |
| 5 | 47 | 18 |
| 6 | 80 | 18 |
| 7 | 107 | 18 |
| 8 | 151 | 18 |
| 9 | 166 | 18 |
| 10 | 174 | 18 |
| 0 | 174 | 18 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(cos.f64 x) |
| Outputs |
|---|
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos.f64 (+.f64 x eps)) |
(cos.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
(cos.f64 x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (+.f64 x eps) | |
| accuracy | 0 | (cos.f64 x) | |
| accuracy | 0.03377913447833954 | (cos.f64 (+.f64 x eps)) | |
| accuracy | 27.855811129695105 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 89.0ms | 179× | 2 | valid |
| 14.0ms | 75× | 1 | valid |
| 0.0ms | 2× | 0 | valid |
Compiled 38 to 14 computations (63.2% saved)
ival-cos: 71.0ms (82.4% of total)adjust: 9.0ms (10.4% of total)ival-sub: 4.0ms (4.6% of total)ival-add: 2.0ms (2.3% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(cos.f64 x) |
| Outputs |
|---|
(- (cos eps) 1) |
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
eps |
(+ eps x) |
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))) |
(- (cos (+ eps x)) (cos x)) |
(cos (+ eps x)) |
x |
(* x (+ 1 (/ eps x))) |
(cos x) |
(- (cos (- eps (* -1 x))) (cos x)) |
(cos (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* eps (sin x))) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(* eps (+ 1 (/ x eps))) |
(- (cos (- x (* -1 eps))) (cos x)) |
(cos (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | 0 | ((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x)) |
| 1.0ms | eps | @ | inf | ((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x)) |
| 1.0ms | eps | @ | 0 | ((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x)) |
| 1.0ms | eps | @ | -inf | ((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x)) |
| 0.0ms | x | @ | inf | ((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 105 | 296 |
| 1 | 277 | 293 |
| 2 | 609 | 293 |
| 3 | 2402 | 292 |
| 4 | 7842 | 292 |
| 0 | 8510 | 272 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- (cos eps) 1) |
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
eps |
(+ eps x) |
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))) |
(- (cos (+ eps x)) (cos x)) |
(cos (+ eps x)) |
x |
(* x (+ 1 (/ eps x))) |
(cos x) |
(- (cos (- eps (* -1 x))) (cos x)) |
(cos (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* eps (sin x))) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(* eps (+ 1 (/ x eps))) |
(- (cos (- x (* -1 eps))) (cos x)) |
(cos (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
| Outputs |
|---|
(- (cos eps) 1) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1) |
(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) |
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1) |
(fma.f64 (fma.f64 (sin.f64 eps) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64)) x)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 eps) (neg.f64 (sin.f64 eps))) x (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(fma.f64 (fma.f64 (sin.f64 eps) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/2 binary64))) x (cos.f64 eps)) |
eps |
(+ eps x) |
(+.f64 eps x) |
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 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(- (cos (+ eps x)) (cos x)) |
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
x |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
(cos x) |
(cos.f64 x) |
(- (cos (- eps (* -1 x))) (cos x)) |
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
(* -1 (* eps (sin x))) |
(*.f64 (neg.f64 eps) (sin.f64 x)) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps (cos.f64 x)) |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
(- (cos (- x (* -1 eps))) (cos x)) |
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 54 | 16 |
| 2 | 380 | 16 |
| 3 | 4694 | 16 |
| 0 | 8209 | 16 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(cos.f64 x) |
| Outputs |
|---|
(*.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 9 binary64)) (pow.f64 (cos.f64 x) #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 3 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (cos.f64 x) (cos.f64 x) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 6 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 4 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #s(literal -1 binary64)) (pow.f64 (/.f64 (*.f64 (cos.f64 (/.f64 (+.f64 #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 (cos.f64 (+.f64 eps x)) (cos.f64 x))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (*.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (*.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x)) (-.f64 (*.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (cos.f64 x)) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 4 binary64)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
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(/.f64 (neg.f64 (*.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x)))) (neg.f64 (cos.f64 (-.f64 eps x)))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (cos.f64 (-.f64 eps x)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (*.f64 (+.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))))) #s(literal 4 binary64)) |
(/.f64 (-.f64 (+.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))) (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x)))) #s(literal 2 binary64)) |
(/.f64 (*.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))) (cos.f64 (-.f64 eps x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (-.f64 eps x)) (*.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (cos.f64 (-.f64 eps x)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (cos.f64 (-.f64 eps x)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)))) |
(fma.f64 (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (*.f64 x x) (-.f64 eps x))) (*.f64 (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 eps x))))) |
(fma.f64 (cos.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))) (*.f64 (sin.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) |
(fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(fma.f64 #s(literal -1 binary64) (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(fma.f64 (+.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))) #s(literal 1/2 binary64) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) |
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) |
(-.f64 (*.f64 (cos.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) (*.f64 (sin.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 eps x))) (/.f64 (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 eps x)))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (fma.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (cos.f64 (-.f64 eps x)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (fma.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (cos.f64 (-.f64 eps x)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64))))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) |
(cos.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps))) |
(cos.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)))) |
(cos.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps)))) |
(cos.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))))) |
(cos.f64 (+.f64 eps x)) |
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (cos.f64 (/.f64 (*.f64 x x) (-.f64 eps x)))) (*.f64 (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 eps x))))) |
(+.f64 (*.f64 (cos.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (cos.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) (*.f64 (sin.f64 (*.f64 x (/.f64 x (-.f64 x eps)))) (sin.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))) |
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) |
(exp.f64 (*.f64 (log.f64 (cos.f64 (+.f64 eps x))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 eps eps (*.f64 x x)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x))) |
(*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (-.f64 eps x) eps))) |
(*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (*.f64 (-.f64 eps x) eps) (-.f64 (*.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) |
(*.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x)) |
(*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (pow.f64 (-.f64 eps x) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (*.f64 (-.f64 x eps) (+.f64 eps x))) |
(*.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) |
(*.f64 #s(literal 1 binary64) (+.f64 eps x)) |
(*.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (pow.f64 (neg.f64 (-.f64 x eps)) #s(literal -1 binary64))) |
(*.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))) #s(literal -1 binary64))) |
(*.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (/.f64 (+.f64 eps x) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (*.f64 (+.f64 eps x) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64)))) |
(*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) |
(*.f64 (+.f64 eps x) (/.f64 (-.f64 x eps) (-.f64 x eps))) |
(*.f64 (+.f64 eps x) (*.f64 (-.f64 x eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))) |
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal -1 binary64)) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 eps eps (*.f64 x x))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) |
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64)))) |
(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64))) (*.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (-.f64 x eps) #s(literal -3 binary64)))) (+.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64)) (*.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x))) |
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (neg.f64 (neg.f64 (-.f64 x eps)))) |
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))) |
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 eps eps (*.f64 x x)) (-.f64 x eps))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps))) |
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(/.f64 (*.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x eps)) (*.f64 (-.f64 x eps) (*.f64 eps eps))) (pow.f64 (-.f64 x eps) #s(literal 2 binary64))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (-.f64 x eps) (fma.f64 eps eps (*.f64 x x)))) |
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x)) |
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (-.f64 x eps) (fma.f64 (*.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 eps x) #s(literal -1 binary64))) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (*.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps)) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) |
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps))) |
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))) |
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps)))) |
(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))) |
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x))) |
(-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps)))) |
(+.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps))))) |
(+.f64 eps x) |
(+.f64 x eps) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))) #s(literal -1 binary64))) |
(pow.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))) |
(cos.f64 (neg.f64 x)) |
(cos.f64 x) |
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64))) |
Compiled 6 613 to 894 computations (86.5% saved)
10 alts after pruning (9 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 242 | 9 | 251 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 242 | 10 | 252 |
| Status | Accuracy | Program |
|---|---|---|
| 56.5% | (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) | |
| ✓ | 56.5% | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 55.8% | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) | |
| ▶ | 55.8% | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
| 55.7% | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) | |
| 55.7% | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) | |
| ▶ | 99.8% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
| ▶ | 55.6% | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
| ▶ | 99.3% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) |
| ▶ | 81.6% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
Compiled 285 to 214 computations (24.9% saved)
| 1× | egg-herbie |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) | |
| cost-diff | 0 | (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) | |
| cost-diff | 0 | (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps) | |
| cost-diff | 0 | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) | |
| cost-diff | 0 | #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (cos.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) | |
| cost-diff | 0 | (sin.f64 x) | |
| cost-diff | 0 | (neg.f64 eps) | |
| cost-diff | 0 | (*.f64 (neg.f64 eps) (sin.f64 x)) | |
| cost-diff | 0 | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) | |
| cost-diff | 0 | (cos.f64 eps) | |
| cost-diff | 0 | (-.f64 (cos.f64 eps) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) | |
| cost-diff | 0 | (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) | |
| cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) | |
| cost-diff | 192 | (+.f64 #s(literal 0 binary64) eps) | |
| cost-diff | 320 | (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 41 | 232 |
| 0 | 69 | 222 |
| 1 | 120 | 222 |
| 2 | 226 | 218 |
| 3 | 393 | 218 |
| 4 | 848 | 218 |
| 5 | 1603 | 218 |
| 6 | 2048 | 218 |
| 7 | 2498 | 218 |
| 8 | 3217 | 218 |
| 9 | 4582 | 218 |
| 10 | 5338 | 218 |
| 11 | 5867 | 218 |
| 12 | 6305 | 218 |
| 13 | 6349 | 218 |
| 14 | 6351 | 218 |
| 15 | 7019 | 218 |
| 16 | 7258 | 218 |
| 17 | 7317 | 218 |
| 18 | 7339 | 218 |
| 19 | 7339 | 218 |
| 20 | 7339 | 218 |
| 0 | 8163 | 214 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) |
#s(literal 1/2 binary64) |
(fma.f64 #s(literal 2 binary64) x eps) |
#s(literal 2 binary64) |
x |
eps |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) |
(+.f64 #s(literal 0 binary64) eps) |
#s(literal 0 binary64) |
#s(literal -2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(cos.f64 eps) |
eps |
#s(literal 1 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
(*.f64 (neg.f64 eps) (sin.f64 x)) |
(neg.f64 eps) |
eps |
(sin.f64 x) |
x |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) |
#s(literal 1/24 binary64) |
(*.f64 x x) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps) |
(-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) |
