
Time bar (total: 11.6s)
| 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)
| 3.1s | 5 776× | 2 | valid |
| 3.1s | 26 412× | 0 | invalid |
| 584.0ms | 2 425× | 1 | valid |
| 54.0ms | 55× | 0 | valid |
ival-cos: 2.2s (42.1% of total)const: 772.0ms (14.8% of total)adjust: 460.0ms (8.8% of total)ival-add: 305.0ms (5.8% of total)ival-mult: 305.0ms (5.8% of total)ival-sub: 293.0ms (5.6% of total)ival-fabs: 266.0ms (5.1% of total)ival-<=: 242.0ms (4.6% of total)ival-<: 221.0ms (4.2% of total)ival-and: 104.0ms (2% of total)exact: 42.0ms (0.8% of total)ival-assert: 12.0ms (0.2% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 128 | 2 | (-8.66964865312651e-160 8.608952818588859e-165) | 0 | - | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 3 | 0 | - | 1 | (140.94885510227076 7.174700119376859e-6) | (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 | 130 | 0 |
cos.f64 | (cos.f64 (+.f64 x eps)) | sensitivity | 2 | 1 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 128 | 0 |
| - | 2 | 126 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 128 | 0 | 0 |
| - | 2 | 0 | 126 |
| number | freq |
|---|---|
| 0 | 126 |
| 1 | 128 |
| 2 | 2 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 136.0ms | 370× | 2 | valid |
| 18.0ms | 142× | 1 | valid |
Compiled 47 to 22 computations (53.2% saved)
ival-cos: 97.0ms (73.6% of total)adjust: 24.0ms (18.2% of total)ival-sub: 6.0ms (4.6% of total)ival-add: 4.0ms (3% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 41 |
| 1 | 46 | 41 |
| 2 | 86 | 41 |
| 3 | 117 | 41 |
| 4 | 125 | 41 |
| 5 | 147 | 41 |
| 6 | 231 | 41 |
| 7 | 792 | 41 |
| 8 | 5144 | 41 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 22 | 7 |
| 2 | 40 | 7 |
| 3 | 65 | 7 |
| 4 | 78 | 7 |
| 5 | 100 | 7 |
| 6 | 184 | 7 |
| 7 | 742 | 7 |
| 8 | 5073 | 7 |
| 0 | 8505 | 7 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 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 |
|---|---|---|
| ▶ | 55.0% | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
| Inputs |
|---|
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
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) |
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 (+ 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) x eps (cos x)) |
| 1.0ms | eps | @ | inf | ((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x)) |
| 1.0ms | eps | @ | -inf | ((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x)) |
| 1.0ms | x | @ | -inf | ((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x)) |
| 0.0ms | eps | @ | 0 | ((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 105 | 296 |
| 1 | 308 | 293 |
| 2 | 814 | 293 |
| 3 | 2685 | 292 |
| 4 | 6556 | 292 |
| 0 | 8099 | 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) |
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 (+ 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 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 eps) x) (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) |
(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) (cos.f64 eps)) x (sin.f64 eps)) (neg.f64 x) (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 eps) x) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) x) (sin.f64 eps)) x (cos.f64 eps)) |
eps |
(+ eps x) |
(+.f64 eps x) |
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 (+ 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 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps) |
(* 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 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps) (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps (cos.f64 x)) |
(* 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 | 18 |
| 0 | 10 | 18 |
| 1 | 62 | 18 |
| 2 | 615 | 18 |
| 0 | 8141 | 18 |
| 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) |
x |
eps |
(cos.f64 x) |
| Outputs |
|---|
(*.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64)))))) |
(*.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64)))))) |
(*.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64)))))) |
(*.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))) |
(*.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))))) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 (neg.f64 x))) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 (neg.f64 x))) #s(literal 2 binary64))))) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 x)) #s(literal 2 binary64))))) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 eps x))) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 eps x))) x) #s(literal 2 binary64))))) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 (neg.f64 x))) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 (neg.f64 x))) #s(literal 2 binary64))))) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) (neg.f64 (neg.f64 x))) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) (neg.f64 (neg.f64 x))) #s(literal 2 binary64))))) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))))) |
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(/.f64 (-.f64 (*.f64 (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64))) (*.f64 (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)))) (-.f64 (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))) (cos.f64 (+.f64 (neg.f64 x) eps))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) (-.f64 (*.f64 (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64))) (*.f64 (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))))) |
(/.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 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))))))) |
(/.f64 (-.f64 (*.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) eps)) (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 (+.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 (neg.f64 x) eps)) (cos.f64 (+.f64 eps x))) (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x)))) #s(literal 2 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 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))))) |
(fma.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))) (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) |
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) #s(literal 0 binary64) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64))) |
(fma.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)) (*.f64 #s(literal 0 binary64) (sin.f64 (+.f64 eps x)))) |
(fma.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64))) |
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (cos.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.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))) |
(sin.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 (-.f64 (neg.f64 x) eps) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) |