(*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) |
(*.f64 (cos.f64 x) #s(literal -1/2 binary64)) |
(cos.f64 x) |
x |
#s(literal -1/2 binary64) |
eps |
(sin.f64 x) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) |
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) |
(fma.f64 eps #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
(fma.f64 #s(literal 2 binary64) x eps) |
(fma.f64 x #s(literal 2 binary64) eps) |
#s(literal 2 binary64) |
x |
eps |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) |
(*.f64 eps #s(literal 1/2 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
eps |
#s(literal 0 binary64) |
#s(literal -2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(cos.f64 eps) |
eps |
#s(literal 1 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps))) |
(*.f64 (neg.f64 eps) (sin.f64 x)) |
(*.f64 (sin.f64 x) (neg.f64 eps)) |
(neg.f64 eps) |
eps |
(sin.f64 x) |
x |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
(-.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
(cos.f64 (+.f64 x eps)) |
(cos.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) |
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) |
#s(literal 1/24 binary64) |
(*.f64 x x) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))) |
(*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)) |
(-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) |
(neg.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))) |
(*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) |
(*.f64 (cos.f64 x) #s(literal -1/2 binary64)) |
(cos.f64 x) |
x |
#s(literal -1/2 binary64) |
eps |
(sin.f64 x) |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0078125 | (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) | |
| accuracy | 0.015625 | (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) | |
| accuracy | 0.1328125 | (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps) | |
| accuracy | 0.29844541109401235 | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) | |
| accuracy | 0.00390625 | (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) | |
| accuracy | 0.03377913447833954 | (cos.f64 (+.f64 x eps)) | |
| accuracy | 0.4567323431023008 | #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) | |
| accuracy | 27.855811129695105 | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) | |
| accuracy | 0 | (sin.f64 x) | |
| accuracy | 0 | (neg.f64 eps) | |
| accuracy | 0.01953125 | (*.f64 (neg.f64 eps) (sin.f64 x)) | |
| accuracy | 11.749150775642846 | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) | |
| accuracy | 0 | (cos.f64 eps) | |
| accuracy | 27.159810044217245 | (-.f64 (cos.f64 eps) #s(literal 1 binary64)) | |
| accuracy | 27.855703891872633 | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) | |
| accuracy | 0 | (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) | |
| accuracy | 0.015625 | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) | |
| accuracy | 0.022684980164287515 | (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) | |
| accuracy | 0.1328125 | (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
| 466.0ms | 182× | 2 | valid |
| 75.0ms | 72× | 1 | valid |
| 1.0ms | 2× | 0 | valid |
Compiled 427 to 79 computations (81.5% saved)
ival-cos: 174.0ms (38.3% of total)ival-neg: 84.0ms (18.5% of total)ival-mult: 71.0ms (15.6% of total)ival-sin: 32.0ms (7% of total)ival-add: 31.0ms (6.8% of total)adjust: 30.0ms (6.6% of total)ival-sub: 27.0ms (5.9% of total)const: 4.0ms (0.9% of total)exact: 1.0ms (0.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) |
(+.f64 #s(literal 0 binary64) eps) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(cos.f64 eps) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
(*.f64 (neg.f64 eps) (sin.f64 x)) |
(neg.f64 eps) |
(sin.f64 x) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps) |
(-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) |
(*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
| Outputs |
|---|
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(* -2 (pow (sin (* 1/2 eps)) 2)) |
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2))))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)))))) |
(pow (sin (* 1/2 eps)) 2) |
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2)) |
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(- (cos eps) 1) |
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1) |
(* -1 (* eps x)) |
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))) |
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)))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
eps |
(+ eps x) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(* -1/2 (pow eps 2)) |
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))) |
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))) |
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2)))) |
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps)))) |
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2)))))))) |
(sin (* 1/2 eps)) |
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps)))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps))))))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps))))))))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))) |
(- (cos (+ eps x)) (cos x)) |
(* -1 (* eps (sin x))) |
(sin x) |
(cos (+ eps x)) |
(* x (+ 1 (/ eps x))) |
(cos x) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(* -1/2 (* eps (cos x))) |
(sin (* 1/2 (+ eps (* 2 x)))) |
(* 1/24 (pow x 4)) |
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) |
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2))))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))) |
(- (cos (- eps (* -1 x))) (cos x)) |
(cos (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(sin (* 1/2 (- eps (* -2 x)))) |
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) |
(* 1/2 (* eps (sin x))) |
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x)))) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x)))))))))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2)) |
(+ 1 (* -1/2 (pow eps 2))) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(* -1 eps) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(* -1 (sin x)) |
(+ (sin x) (* 1/2 (* eps (cos x)))) |
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x))))) |
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x)))))))) |
(* 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)))) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* -1/2 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))) |
(- (cos (- x (* -1 eps))) (cos x)) |
(cos (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))) |
(sin (* 1/2 (- (* 2 x) (* -1 eps)))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 16.0ms | x | @ | inf | ((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1)) |
| 6.0ms | eps | @ | 0 | ((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1)) |
| 4.0ms | x | @ | -inf | ((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1)) |
| 3.0ms | eps | @ | inf | ((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1)) |
| 3.0ms | x | @ | 0 | ((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* (+ (* 1/24 (* x x)) -1/2) (* x x)) 1)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 377 | 1403 |
| 1 | 1132 | 1352 |
| 2 | 2972 | 1306 |
| 3 | 6899 | 1306 |
| 0 | 8605 | 1194 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(* -2 (pow (sin (* 1/2 eps)) 2)) |
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2))))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)))))) |
(pow (sin (* 1/2 eps)) 2) |
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2)) |
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(- (cos eps) 1) |
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1) |
(* -1 (* eps x)) |
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))) |
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)))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
eps |
(+ eps x) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(* -1/2 (pow eps 2)) |
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))) |
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))) |
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2)))) |
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps)))) |
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2)))))))) |
(sin (* 1/2 eps)) |
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps)))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps))))))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps))))))))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))) |
(- (cos (+ eps x)) (cos x)) |
(* -1 (* eps (sin x))) |
(sin x) |
(cos (+ eps x)) |
(* x (+ 1 (/ eps x))) |
(cos x) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(* -1/2 (* eps (cos x))) |
(sin (* 1/2 (+ eps (* 2 x)))) |
(* 1/24 (pow x 4)) |
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) |
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2))))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))) |
(- (cos (- eps (* -1 x))) (cos x)) |
(cos (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(sin (* 1/2 (- eps (* -2 x)))) |
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) |
(* 1/2 (* eps (sin x))) |
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x)))) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x)))))))))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2)) |
(+ 1 (* -1/2 (pow eps 2))) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(* -1 eps) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(* -1 (sin x)) |
(+ (sin x) (* 1/2 (* eps (cos x)))) |
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x))))) |
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x)))))))) |
(* 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)))) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* -1/2 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))) |
(- (cos (- x (* -1 eps))) (cos x)) |
(cos (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))) |
(sin (* 1/2 (- (* 2 x) (* -1 eps)))) |
| Outputs |
|---|
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(* -2 (pow (sin (* 1/2 eps)) 2)) |
(*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64)) |
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2))))) |
(fma.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (*.f64 (*.f64 (*.f64 #s(literal -2 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)))))) |
(fma.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal -2 binary64) (*.f64 x (*.f64 #s(literal 1/3 binary64) x))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) x)) x (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))) |
(pow (sin (* 1/2 eps)) 2) |
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2)) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #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)))) |
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(- (cos eps) 1) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1) |
(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) |
(fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1) |
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 eps) x) (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(* -1 (* eps x)) |
(*.f64 (neg.f64 x) eps) |
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))) |
(*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (*.f64 (neg.f64 x) eps)) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))) |
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)))) 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)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) x) |
(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 eps) (neg.f64 (sin.f64 eps))) x (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(fma.f64 (fma.f64 (sin.f64 eps) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/2 binary64))) x (cos.f64 eps)) |
eps |
(+ eps x) |
(+.f64 eps x) |
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 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(* -1/2 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) |
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x)) |
(* -1/2 eps) |
(*.f64 #s(literal -1/2 binary64) eps) |
(+ (* -1 x) (* -1/2 eps)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))) |
(fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)) |
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) |
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2)))) |
(*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) |
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps)))) |
(fma.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) x) x (*.f64 #s(literal -1/2 binary64) eps)) |
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2)))))))) |
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal 1/1440 binary64) (*.f64 x x) #s(literal -1/48 binary64))) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps)))) |
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps))))))) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) x)) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps))))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (cos (+ eps x)) (cos x)) |
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(* -1 (* eps (sin x))) |
(*.f64 (neg.f64 (sin.f64 x)) eps) |
(sin x) |
(sin.f64 x) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(* x (+ 1 (/ eps x))) |
(fma.f64 (/.f64 eps x) x x) |
(cos x) |
(cos.f64 x) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) |
(* -1/2 (* eps (cos x))) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(sin (* 1/2 (+ eps (* 2 x)))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* 1/24 (pow x 4)) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) |
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2))))) |
(*.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2))))) |
(*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/24 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x) x) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (cos (- eps (* -1 x))) (cos x)) |
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 (/.f64 eps x) x x) |
(sin (* 1/2 (- eps (* -2 x)))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) |
(*.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps) |
(* 1/2 (* eps (sin x))) |
(*.f64 (*.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps) |
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x)))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps (*.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x)))))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/48 binary64))) eps (*.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(*.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) eps)) eps (neg.f64 (sin.f64 x))) eps) |
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) |
(*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2)) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (*.f64 eps eps) #s(literal -1/720 binary64)) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps) |
(+ 1 (* -1/2 (pow eps 2))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) |
(* -1 eps) |
(neg.f64 eps) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(fma.f64 (neg.f64 (sin.f64 x)) eps (cos.f64 x)) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps (cos.f64 x)) |
(* -1 (sin x)) |
(neg.f64 (sin.f64 x)) |
(+ (sin x) (* 1/2 (* eps (cos x)))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x)))))))) |
(fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps)) eps (sin.f64 x)) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 (fma.f64 (fma.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)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (/ x eps))) |
(*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 (/.f64 x eps) eps eps) |
(* -1/2 (* (pow eps 2) (cos x))) |
(*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps) |
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(*.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) eps) |
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (cos (- x (* -1 eps))) (cos x)) |
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (/.f64 x eps) eps eps) |
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) |
(sin (* 1/2 (- (* 2 x) (* -1 eps)))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 41 | 188 |
| 0 | 69 | 180 |
| 1 | 242 | 180 |
| 2 | 1811 | 180 |
| 0 | 8797 | 180 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) |
(+.f64 #s(literal 0 binary64) eps) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(cos.f64 eps) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
(*.f64 (neg.f64 eps) (sin.f64 x)) |
(neg.f64 eps) |
(sin.f64 x) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps) |
(-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) |
(*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) |
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
| Outputs |
|---|
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) |
(/.f64 (+.f64 (pow.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) #s(literal 3 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (-.f64 (pow.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (*.f64 eps #s(literal 1/2 binary64)))))) |
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (+.f64 (pow.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)))) (neg.f64 (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (pow.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64))))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64))))))) |
(/.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps))) |
(/.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps))) (fma.f64 x #s(literal 2 binary64) (neg.f64 eps))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (pow.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64)))) |
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)))) (+.f64 (pow.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64)))))) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 eps #s(literal 0 binary64))) (*.f64 #s(literal 1 binary64) x)) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (*.f64 #s(literal 1 binary64) x)) |
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 (neg.f64 (*.f64 eps eps)) #s(literal -1 binary64)) (*.f64 #s(literal 1 binary64) x)) |
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 #s(literal 1/2 binary64) (-.f64 eps #s(literal 0 binary64))) (*.f64 #s(literal 1 binary64) x)) |
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1 binary64) x)) |
(fma.f64 (/.f64 (neg.f64 (*.f64 eps eps)) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1 binary64) x)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 #s(literal -1/2 binary64) (neg.f64 eps) (*.f64 #s(literal 1 binary64) x)) |
(fma.f64 (neg.f64 eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) x)) |
(fma.f64 #s(literal 1 binary64) x (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) x)) |
(fma.f64 x #s(literal 1 binary64) (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)) (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)) (*.f64 eps #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1 binary64) x)) |
(-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64))))) |
(+.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64)) (*.f64 eps #s(literal 1/2 binary64))) |
(+.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 eps #s(literal 1/2 binary64))) |
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) x)) |
(*.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (-.f64 eps #s(literal 0 binary64)))) |
(*.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps)) |
(*.f64 (/.f64 eps eps) (/.f64 (*.f64 eps eps) eps)) |
(*.f64 (/.f64 eps eps) eps) |
(*.f64 (/.f64 (*.f64 eps eps) eps) (/.f64 eps (-.f64 eps #s(literal 0 binary64)))) |
(*.f64 (/.f64 (*.f64 eps eps) eps) (/.f64 eps eps)) |
(*.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64))) |
(pow.f64 (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64)) |
(pow.f64 eps #s(literal 1 binary64)) |
(/.f64 (neg.f64 (/.f64 (neg.f64 (*.f64 eps eps)) #s(literal -1 binary64))) (neg.f64 eps)) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 (*.f64 eps eps)))) (neg.f64 eps)) |
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (neg.f64 eps)) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (*.f64 eps eps)) |
(/.f64 (/.f64 (neg.f64 (*.f64 eps eps)) #s(literal -1 binary64)) eps) |
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) eps) |
(/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (neg.f64 (*.f64 eps eps))) |
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 (-.f64 eps #s(literal 0 binary64)))) |
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 eps #s(literal -1 binary64)))) |
(/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64))) |
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 (neg.f64 (*.f64 eps eps)))) |
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps)) |
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal -1 binary64))) |
(neg.f64 (neg.f64 eps)) |
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (-.f64 eps #s(literal 0 binary64))) #s(literal 0 binary64)) |
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) #s(literal 0 binary64)) |
(fma.f64 (/.f64 eps eps) (/.f64 (*.f64 eps eps) eps) #s(literal 0 binary64)) |
(fma.f64 (/.f64 eps eps) eps #s(literal 0 binary64)) |
(fma.f64 (/.f64 (*.f64 eps eps) eps) (/.f64 eps (-.f64 eps #s(literal 0 binary64))) #s(literal 0 binary64)) |
(fma.f64 (/.f64 (*.f64 eps eps) eps) (/.f64 eps eps) #s(literal 0 binary64)) |
(fma.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps) #s(literal 0 binary64)) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64)) #s(literal 0 binary64)) |
(-.f64 (/.f64 #s(literal 0 binary64) eps) (neg.f64 eps)) |
(-.f64 eps (/.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64)))) |
(+.f64 #s(literal 0 binary64) eps) |
(+.f64 eps #s(literal 0 binary64)) |
eps |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal -2 binary64))) |
(*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(/.f64 (neg.f64 (*.f64 (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))) #s(literal -2 binary64))) #s(literal -2 binary64)) |
(/.f64 (neg.f64 (*.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))))) #s(literal -2 binary64)) |
(/.f64 (*.f64 (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))) #s(literal -2 binary64)) #s(literal 2 binary64)) |
(/.f64 (*.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))))) #s(literal 2 binary64)) |
(*.f64 (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))) #s(literal 1/2 binary64)) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(*.f64 (sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))))) #s(literal 2 binary64)) |
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))))) #s(literal -2 binary64)) |
(/.f64 (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))))) #s(literal 4 binary64)) |
(/.f64 (neg.f64 (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))))) #s(literal -2 binary64)) |
(/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))) #s(literal 2 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))))))) |
(/.f64 (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))) #s(literal 2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)))))) |
(-.f64 (/.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (/.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) #s(literal 2 binary64))) |
(-.f64 (/.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) #s(literal 2 binary64)) (/.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))) #s(literal 2 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(*.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal -1 binary64))) |
(*.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) |
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (cos.f64 eps))))) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps))))) |
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(fma.f64 (sin.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(fma.f64 (sin.f64 (*.f64 #s(literal 1 binary64) x)) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal 1 binary64) x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(fma.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x)) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) |
(sin.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(+.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (cos.f64 (fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) |
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1 binary64) x)) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (cos.f64 (*.f64 #s(literal 1 binary64) x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))))) |
(fma.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64))) |
(fma.f64 #s(literal 0 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64))) |
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(*.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x)) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x)) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x))))) |
(/.f64 (neg.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x)))) |
(/.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x)) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))))) |
(/.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x)))) |
(/.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x)) (fma.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) |
(fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) (*.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) |
(fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64)) |
(fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x) #s(literal 1 binary64) #s(literal 1 binary64)) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x) #s(literal 1 binary64)) |
(fma.f64 x (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) #s(literal 1 binary64)) |
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x))) (/.f64 (*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x)))) |
(-.f64 (/.f64 (*.f64 (pow.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64))) (pow.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(+.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x) #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) x) x)) |
Compiled 18 755 to 2 571 computations (86.3% saved)
20 alts after pruning (18 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 604 | 16 | 620 |
| Fresh | 2 | 2 | 4 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 1 | 1 |
| Total | 610 | 20 | 630 |
| Status | Accuracy | Program |
|---|---|---|
| 56.5% | (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) | |
| ✓ | 56.5% | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| ▶ | 55.7% | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
| ▶ | 99.8% | (*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
| ▶ | 99.6% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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)) |
| 99.6% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.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)) | |
| 99.5% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) | |
| 99.8% | (*.f64 #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) | |
| 99.3% | #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps))) | |
| 85.8% | #s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps (sin.f64 x)))) | |
| 99.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) | |
| ✓ | 81.6% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
| 99.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) | |
| ▶ | 98.3% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
| 98.3% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) | |
| 56.5% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) | |
| 98.4% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) | |
| 99.0% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x)))) | |
| 81.5% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) | |
| ▶ | 81.2% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
Compiled 976 to 678 computations (30.5% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) | |
| cost-diff | 0 | (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) | |
| cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 | 320 | (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) | |
| cost-diff | 0 | #s(approx (cos x) #s(literal 1 binary64)) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (cos.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) | |
| cost-diff | 0 | (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)) | |
| cost-diff | 0 | #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) | |
| cost-diff | 0 | (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps) | |
| cost-diff | 0 | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) | |
| cost-diff | 0 | (neg.f64 x) | |
| cost-diff | 0 | (*.f64 (neg.f64 x) eps) | |
| cost-diff | 0 | #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)) | |