(sin.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 eps x))) (/.f64 (pow.f64 (*.f64 (sin.f64 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)) (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))))) (/.f64 (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))))))) |
(-.f64 (*.f64 (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (cos.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))) (*.f64 (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 (neg.f64 eps)) (neg.f64 (sin.f64 x)))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (neg.f64 eps)))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) |
(cos.f64 (neg.f64 (neg.f64 (neg.f64 (+.f64 eps x))))) |
(cos.f64 (neg.f64 (-.f64 (neg.f64 x) eps))) |
(cos.f64 (neg.f64 (neg.f64 (+.f64 eps x)))) |
(cos.f64 (-.f64 (neg.f64 x) eps)) |
(cos.f64 (neg.f64 (+.f64 eps x))) |
(cos.f64 (+.f64 eps x)) |
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) |
(+.f64 (*.f64 (neg.f64 (sin.f64 (+.f64 eps x))) #s(literal 0 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64))) |
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (*.f64 #s(literal 0 binary64) (sin.f64 (+.f64 eps x)))) |
(+.f64 (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 x))) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(+.f64 (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64))) |
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (+.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (*.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))) (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps)) (fma.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)) (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))))) |
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (-.f64 (*.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x))) |
(/.f64 (neg.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)))) (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 eps (-.f64 eps x) (*.f64 x x))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x eps)) (*.f64 (-.f64 x eps) (*.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps))) |
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (*.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) |
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x)) |
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 x eps))) (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 eps eps (-.f64 (*.f64 x x) (*.f64 eps x))))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) |
(/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps)) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x)))) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) |
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x))) |
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) |
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x))))) |
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x))))) |
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) |
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) |
(+.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps))) |
(+.f64 eps x) |
(+.f64 x eps) |
x |
eps |
(/.f64 (-.f64 (*.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (sin.f64 x) #s(literal 0 binary64))) (*.f64 (*.f64 (cos.f64 x) #s(literal 1 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))) (-.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (sin.f64 x) #s(literal 0 binary64)) (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal 1 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))))) |
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64))) |
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64))) |
(sin.f64 (+.f64 (neg.f64 (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) |
(cos.f64 (neg.f64 (neg.f64 (neg.f64 x)))) |
(cos.f64 (neg.f64 (neg.f64 x))) |
(cos.f64 (neg.f64 x)) |
(cos.f64 x) |
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))) |
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x))) |
(+.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))) |
Compiled 4 801 to 712 computations (85.2% saved)
9 alts after pruning (8 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 156 | 8 | 164 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 156 | 9 | 165 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 55.0% | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 53.8% | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) | |
| ▶ | 82.2% | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64)) |
| 55.3% | (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))))) | |
| ▶ | 53.6% | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
| 99.5% | #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))) | |
| ▶ | 99.8% | #s(approx (- (cos (+ x eps)) (cos 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)) |
| ▶ | 99.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) |
| ▶ | 80.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
Compiled 333 to 220 computations (33.9% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos 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)) |
(*.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) |
(-.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)) |
(*.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) |
(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))) |
(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) |
(sin.f64 x) |
x |
#s(literal 1/6 binary64) |
(*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
eps |
#s(literal 1/24 binary64) |
(*.f64 (cos.f64 x) #s(literal -1/2 binary64)) |
#s(literal -1/2 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) |
#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) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64)) |
(*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) |
(sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) |
(/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)) |
(+.f64 (+.f64 eps x) x) |
(+.f64 eps x) |
#s(literal 2 binary64) |
(sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) |
(/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)) |
(-.f64 (+.f64 eps x) x) |
#s(literal -2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps) |
(-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) |
(*.f64 (sin.f64 x) eps) |
| 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) |
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) |
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(* eps (- (* 1/24 (pow eps 2)) 1/2)) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1))) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1))) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1))) |
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2))) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))))) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))))))) |
(- (* 1/24 (pow eps 2)) 1/2) |
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2) |