| cost-diff | 0 | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) | |
| cost-diff | 0 | (*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) | |
| cost-diff | 128 | (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) | |
| cost-diff | 192 | (+.f64 #s(literal 0 binary64) eps) | |
| cost-diff | 320 | (*.f64 #s(literal 1 binary64) x) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 64 | 461 |
| 0 | 103 | 423 |
| 1 | 190 | 419 |
| 2 | 470 | 419 |
| 3 | 1219 | 419 |
| 4 | 3176 | 419 |
| 5 | 4605 | 419 |
| 6 | 6587 | 419 |
| 0 | 8069 | 412 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 eps #s(literal 1/2 binary64)) |
eps |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 #s(literal 1 binary64) x)) |
(*.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x))) |
(cos.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 #s(literal 1 binary64) x)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) |
(+.f64 #s(literal 0 binary64) eps) |
#s(literal 0 binary64) |
#s(literal -2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)) |
(*.f64 (neg.f64 x) eps) |
(neg.f64 x) |
x |
eps |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
(*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps) |
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) |
(fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)) |
eps |
(fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) |
(*.f64 x x) |
x |
#s(literal 1/4 binary64) |
#s(literal -1/2 binary64) |
(neg.f64 x) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(approx (cos x) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) |
#s(literal 1/2 binary64) |
(fma.f64 #s(literal 2 binary64) x eps) |
#s(literal 2 binary64) |
x |
eps |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) |
(fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) |
#s(literal -1/645120 binary64) |
(*.f64 eps eps) |
#s(literal 1/3840 binary64) |
#s(literal -1/48 binary64) |
#s(literal -2 binary64) |
| Outputs |
|---|
(*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (fma.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(*.f64 (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) |
(*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 eps #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) eps) |
eps |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 #s(literal 1 binary64) x)) |
(cos.f64 x) |
(*.f64 #s(literal 1 binary64) x) |
x |
#s(literal 1 binary64) |
x |
(*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x))) |
(*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(cos.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) |
(sin.f64 (*.f64 #s(literal 1 binary64) x)) |
(sin.f64 x) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
(+.f64 #s(literal 0 binary64) eps) |
eps |
#s(literal 0 binary64) |
#s(literal -2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)) |
(*.f64 (neg.f64 x) eps) |
(neg.f64 x) |
x |
eps |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x))) eps)) |
(*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps) |
(*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x))) eps) |
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) |
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x))) |
(fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)) |
(fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x)) |
eps |
(fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) |
(fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) |
(*.f64 x x) |
x |
#s(literal 1/4 binary64) |
#s(literal -1/2 binary64) |
(neg.f64 x) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
#s(approx (cos x) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) |
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
#s(literal 1/2 binary64) |
(fma.f64 #s(literal 2 binary64) x eps) |
#s(literal 2 binary64) |
x |
eps |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #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 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #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 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) |
(fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) |
(fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) |
#s(literal -1/645120 binary64) |
(*.f64 eps eps) |
#s(literal 1/3840 binary64) |
#s(literal -1/48 binary64) |
#s(literal -2 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.015625 | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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)) | |
| accuracy | 0.022684980164287515 | (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) | |
| accuracy | 0.09783055906068203 | #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) | |
| accuracy | 0.1328125 | (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) | |
| accuracy | 0 | (+.f64 x eps) | |
| accuracy | 0.03377913447833954 | (cos.f64 (+.f64 x eps)) | |
| accuracy | 1.0534121842532849 | #s(approx (cos x) #s(literal 1 binary64)) | |
| accuracy | 27.855811129695105 | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) | |
| accuracy | 0.015625 | (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)) | |
| accuracy | 0.1328125 | (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps) | |
| accuracy | 0.29844541109401235 | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) | |
| accuracy | 1.0125862664240874 | #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) | |
| accuracy | 0 | (*.f64 (neg.f64 x) eps) | |
| accuracy | 0 | (neg.f64 x) | |
| accuracy | 1.0102058434063175 | #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)) | |
| accuracy | 11.749150775642846 | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) | |
| accuracy | 0.01171875 | (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) | |
| accuracy | 0.015625 | (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) | |
| accuracy | 0.015625 | (*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) | |
| accuracy | 0.1328125 | (*.f64 (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
| 220.0ms | 177× | 2 | valid |
| 80.0ms | 77× | 1 | valid |
| 1.0ms | 2× | 0 | valid |
Compiled 819 to 127 computations (84.5% saved)
adjust: 69.0ms (27.9% of total)ival-cos: 62.0ms (25% of total)ival-mult: 57.0ms (23% of total)const: 23.0ms (9.3% of total)ival-add: 14.0ms (5.7% of total)ival-sin: 13.0ms (5.2% of total)ival-sub: 6.0ms (2.4% of total)ival-neg: 2.0ms (0.8% of total)exact: 1.0ms (0.4% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(*.f64 #s(literal 1 binary64) x) |
(+.f64 #s(literal 0 binary64) eps) |
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) |
(*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)) |
(*.f64 (neg.f64 x) eps) |
(neg.f64 x) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
(*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps) |
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) |
(fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
#s(approx (cos x) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) |
(*.f64 (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
| Outputs |
|---|
x |
(sin (* 1/2 eps)) |
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps)))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps))))))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps))))))))) |
(* -2 (pow (sin (* 1/2 eps)) 2)) |
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2))))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)))))) |
(- (cos eps) 1) |
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1) |
(* -1 (* eps x)) |
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))) |
(* -1 x) |
(* -1/2 (pow eps 2)) |
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))) |
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
eps |
(+ eps x) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(pow (sin (* 1/2 eps)) 2) |
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2)) |
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps))))) |
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps))))))) |
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps)))))))) |
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) |
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) |
(- (cos (+ eps x)) (cos x)) |
(* -1 (* eps (sin x))) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(* 1/4 (* eps (pow x 2))) |
(* (pow x 2) (- (* 1/4 eps) (/ 1 x))) |
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x))) |
(cos (+ eps x)) |
(* x (+ 1 (/ eps x))) |
(cos x) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))) |
(sin (* 1/2 (+ eps (* 2 x)))) |
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) |
(* (cos x) (sin (* 1/2 eps))) |
(- (cos (- eps (* -1 x))) (cos x)) |
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps))) |
(cos (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))) |
(sin (* 1/2 (- eps (* -2 x)))) |
(sin x) |
(+ (sin x) (* 1/2 (* eps (cos x)))) |
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x))))) |
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x)))))))) |
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(* -1 (sin x)) |
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(* 1/2 (* eps (sin x))) |
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x)))) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x)))))))))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x))))))) |
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x)))))))) |
(* 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)))) |
(* -1/2 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(* -1/2 (* eps (cos x))) |
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(* eps (- (* 1/4 (pow x 2)) 1/2)) |
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(- (cos (- x (* -1 eps))) (cos x)) |
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))) |
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps)))) |
(cos (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))) |
(sin (* 1/2 (- (* 2 x) (* -1 eps)))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | eps | @ | 0 | ((* 1 x) (+ 0 eps) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (* (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) -2) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) (* (sin (* eps 1/2)) (cos (* 1 x))) (sin (* 1/2 (+ 0 eps)))) |
| 4.0ms | x | @ | inf | ((* 1 x) (+ 0 eps) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (* (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) -2) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) (* (sin (* eps 1/2)) (cos (* 1 x))) (sin (* 1/2 (+ 0 eps)))) |
| 4.0ms | x | @ | -inf | ((* 1 x) (+ 0 eps) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (* (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) -2) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) (* (sin (* eps 1/2)) (cos (* 1 x))) (sin (* 1/2 (+ 0 eps)))) |
| 4.0ms | eps | @ | inf | ((* 1 x) (+ 0 eps) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (* (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) -2) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) (* (sin (* eps 1/2)) (cos (* 1 x))) (sin (* 1/2 (+ 0 eps)))) |
| 4.0ms | eps | @ | -inf | ((* 1 x) (+ 0 eps) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (* (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) -2) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) (* (sin (* eps 1/2)) (cos (* 1 x))) (sin (* 1/2 (+ 0 eps)))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 375 | 1503 |
| 1 | 1156 | 1425 |
| 2 | 3154 | 1384 |
| 3 | 7243 | 1384 |
| 0 | 8346 | 1273 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
x |
(sin (* 1/2 eps)) |
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps)))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps))))))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps))))))))) |
(* -2 (pow (sin (* 1/2 eps)) 2)) |
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2))))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)))))) |
(- (cos eps) 1) |
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1) |
(* -1 (* eps x)) |
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))) |
(* -1 x) |
(* -1/2 (pow eps 2)) |
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))) |
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
eps |
(+ eps x) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(pow (sin (* 1/2 eps)) 2) |
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2)) |
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps))))) |
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps))))))) |
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps)))))))) |
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) |
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) |
(- (cos (+ eps x)) (cos x)) |
(* -1 (* eps (sin x))) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(* 1/4 (* eps (pow x 2))) |
(* (pow x 2) (- (* 1/4 eps) (/ 1 x))) |
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x))) |
(cos (+ eps x)) |
(* x (+ 1 (/ eps x))) |
(cos x) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))) |
(sin (* 1/2 (+ eps (* 2 x)))) |
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) |
(* (cos x) (sin (* 1/2 eps))) |
(- (cos (- eps (* -1 x))) (cos x)) |
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps))) |
(cos (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))) |
(sin (* 1/2 (- eps (* -2 x)))) |
(sin x) |
(+ (sin x) (* 1/2 (* eps (cos x)))) |
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x))))) |
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x)))))))) |
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(* -1 (sin x)) |
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(* 1/2 (* eps (sin x))) |
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x)))) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x)))))))))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x))))))) |
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x)))))))) |
(* 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)))) |
(* -1/2 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(* -1/2 (* eps (cos x))) |
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(* eps (- (* 1/4 (pow x 2)) 1/2)) |
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(- (cos (- x (* -1 eps))) (cos x)) |
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))) |
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps)))) |
(cos (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))) |
(sin (* 1/2 (- (* 2 x) (* -1 eps)))) |