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2) |
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2) |
(* 1/24 eps) |
(+ (* 1/24 eps) (* 1/6 x)) |
(+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x))))) |
(+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps)))))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps)) |
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2)))))) |
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps)))))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
-1/2 |
(- (* 1/4 (pow x 2)) 1/2) |
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2) |
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2) |
(* -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))))))))) |
(* -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)) |
(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))))))))) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(+ eps (* 2 x)) |
(+ eps x) |
(* -1/2 (pow eps 2)) |
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))))))) |
(* -1/2 eps) |
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1))) |
(+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x))) |
(+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))))) |
(+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* 1/4 eps)))))) |
(- (* 1/6 (* eps x)) 1/2) |
(- (* x (+ (* 1/6 eps) (* 1/4 x))) 1/2) |
(- (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/36 (* eps x)))))) 1/2) |
(* eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
(- (cos (+ eps x)) (cos x)) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))) |
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)) |
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) |
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))) |
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))) |
(sin x) |
(* 1/24 (* eps (cos x))) |
(* eps (cos x)) |
(cos x) |
(* -1/2 (cos x)) |
(* -1 (* eps (sin 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)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* 2 x) |
(* x (+ 2 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)) |
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) |
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))) |
(* eps (sin x)) |
(- (cos (- eps (* -1 x))) (cos 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)))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 2))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))) |
(* -1 (sin x)) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(* -1/2 (* eps (cos x))) |
(* 1/6 (sin x)) |
(* (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) |
(* 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)))))))))) |
(+ (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)))) |
(* 1/24 (* (pow eps 4) (cos x))) |
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))) |
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))) |
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))) |
(* 1/24 (* (pow eps 3) (cos x))) |
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))) |
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))) |
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))) |
(* 1/24 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))) |
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))) |
(* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))) |
(cos eps) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1 (* 2 (/ x eps)))) |
(* eps (+ 1 (/ x eps))) |
(* 1/6 (* (pow eps 3) (sin x))) |
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(* 1/6 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(* 1/6 (* eps (sin x))) |
(* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(- (cos (- x (* -1 eps))) (cos x)) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x)))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x)))) |
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x))))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x)))) |
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x))))) |
(* -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)))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -2 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x)))) |
(* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 9.0ms | x | @ | -inf | ((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* (cos x) -1/2) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (* (sin x) eps)) |
| 6.0ms | x | @ | 0 | ((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* (cos x) -1/2) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (* (sin x) eps)) |
| 5.0ms | x | @ | inf | ((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* (cos x) -1/2) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (* (sin x) eps)) |
| 5.0ms | eps | @ | -inf | ((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* (cos x) -1/2) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (* (sin x) eps)) |
| 5.0ms | eps | @ | inf | ((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* (cos x) -1/2) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (* (sin x) eps)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 593 | 2732 |
| 1 | 2209 | 2682 |
| 0 | 8624 | 2460 |
| 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) |
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) |
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(* eps (- (* 1/24 (pow eps 2)) 1/2)) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1))) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1))) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1))) |
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2))) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))))) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))))))) |
(- (* 1/24 (pow eps 2)) 1/2) |
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2) |
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2) |
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2) |
(* 1/24 eps) |
(+ (* 1/24 eps) (* 1/6 x)) |
(+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x))))) |
(+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps)))))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps)) |
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2)))))) |
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps)))))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
-1/2 |
(- (* 1/4 (pow x 2)) 1/2) |
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2) |
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2) |
(* -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))))))))) |
(* -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)) |
(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))))))))) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(+ eps (* 2 x)) |
(+ eps x) |
(* -1/2 (pow eps 2)) |
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))))))) |
(* -1/2 eps) |
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1))) |
(+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x))) |
(+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))))) |
(+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* 1/4 eps)))))) |
(- (* 1/6 (* eps x)) 1/2) |
(- (* x (+ (* 1/6 eps) (* 1/4 x))) 1/2) |
(- (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/36 (* eps x)))))) 1/2) |
(* eps x) |
(* x (+ eps (* -1/6 (* eps (pow x 2))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))) |
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))) |
(- (cos (+ eps x)) (cos x)) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))) |
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)) |
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) |
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))) |
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))) |
(sin x) |
(* 1/24 (* eps (cos x))) |
(* eps (cos x)) |
(cos x) |
(* -1/2 (cos x)) |
(* -1 (* eps (sin 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)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* 2 x) |
(* x (+ 2 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)) |
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) |
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))) |
(* eps (sin x)) |
(- (cos (- eps (* -1 x))) (cos 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)))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 2))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))) |
(* -1 (sin x)) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(* -1/2 (* eps (cos x))) |
(* 1/6 (sin x)) |
(* (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) |
(* 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)))))))))) |
(+ (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)))) |
(* 1/24 (* (pow eps 4) (cos x))) |
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))) |
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))) |
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))) |
(* 1/24 (* (pow eps 3) (cos x))) |
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))) |
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))) |
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))) |
(* 1/24 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))) |
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))) |
(* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))) |
(cos eps) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1 (* 2 (/ x eps)))) |
(* eps (+ 1 (/ x eps))) |
(* 1/6 (* (pow eps 3) (sin x))) |
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(* 1/6 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(* 1/6 (* eps (sin x))) |
(* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(- (cos (- x (* -1 eps))) (cos x)) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x)))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x)))) |
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x))))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x)))) |
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x))))) |
(* -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)))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -2 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x)))) |
(* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))))) |
| 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 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 eps) x) (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))) |
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) |
(*.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps) eps) |
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(fma.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)) |
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(fma.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps) eps (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps) x) eps (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x)) |
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(fma.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps) eps (*.f64 (fma.f64 (fma.f64 (*.f64 eps (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))) x (*.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x)) |
(* eps (- (* 1/24 (pow eps 2)) 1/2)) |
(*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1))) |
(fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps)) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps)) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps)) |
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2))) |
(fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/6 binary64) (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps)) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps)) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/36 binary64) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps)) |
(- (* 1/24 (pow eps 2)) 1/2) |
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) |
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2) |
(fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) |
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) |
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64))) x (*.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) |
(* 1/24 eps) |
(*.f64 #s(literal 1/24 binary64) eps) |
(+ (* 1/24 eps) (* 1/6 x)) |
(fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) |
(+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x))))) |
(fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/48 binary64) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/24 binary64) eps)) |
(+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps)))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (*.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/24 binary64) eps)) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) |
(+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps)) |
(fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/48 binary64) (*.f64 #s(literal 1/24 binary64) eps)) |
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2)))))) |
(fma.f64 (*.f64 (fma.f64 #s(literal 1/576 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/48 binary64) eps)) x) x (*.f64 #s(literal 1/24 binary64) eps)) |
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps)))))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/17280 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/576 binary64) eps)) x) x (*.f64 #s(literal -1/48 binary64) eps)) (*.f64 x x) (*.f64 #s(literal 1/24 binary64) eps)) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps eps) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
-1/2 |
#s(literal -1/2 binary64) |
(- (* 1/4 (pow x 2)) 1/2) |
(-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) |
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2) |