| Outputs |
|---|
x |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps)))) |
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps))))))) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) x)) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps))))))))) |
(fma.f64 (fma.f64 (fma.f64 x (*.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* -2 (pow (sin (* 1/2 eps)) 2)) |
(*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64)) |
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2))))) |
(fma.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (*.f64 (*.f64 (*.f64 #s(literal -2 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)))))) |
(fma.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal -2 binary64) (*.f64 x (*.f64 #s(literal 1/3 binary64) x))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) x)) x (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))) |
(- (cos eps) 1) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1) |
(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) |
(fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1) |
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 eps) x) (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(* -1 (* eps x)) |
(*.f64 (neg.f64 x) eps) |
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))) |
(*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 eps (fma.f64 #s(literal -1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64))) (*.f64 (neg.f64 x) eps)) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))) |
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal -1/120 binary64))) (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)))) x) |
(* -1 x) |
(neg.f64 x) |
(* -1/2 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) |
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x)) |
(* -1/2 eps) |
(*.f64 #s(literal -1/2 binary64) eps) |
(+ (* -1 x) (* -1/2 eps)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))) |
(fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x)) |
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) |
(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 eps) (neg.f64 (sin.f64 eps))) x (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(fma.f64 (fma.f64 (sin.f64 eps) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/2 binary64))) x (cos.f64 eps)) |
eps |
(+ eps x) |
(+.f64 eps x) |
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 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(pow (sin (* 1/2 eps)) 2) |
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2)) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #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)))) |
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(fma.f64 (fma.f64 (fma.f64 x (*.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps))))) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps))))))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps)))))))) |
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) |
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) |
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) |
(*.f64 (*.f64 #s(literal -2 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (cos (+ eps x)) (cos x)) |
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(* -1 (* eps (sin x))) |
(*.f64 (neg.f64 (sin.f64 x)) eps) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) |
(* 1/4 (* eps (pow x 2))) |
(*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) eps) |
(* (pow x 2) (- (* 1/4 eps) (/ 1 x))) |
(*.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x)) (*.f64 x x)) |
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x))) |
(*.f64 (*.f64 (fma.f64 eps (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) x) x) |
(cos (+ eps x)) |
(cos.f64 (+.f64 eps x)) |
(* x (+ 1 (/ eps x))) |
(fma.f64 (/.f64 eps x) x x) |
(cos x) |
(cos.f64 x) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin (* 1/2 (+ eps (* 2 x)))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) |
(*.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* (cos x) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) |
(- (cos (- eps (* -1 x))) (cos x)) |
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps))) |
(*.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))) x) x) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 eps x)) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 (/.f64 eps x) x x) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x) x) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin (* 1/2 (- eps (* -2 x)))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* 1/2 (* eps (cos x)))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x)))))))) |
(fma.f64 (fma.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps)) eps (sin.f64 x)) |
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) |
(*.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(*.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps) |
(* -1 (sin x)) |
(neg.f64 (sin.f64 x)) |
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x) |
(fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (neg.f64 x)) |
(+ (cos x) (* -1 (* eps (sin x)))) |
(fma.f64 (neg.f64 (sin.f64 x)) eps (cos.f64 x)) |
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps (cos.f64 x)) |
(* 1/2 (* eps (sin x))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 x)) eps) |
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x)))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps (*.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x)))))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps) |
(* 1/2 (* eps (cos x))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps) |
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x)))) |
(*.f64 (*.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))) eps) |
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x))))))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps)) |
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x)))))))) |
(*.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 (cos.f64 x) (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64))) (*.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #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 (fma.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)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(* -1/2 (* (pow eps 2) (cos x))) |
(*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps) |
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(*.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) eps) |
(* -1/2 (* eps (cos x))) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) |
(* eps (- (* 1/4 (pow x 2)) 1/2)) |
(*.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps) |
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)) |
(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 (/.f64 x eps) eps eps) |
(* eps (+ 1/2 (/ x eps))) |
(*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps) |
(- (cos (- x (* -1 eps))) (cos x)) |
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) |
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps)))) |
(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 eps x)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (/.f64 x eps) eps eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin (* 1/2 (- (* 2 x) (* -1 eps)))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 64 | 330 |
| 0 | 103 | 310 |
| 1 | 354 | 271 |
| 2 | 2758 | 271 |
| 0 | 8454 | 264 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 #s(literal 1 binary64) x) |
(+.f64 #s(literal 0 binary64) eps) |
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) |
(*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)) |
(*.f64 (neg.f64 x) eps) |
(neg.f64 x) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
(*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps) |
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) |
(fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
#s(approx (cos x) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) |
(*.f64 (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
| Outputs |
|---|
(*.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(*.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 2 binary64) (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) x)) |
(*.f64 x #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) x) |
(pow.f64 x #s(literal 1 binary64)) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 1 binary64))) |
x |
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eps |
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(/.f64 (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64))))) (neg.f64 (fma.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (cos.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) |
(/.f64 (*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x)))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (fma.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)))) |
(/.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x)))) |
(/.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)))) (fma.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)))) |
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(fma.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(fma.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+.f64 (*.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(*.f64 (+.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 1/2 binary64)) |
(*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) |
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (neg.f64 (+.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 2 binary64)) |
(/.f64 (neg.f64 (+.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))) |
(/.f64 (+.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
Compiled 21 034 to 2 678 computations (87.3% saved)
22 alts after pruning (17 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 563 | 6 | 569 |
| Fresh | 2 | 11 | 13 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 2 | 2 |
| Total | 567 | 22 | 589 |
| Status | Accuracy | Program |
|---|---|---|
| 56.5% | (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) | |
| 86.3% | (/.f64 (*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x)))) | |
| ✓ | 56.5% | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| ✓ | 55.7% | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
| ▶ | 99.8% | (*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
| 99.6% | (*.f64 (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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)) | |
| ▶ | 99.8% | (*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) |
| 99.6% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.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)) | |
| 99.5% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) | |
| 99.3% | #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps))) | |
| ▶ | 99.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
| ✓ | 81.6% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
| 99.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) | |
| ✓ | 98.3% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
| 98.3% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) | |
| ▶ | 56.5% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
| ▶ | 98.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
| 98.4% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) | |
| 99.0% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x)))) | |
| 73.8% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 x)) (neg.f64 eps)))) | |
| 81.5% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) | |
| ✓ | 81.2% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
Compiled 999 to 689 computations (31% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (fma.f64 #s(literal 1/2 binary64) eps x) | |
| cost-diff | 0 | (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) | |
| cost-diff | 0 | (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) | |
| cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) | |
| cost-diff | 0 | #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) | |
| cost-diff | 0 | (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) | |
| cost-diff | 0 | (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps) | |
| cost-diff | 0 | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) | |
| cost-diff | 0 | #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) | |
| cost-diff | 0 | (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps) | |
| cost-diff | 0 | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) | |
| cost-diff | 576 | (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps) | |
| cost-diff | 0 | (*.f64 #s(literal -1/2 binary64) eps) | |
| cost-diff | 0 | #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) | |
| cost-diff | 0 | (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps) | |
| cost-diff | 0 | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) | |
| cost-diff | 0 | (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) | |
| cost-diff | 0 | (*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) | |
| cost-diff | 128 | (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) | |
| cost-diff | 192 | (+.f64 #s(literal 0 binary64) eps) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 58 | 479 |
| 0 | 91 | 465 |
| 1 | 150 | 465 |
| 2 | 299 | 465 |
| 3 | 584 | 465 |
| 4 | 1021 | 465 |
| 5 | 1490 | 460 |
| 6 | 2160 | 460 |
| 7 | 3233 | 460 |
| 8 | 5041 | 460 |
| 9 | 6609 | 460 |
| 10 | 7434 | 460 |
| 11 | 7651 | 460 |
| 12 | 7852 | 460 |
| 0 | 8138 | 457 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin.f64 x) |
x |
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
eps |
(*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(cos.f64 x) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) |
(+.f64 #s(literal 0 binary64) eps) |
#s(literal 0 binary64) |
#s(literal -2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
(*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps) |
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(literal -1/2 binary64) |
eps |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
(*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps) |
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) |
#s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps)) |
(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps) |
(fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) |
x |
(fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) |
#s(literal 1/4 binary64) |
(/.f64 #s(literal -1 binary64) eps) |
#s(literal -1 binary64) |
eps |
#s(literal -1/2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
(*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps) |
(-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) |
#s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) |
(*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) |
eps |
(fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) |
(*.f64 x x) |
x |
#s(literal 1/4 binary64) |
#s(literal -1/2 binary64) |
(sin.f64 x) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin.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 |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal -2 binary64) |
| Outputs |
|---|
(*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x))))) |
(*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
(*.f64 (fma.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(fma.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x))) |
(*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) |
(sin.f64 x) |
x |
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
eps |
(*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) |
(cos.f64 x) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) |
(*.f64 eps #s(literal 1/2 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
eps |
#s(literal 0 binary64) |
#s(literal -2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
(*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps) |
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(literal -1/2 binary64) |
eps |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps)) |
(*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps) |
(*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) eps) |
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) |
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)))) |
#s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps)) |
#s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x))) |
(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x)) |
(fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) |
(fma.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x #s(literal -1/2 binary64)) |
x |
(fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) |
(fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) |
#s(literal 1/4 binary64) |
(/.f64 #s(literal -1 binary64) eps) |
#s(literal -1 binary64) |
eps |
#s(literal -1/2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)) (sin.f64 x)) eps)) |
(*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps) |
(*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)) (sin.f64 x)) eps) |
(-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) |
(-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)) (sin.f64 x)) |
#s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) |
#s(approx (* (* (cos x) -1/2) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)) |
(*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps) |
eps |
(fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) |
(*.f64 x x) |
x |
#s(literal 1/4 binary64) |
#s(literal -1/2 binary64) |
(sin.f64 x) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(fma.f64 eps #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
eps |
x |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
#s(literal -2 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) | |
| accuracy | 0.015625 | (*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) | |
| accuracy | 0.022684980164287515 | (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) | |
| accuracy | 0.1328125 | (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) | |
| accuracy | 0.015625 | (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) | |
| accuracy | 0.1328125 | (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps) | |
| accuracy | 0.29844541109401235 | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) | |
| accuracy | 0.5499404098066911 | #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) | |
| accuracy | 0.2421875 | (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps) | |
| accuracy | 0.2578125 | (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) | |
| accuracy | 0.29844541109401235 | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) | |
| accuracy | 1.0125862664240874 | #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) | |
| accuracy | 0 | (*.f64 #s(literal -1/2 binary64) eps) | |
| accuracy | 0.1328125 | (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps) | |
| accuracy | 0.29844541109401235 | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) | |
| accuracy | 59.14851230847842 | #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) | |
| accuracy | 0.01171875 | (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) | |
| accuracy | 0.015625 | (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) | |
| accuracy | 0.015625 | (*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) | |
| accuracy | 0.1328125 | (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
| 174.0ms | 177× | 2 | valid |
| 55.0ms | 77× | 1 | valid |
| 1.0ms | 2× | 0 | valid |
Compiled 808 to 107 computations (86.8% saved)
ival-cos: 58.0ms (31.9% of total)ival-mult: 44.0ms (24.2% of total)adjust: 35.0ms (19.3% of total)ival-add: 25.0ms (13.8% of total)ival-sin: 9.0ms (5% of total)ival-sub: 6.0ms (3.3% of total)ival-div: 4.0ms (2.2% of total)exact: 1.0ms (0.6% of total)ival-neg: 1.0ms (0.6% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(+.f64 #s(literal 0 binary64) eps) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
(*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps) |
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) |
(*.f64 #s(literal -1/2 binary64) eps) |
(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
(*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps) |
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
(*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps) |
(-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) |
#s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
| Outputs |
|---|
(sin (* 1/2 eps)) |
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps)))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps))))))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps))))))))) |
(* -2 (pow (sin (* 1/2 eps)) 2)) |
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2))))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)))))) |
(pow (sin (* 1/2 eps)) 2) |
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2)) |
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(- (cos eps) 1) |
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1) |
(* -1/2 (pow eps 2)) |
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))) |
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))) |
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2)))) |
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps)))) |
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2)))))))) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps))))) |
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps))))))) |
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps)))))))) |
-1/2 |
(- (* -1 (/ x eps)) 1/2) |
(- (* x (- (* 1/4 x) (/ 1 eps))) 1/2) |
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) |
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) |
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) |
(- (cos (+ eps x)) (cos x)) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(* 1/4 (* eps (pow x 2))) |
(* (pow x 2) (- (* 1/4 eps) (/ 1 x))) |
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x))) |
(* -1/2 (* eps (cos x))) |
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))) |
(sin (+ x (* 1/2 eps))) |
x |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* (cos x) (sin (* 1/2 eps))) |
(* 1/4 (pow x 2)) |
(* (pow x 2) (- 1/4 (/ 1 (* eps x)))) |
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x)))) |
(- (cos (- eps (* -1 x))) (cos x)) |
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps))) |
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))) |
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))) |
(sin (- (* 1/2 eps) (* -1 x))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
eps |
(sin x) |
(+ (sin x) (* 1/2 (* eps (cos x)))) |
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x))))) |
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x)))))))) |
(* -1 (* eps (sin x))) |
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) |
(* 1/2 (* eps (sin x))) |
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x)))) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x)))))))))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(* -1 (sin x)) |
(* -1 x) |
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x))))))) |
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x)))))))) |
(* -1 (/ x eps)) |
(/ (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 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)))) |
(* -1/2 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(* eps (- (* 1/4 (pow x 2)) 1/2)) |
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)) |
(* eps (+ 1/2 (/ x eps))) |
(- (* 1/4 (pow x 2)) 1/2) |
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2) |
(- (cos (- x (* -1 eps))) (cos x)) |
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))) |
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps)))) |
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))) |
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))) |
(sin (- x (* -1/2 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 8.0ms | x | @ | inf | ((+ 0 eps) (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (* (* (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/2 eps) (* (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (* (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) -2) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) (* (cos x) (sin (* 1/2 eps))) (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (sin (* 1/2 eps))) |
| 3.0ms | eps | @ | -inf | ((+ 0 eps) (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (* (* (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/2 eps) (* (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (* (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) -2) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) (* (cos x) (sin (* 1/2 eps))) (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (sin (* 1/2 eps))) |
| 3.0ms | x | @ | -inf | ((+ 0 eps) (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (* (* (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/2 eps) (* (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (* (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) -2) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) (* (cos x) (sin (* 1/2 eps))) (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (sin (* 1/2 eps))) |
| 3.0ms | eps | @ | inf | ((+ 0 eps) (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (* (* (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/2 eps) (* (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (* (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) -2) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) (* (cos x) (sin (* 1/2 eps))) (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (sin (* 1/2 eps))) |
| 2.0ms | eps | @ | 0 | ((+ 0 eps) (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (* (* (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin x) (cos (* 1/2 eps))) (* (cos x) (sin (* 1/2 eps)))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* -1/2 eps) (* (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) eps) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (* (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) -2) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) (* (cos x) (sin (* 1/2 eps))) (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (sin (* 1/2 eps))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 343 | 1393 |
| 1 | 1064 | 1333 |
| 2 | 2960 | 1287 |
| 3 | 6592 | 1287 |
| 0 | 8225 | 1183 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sin (* 1/2 eps)) |
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps)))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps))))))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps))))))))) |
(* -2 (pow (sin (* 1/2 eps)) 2)) |
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2))))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)))))) |
(pow (sin (* 1/2 eps)) 2) |
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2)) |
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(- (cos eps) 1) |
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1) |
(* -1/2 (pow eps 2)) |
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))) |
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))) |
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2)))) |
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps)))) |
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2)))))))) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps))))) |
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps))))))) |
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps)))))))) |
-1/2 |
(- (* -1 (/ x eps)) 1/2) |
(- (* x (- (* 1/4 x) (/ 1 eps))) 1/2) |
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) |
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) |
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) |
(- (cos (+ eps x)) (cos x)) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(* 1/4 (* eps (pow x 2))) |
(* (pow x 2) (- (* 1/4 eps) (/ 1 x))) |
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x))) |
(* -1/2 (* eps (cos x))) |
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))) |
(sin (+ x (* 1/2 eps))) |
x |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* (cos x) (sin (* 1/2 eps))) |
(* 1/4 (pow x 2)) |
(* (pow x 2) (- 1/4 (/ 1 (* eps x)))) |
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x)))) |
(- (cos (- eps (* -1 x))) (cos x)) |
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps))) |
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))) |
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))) |
(sin (- (* 1/2 eps) (* -1 x))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
eps |
(sin x) |
(+ (sin x) (* 1/2 (* eps (cos x)))) |
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x))))) |
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x)))))))) |