(-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64)) |
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2) |
(-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64)) |
(* -1 (* eps x)) |
(*.f64 (neg.f64 eps) x) |
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))) |
(*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))) |
(*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 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 #s(literal -2 binary64) (*.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))))) |
(+ (* -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 #s(literal -2 binary64) (*.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)))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x x))) |
(+ (* -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 #s(literal -2 binary64) (*.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)))) (*.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 x 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 (*.f64 x (*.f64 #s(literal -1/2 binary64) x)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.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 (+ (* 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 (*.f64 #s(literal -1/6 binary64) x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -1/2 binary64))) x (*.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))) |
(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 #s(literal -1/2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (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)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) x (sin.f64 (*.f64 #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) |
(+ eps (* 2 x)) |
(fma.f64 #s(literal 2 binary64) x eps) |
(+ eps x) |
(+.f64 eps x) |
(* -1/2 (pow eps 2)) |
(*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps) |
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))))))) |
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(fma.f64 (/.f64 x eps) eps eps) |
(* 1/6 (* (pow eps 3) (sin x))) |
(*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64)) (sin.f64 x)) |
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (pow.f64 eps #s(literal 3 binary64))) |
(* 1/6 (* (pow eps 2) (sin x))) |
(*.f64 (*.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal 1/6 binary64)) |
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(*.f64 (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) eps) |
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(*.f64 (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps) eps) |
(* 1/6 (* eps (sin x))) |
(*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) |
(* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) |
(- (cos (- x (* -1 eps))) (cos x)) |
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x)))) |
(*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)) (pow.f64 eps #s(literal 4 binary64))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x)))) |
(*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64))) |
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x))))) |
(*.f64 (neg.f64 (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (*.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64)))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x))))) |
(*.f64 (neg.f64 (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (neg.f64 eps)))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x))))) |
(*.f64 (neg.f64 (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (neg.f64 eps)))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x)))) |
(*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)) (*.f64 eps eps)) |
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x))))) |
(*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (*.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64)))) |
(* -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)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))) |
(* -1 (* eps (- (* -2 (/ x eps)) 1))) |
(*.f64 (neg.f64 eps) (-.f64 (*.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))) |
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))))) |
(*.f64 (neg.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) #s(literal -1/6 binary64)))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x)))) |
(*.f64 (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps) eps) |
(* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))))) |
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) #s(literal -1/6 binary64)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 44 | 345 |
| 0 | 75 | 333 |
| 1 | 275 | 325 |
| 0 | 2348 | 321 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos 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)) |
(*.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) |
(-.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)) |
(*.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) |
(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))) |
(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) |
(sin.f64 x) |
x |
#s(literal 1/6 binary64) |
(*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
eps |
#s(literal 1/24 binary64) |
(*.f64 (cos.f64 x) #s(literal -1/2 binary64)) |
#s(literal -1/2 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) |
#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) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64)) |
(*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) |
(sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) |
(/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)) |
(+.f64 (+.f64 eps x) x) |
(+.f64 eps x) |
#s(literal 2 binary64) |
(sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) |
(/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)) |
(-.f64 (+.f64 eps x) x) |
#s(literal -2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps) |
(-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) |
(*.f64 (sin.f64 x) eps) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps) |
(*.f64 eps (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x))) |
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)))) |
(/.f64 (*.f64 eps (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x))) |
(/.f64 (*.f64 eps (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))) |
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(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) |
(fma.f64 eps (*.f64 (cos.f64 x) #s(literal 1/24 binary64)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) |
(-.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal -1/24 binary64) (*.f64 (cos.f64 x) eps)))) (/.f64 (pow.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal -1/24 binary64) (*.f64 (cos.f64 x) eps))))) |
(-.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 #s(literal -1/24 binary64) (*.f64 (cos.f64 x) eps))) |