(* -1 (* eps (sin x))) |
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) |
(* 1/2 (* eps (sin x))) |
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x)))) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x)))))))))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(* -1 (sin x)) |
(* -1 x) |
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x))))))) |
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x)))))))) |
(* -1 (/ x eps)) |
(/ (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 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)))) |
(* -1/2 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(* eps (- (* 1/4 (pow x 2)) 1/2)) |
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)) |
(* eps (+ 1/2 (/ x eps))) |
(- (* 1/4 (pow x 2)) 1/2) |
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2) |
(- (cos (- x (* -1 eps))) (cos x)) |
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))) |
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps)))) |
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))) |
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))) |
(sin (- x (* -1/2 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
| Outputs |
|---|
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps)))) |
(fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps))))))) |
(fma.f64 (fma.f64 x (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x)) |
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps))))))))) |
(fma.f64 (fma.f64 (fma.f64 x (*.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* -2 (pow (sin (* 1/2 eps)) 2)) |
(*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64)) |
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2))))) |
(fma.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (*.f64 (*.f64 (*.f64 #s(literal -2 binary64) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)))))) |
(fma.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal -2 binary64) (*.f64 x (*.f64 #s(literal 1/3 binary64) x))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) x)) x (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))) |
(pow (sin (* 1/2 eps)) 2) |
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) |
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2)) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(fma.f64 (fma.f64 x (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #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)))) |
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2)) |
(fma.f64 (fma.f64 (fma.f64 x (*.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(- (cos eps) 1) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1) |
(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1) |
(fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1) |
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 eps) x) (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(* -1/2 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) |
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 x eps) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))) |
(fma.f64 (*.f64 x x) (*.f64 eps (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) |
(* -1/2 eps) |
(*.f64 #s(literal -1/2 binary64) eps) |
(+ (* -1 x) (* -1/2 eps)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) |
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) |
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2)))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps) |
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps)))) |
(fma.f64 (*.f64 #s(literal -1/48 binary64) eps) (pow.f64 x #s(literal 4 binary64)) (*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps)) |
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2)))))))) |
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal 1/1440 binary64) (*.f64 x x) #s(literal -1/48 binary64))) (*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps)) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps))))) |
(*.f64 (fma.f64 x (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps))))))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps)))))))) |
(fma.f64 (fma.f64 x (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))))) |
-1/2 |
#s(literal -1/2 binary64) |
(- (* -1 (/ x eps)) 1/2) |
(-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) |
(- (* x (- (* 1/4 x) (/ 1 eps))) 1/2) |
(fma.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x #s(literal -1/2 binary64)) |
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) |
(fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) |
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))) |
(*.f64 (*.f64 #s(literal -2 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) |
(*.f64 (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(- (cos (+ eps x)) (cos x)) |
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) |
(* 1/4 (* eps (pow x 2))) |
(*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) x) x) eps) |
(* (pow x 2) (- (* 1/4 eps) (/ 1 x))) |
(*.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x)) (*.f64 x x)) |
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x))) |
(*.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x)) x) x) |
(* -1/2 (* eps (cos x))) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin (+ x (* 1/2 eps))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
x |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) |
(* (cos x) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) |
(* 1/4 (pow x 2)) |
(*.f64 (*.f64 #s(literal 1/4 binary64) x) x) |
(* (pow x 2) (- 1/4 (/ 1 (* eps x)))) |
(*.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) eps)) x) x) |
(* (pow x 2) (+ 1/4 (* -1 (/ (+ (/ 1 eps) (* 1/2 (/ 1 x))) x)))) |
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/2 binary64) x)) x)) (*.f64 x x)) |
(- (cos (- eps (* -1 x))) (cos x)) |
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps))) |
(*.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x)) x) x) |
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin (- (* 1/2 eps) (* -1 x))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) |
eps |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* 1/2 (* eps (cos x)))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) |
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x)))))))) |
(fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) (*.f64 (*.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps)) eps (sin.f64 x)) |
(* -1 (* eps (sin x))) |
(*.f64 (neg.f64 (sin.f64 x)) eps) |
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x)))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x))))))))) |
(*.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps) |
(* 1/2 (* eps (sin x))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 x)) eps) |
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x)))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps (*.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps) |
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x)))))))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/48 binary64))) eps (*.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(*.f64 (fma.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps)) eps (neg.f64 (sin.f64 x))) eps) |
(* -1 (sin x)) |
(neg.f64 (sin.f64 x)) |
(* -1 x) |
(neg.f64 x) |
(+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) |
(* 1/2 (* eps (cos x))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps) |
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x)))) |
(*.f64 (*.f64 (cos.f64 x) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64))) eps) |
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x))))))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 (cos.f64 x) (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps)) |
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x)))))))) |
(*.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 (cos.f64 x) (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64))) (*.f64 (cos.f64 x) (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)))) eps) |
(* -1 (/ x eps)) |
(/.f64 (neg.f64 x) eps) |
(/ (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))) eps) |
(/.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps (neg.f64 x)) eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 (fma.f64 (fma.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)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(* -1/2 (* (pow eps 2) (cos x))) |
(*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps) |
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(*.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) eps) |
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) |
(* eps (- (* 1/4 (pow x 2)) 1/2)) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps) |
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2)) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x #s(literal -1/2 binary64)) eps) |
(* eps (+ 1/2 (/ x eps))) |
(*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps) |
(- (* 1/4 (pow x 2)) 1/2) |
(fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) |
(- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2) |
(fma.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x #s(literal -1/2 binary64)) |
(- (cos (- x (* -1 eps))) (cos x)) |
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) |
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps)))) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x #s(literal -1/2 binary64)) eps) |
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin (- x (* -1/2 eps))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 58 | 372 |
| 0 | 91 | 333 |
| 1 | 311 | 333 |
| 2 | 2518 | 333 |
| 0 | 8490 | 333 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(+.f64 #s(literal 0 binary64) eps) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
(*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps) |
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) |
(*.f64 #s(literal -1/2 binary64) eps) |
(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
(*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps) |
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
(*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps) |
(-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) |
#s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
| Outputs |
|---|
(*.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)) |
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64))) |
(pow.f64 (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64)) |
(pow.f64 eps #s(literal 1 binary64)) |
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (neg.f64 eps)) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (*.f64 eps eps)) |
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) (neg.f64 (neg.f64 eps))) |
(/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (neg.f64 (*.f64 eps eps))) |
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps)) |
(/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64))) |
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps)) |
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps)))) |
(/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal -1 binary64))) |
(fma.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps) #s(literal 0 binary64)) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64)) #s(literal 0 binary64)) |
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps)) (/.f64 (*.f64 eps eps) (neg.f64 eps))) |
(+.f64 eps #s(literal 0 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
eps |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (pow.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -1 binary64))) |
(*.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64))) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64)))) #s(literal -1 binary64)) |
(/.f64 (-.f64 (*.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)))) (pow.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))) |
(/.f64 (fma.f64 (+.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 (+.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))) #s(literal -4 binary64)) |
(/.f64 (fma.f64 (+.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))) |
(/.f64 (fma.f64 (+.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 4 binary64)) |
(/.f64 (fma.f64 (neg.f64 (+.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) (+.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal -4 binary64)) |
(/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) (+.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))) (*.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))) |
(/.f64 (fma.f64 (+.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 4 binary64)) |
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x)))) |
(/.f64 (neg.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))))) (neg.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64))))) |
(/.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (cos.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x))) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))))) |
(fma.f64 (sin.f64 (+.f64 x #s(literal 0 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (+.f64 x #s(literal 0 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(fma.f64 (+.f64 (sin.f64 (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) |
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) |
(fma.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) |
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) |
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(/.f64 (fma.f64 #s(literal 1 binary64) (*.f64 eps #s(literal -1 binary64)) (*.f64 (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64))) (*.f64 x #s(literal 1 binary64)))) (*.f64 (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64))) (*.f64 eps #s(literal -1 binary64)))) |
(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 eps) (*.f64 (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64))) (*.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64))) (neg.f64 eps))) |
(/.f64 (fma.f64 #s(literal 1 binary64) (*.f64 eps #s(literal -1 binary64)) (*.f64 (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64))) (*.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64))) (*.f64 eps #s(literal -1 binary64)))) |
(/.f64 (fma.f64 #s(literal 1 binary64) eps (*.f64 (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64))) (neg.f64 x))) (*.f64 (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64))) eps)) |
(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 eps) (*.f64 (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64))) x)) (*.f64 (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64))) (neg.f64 eps))) |
(/.f64 (fma.f64 #s(literal 1 binary64) (*.f64 eps #s(literal -1 binary64)) (*.f64 (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64))) x)) (*.f64 (/.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64))) (*.f64 eps #s(literal -1 binary64)))) |
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal 2 binary64))) (-.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x #s(literal 1/2 binary64)))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal 3 binary64)) #s(literal -1/8 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal -1/2 binary64))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x #s(literal 1/2 binary64))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal -1/2 binary64))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal -1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x #s(literal 1/2 binary64)) (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal -1/2 binary64))) (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal 3 binary64)) #s(literal -1/8 binary64)))) |
(fma.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64)) (pow.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal 1/2 binary64)) #s(literal -1 binary64)) (/.f64 (neg.f64 x) eps)) |
(fma.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64) #s(literal -1/8 binary64)) (pow.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/8 binary64)))) #s(literal -1 binary64)) (/.f64 (neg.f64 x) eps)) |
(fma.f64 (*.f64 #s(literal 1/4 binary64) x) x (fma.f64 (/.f64 #s(literal -1 binary64) eps) x #s(literal -1/2 binary64))) |
(fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (fma.f64 (/.f64 #s(literal -1 binary64) eps) x #s(literal -1/2 binary64))) |
(fma.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x #s(literal -1/2 binary64)) |
(fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (fma.f64 (/.f64 #s(literal -1 binary64) eps) x #s(literal -1/2 binary64))) |
(fma.f64 x (*.f64 #s(literal 1/4 binary64) x) (fma.f64 (/.f64 #s(literal -1 binary64) eps) x #s(literal -1/2 binary64))) |
(fma.f64 x (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) |
(-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x #s(literal 1/2 binary64)))) |
(+.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) x) x) (fma.f64 (/.f64 #s(literal -1 binary64) eps) x #s(literal -1/2 binary64))) |
(+.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x) #s(literal -1/2 binary64)) |
(+.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (/.f64 (neg.f64 x) eps)) |
(+.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal -1 binary64) eps)) x)) |
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 0 binary64))) |
(fma.f64 #s(literal 0 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 0 binary64))) |
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal 1 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
Compiled 19 400 to 2 197 computations (88.7% saved)
24 alts after pruning (15 fresh and 9 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 418 | 7 | 425 |
| Fresh | 4 | 8 | 12 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 5 | 5 |
| Total | 423 | 24 | 447 |
| Status | Accuracy | Program |
|---|---|---|
| 56.5% | (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) | |
| 86.3% | (/.f64 (*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x)))) | |
| ✓ | 56.5% | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| ✓ | 55.7% | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
| 99.8% | (*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) | |
| 99.6% | (*.f64 (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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)) | |
| ✓ | 99.8% | (*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) |
| 99.6% | (*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.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)) | |
| 99.5% | (*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) | |
| 99.2% | #s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)) eps (*.f64 (neg.f64 (sin.f64 x)) eps))) | |
| ✓ | 99.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
| ✓ | 81.6% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
| 99.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) | |
| ✓ | 98.3% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
| 98.3% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) | |
| ✓ | 56.5% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
| ✓ | 98.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
| 98.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 #s(approx (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps))) eps)) | |
| 98.4% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x eps) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) | |
| 99.0% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 x x) (*.f64 eps (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))) | |
| 99.0% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x)))) | |
| 73.8% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 x)) (neg.f64 eps)))) | |
| 81.5% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) | |
| ✓ | 81.2% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
Compiled 1 619 to 680 computations (58% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 #s(approx (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 x)) (neg.f64 eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x eps) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 x x) (*.f64 eps (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)) eps (*.f64 (neg.f64 (sin.f64 x)) eps))) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.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 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.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 (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) |
(*.f64 #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
(/.f64 (*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x)))) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) |
(*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1 binary64) x))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps (sin.f64 x)))) |
| Outputs |
|---|
(*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) |
3 calls:
| 11.0ms | x |
| 10.0ms | eps |
| 8.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
| 99.8% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 #s(approx (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 x)) (neg.f64 eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x eps) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 x x) (*.f64 eps (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)) eps (*.f64 (neg.f64 (sin.f64 x)) eps))) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.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 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.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 (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) |
(*.f64 #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) |
(/.f64 (*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x)))) (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x)))) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) |
| Outputs |
|---|
(*.f64 #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) |
3 calls:
| 9.0ms | x |
| 9.0ms | eps |
| 7.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
| 99.8% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 #s(approx (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 x)) (neg.f64 eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x eps) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 x x) (*.f64 eps (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)) eps (*.f64 (neg.f64 (sin.f64 x)) eps))) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.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 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.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 (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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)) |
3 calls:
| 7.0ms | x |
| 7.0ms | eps |
| 6.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | x |
| 99.6% | 1 | eps |
| 99.6% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 #s(approx (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 x)) (neg.f64 eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x eps) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 x x) (*.f64 eps (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)) eps (*.f64 (neg.f64 (sin.f64 x)) eps))) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.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 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.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)) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.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)) |
3 calls:
| 7.0ms | eps |
| 7.0ms | x |
| 5.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | x |
| 99.6% | 1 | eps |
| 99.6% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 #s(approx (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 x)) (neg.f64 eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x eps) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 x x) (*.f64 eps (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)) eps (*.f64 (neg.f64 (sin.f64 x)) eps))) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) |
3 calls:
| 6.0ms | x |
| 6.0ms | eps |
| 5.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | x |
| 99.5% | 1 | eps |
| 99.5% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 #s(approx (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 x)) (neg.f64 eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x eps) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 x x) (*.f64 eps (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)) eps (*.f64 (neg.f64 (sin.f64 x)) eps))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
3 calls:
| 6.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 5.0ms | x |
| 5.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.2% | 1 | x |
| 99.2% | 1 | eps |
| 99.2% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 #s(approx (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 x)) (neg.f64 eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x eps) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 x x) (*.f64 eps (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 x x) (*.f64 eps (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))) |
3 calls:
| 5.0ms | x |
| 5.0ms | eps |
| 4.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.0% | 1 | x |
| 99.0% | 1 | eps |
| 99.0% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 #s(approx (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 x)) (neg.f64 eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x eps) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) x (neg.f64 eps)) x)))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
3 calls:
| 4.0ms | eps |
| 4.0ms | x |
| 3.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.0% | 1 | x |
| 99.0% | 1 | eps |
| 99.0% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 #s(approx (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 x)) (neg.f64 eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps)) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
3 calls:
| 3.0ms | x |
| 3.0ms | eps |
| 2.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.3% | 1 | x |
| 98.3% | 1 | eps |
| 98.3% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (*.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 #s(approx (+ (* x (+ (* x 1/4) (/ -1 eps))) -1/2) (-.f64 #s(literal -1/2 binary64) (/.f64 x eps))) eps))) eps)) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
3 calls:
| 2.0ms | x |
| 2.0ms | eps |
| 2.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.3% | 1 | x |
| 98.3% | 1 | eps |
| 98.3% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
Total -15.9b remaining (-131.8%)
Threshold costs -15.9b (-131.8%)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
3 calls:
| 1.0ms | x |
| 1.0ms | eps |
| 1.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 81.2% | 1 | x |
| 81.2% | 1 | eps |
| 81.2% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 105 | 304 |
| 1 | 140 | 304 |
| 2 | 151 | 304 |
| 3 | 160 | 304 |
| 4 | 164 | 304 |
| 5 | 165 | 304 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) |
(*.f64 #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.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 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 x x) (*.f64 eps (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
| Outputs |
|---|
(*.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64)) |
(*.f64 #s(literal -2 binary64) (*.f64 (+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(*.f64 #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 #s(approx (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #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 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.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 (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)))) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps)) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 x x) (*.f64 eps (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (*.f64 x x) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 58 | 372 |
| 0 | 91 | 333 |
| 1 | 311 | 333 |
| 2 | 2518 | 333 |
| 0 | 8490 | 333 |
| 0 | 64 | 330 |
| 0 | 103 | 310 |
| 1 | 354 | 271 |
| 2 | 2758 | 271 |
| 0 | 8454 | 264 |
| 0 | 343 | 1393 |
| 1 | 1064 | 1333 |
| 2 | 2960 | 1287 |
| 3 | 6592 | 1287 |
| 0 | 8225 | 1183 |
| 0 | 41 | 188 |
| 0 | 69 | 180 |
| 1 | 242 | 180 |
| 2 | 1811 | 180 |
| 0 | 8797 | 180 |
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 54 | 16 |
| 2 | 380 | 16 |
| 3 | 4694 | 16 |
| 0 | 8209 | 16 |
| 0 | 377 | 1403 |
| 1 | 1132 | 1352 |
| 2 | 2972 | 1306 |
| 3 | 6899 | 1306 |
| 0 | 8605 | 1194 |
| 0 | 105 | 296 |
| 1 | 277 | 293 |
| 2 | 609 | 293 |
| 3 | 2402 | 292 |
| 4 | 7842 | 292 |
| 0 | 8510 | 272 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 802 to 419 computations (47.8% saved)
Compiled 656 to 256 computations (61% saved)
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