(-.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (*.f64 #s(literal 1/24 binary64) eps))) |
(-.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (neg.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps)))) |
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps)) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) |
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps)) (*.f64 (neg.f64 (sin.f64 x)) #s(literal 1/6 binary64))) |
(+.f64 (/.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (/.f64 (pow.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps)) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))))) |
(+.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (neg.f64 (*.f64 (neg.f64 eps) (cos.f64 x))) #s(literal 1/24 binary64))) |
(+.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) |
(+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) |
(sin.f64 x) |
x |
#s(literal 1/6 binary64) |
(*.f64 (*.f64 #s(literal 1/24 binary64) (cos.f64 x)) eps) |
(*.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x)) |
(*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps)) |
(*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)) |
(*.f64 (cos.f64 x) (*.f64 #s(literal 1/24 binary64) eps)) |
(*.f64 eps (*.f64 (cos.f64 x) #s(literal 1/24 binary64))) |
(*.f64 (cos.f64 x) eps) |
(*.f64 eps (cos.f64 x)) |
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))) |
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) |
(cos.f64 (neg.f64 (neg.f64 x))) |
(cos.f64 (neg.f64 x)) |
(cos.f64 x) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))) |
eps |
#s(literal 1/24 binary64) |
(*.f64 #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 (cos.f64 x) #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(/.f64 (neg.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) #s(literal -1 binary64))) (neg.f64 (-.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (-.f64 (cos.f64 eps) #s(literal -1 binary64))))) |
(/.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) #s(literal -1 binary64)) (-.f64 (cos.f64 eps) #s(literal -1 binary64))) |
(/.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (-.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(fma.f64 #s(literal 1 binary64) (cos.f64 eps) #s(literal -1 binary64)) |
(fma.f64 (cos.f64 eps) #s(literal 1 binary64) #s(literal -1 binary64)) |
(-.f64 (/.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (-.f64 (cos.f64 eps) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(-.f64 (/.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (-.f64 (cos.f64 eps) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 eps) (cos.f64 eps) (-.f64 (cos.f64 eps) #s(literal -1 binary64))))) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(+.f64 (cos.f64 eps) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (cos.f64 eps)) |
(*.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(fma.f64 (sin.f64 eps) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 eps) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))) |
(sin.f64 (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps)) |
(cos.f64 (neg.f64 (neg.f64 eps))) |
(cos.f64 (neg.f64 eps)) |
(cos.f64 eps) |
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 eps) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(literal 1 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
(*.f64 (neg.f64 (sin.f64 x)) eps) |
(*.f64 (neg.f64 eps) (sin.f64 x)) |
(*.f64 (sin.f64 x) (neg.f64 eps)) |
(*.f64 eps (neg.f64 (sin.f64 x))) |
(neg.f64 (*.f64 (sin.f64 x) eps)) |
(neg.f64 eps) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 2 binary64))))) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))))) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64))))) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) #s(literal -2 binary64)) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal -2 binary64))) |
(*.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))))) |
(/.f64 (*.f64 (-.f64 (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64)))) #s(literal -2 binary64)) #s(literal 2 binary64)) |
(/.f64 (*.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))))) #s(literal 2 binary64)) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) |
(neg.f64 (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) #s(literal 2 binary64))) |
(neg.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))) |
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))) |
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) |
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) |
(*.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) |
(/.f64 (neg.f64 (-.f64 (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))))) #s(literal -2 binary64)) |
(/.f64 (-.f64 (cos.f64 (-.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (/.f64 (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (cos.f64 (/.f64 (+.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))) #s(literal 2 binary64))) |
(fma.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64))))) |
(sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) |
(+.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64)) (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64)))) (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) |
(/.f64 (+.f64 (pow.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64)) (/.f64 (+.f64 eps x) #s(literal 2 binary64)) (-.f64 (*.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64))) (*.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64)))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps))) #s(literal 2 binary64)) |
(/.f64 (fma.f64 (+.f64 eps x) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)) #s(literal 4 binary64)) |
(/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) |
(/.f64 (+.f64 (pow.f64 (+.f64 eps x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (*.f64 (fma.f64 x (-.f64 x (+.f64 eps x)) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 2 binary64))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) #s(literal -2 binary64)) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) |
(neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 2 binary64))) |
(+.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) |
(+.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 (+.f64 eps x) #s(literal 2 binary64))) |
(+.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64))) |
(*.f64 (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (fma.f64 #s(literal 2 binary64) x eps) (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))) |
(*.f64 (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps))) (fma.f64 #s(literal 2 binary64) x eps)) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 2 binary64) x))) (-.f64 eps (*.f64 #s(literal 2 binary64) x))) |
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (-.f64 x (+.f64 eps x))) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 2 binary64) x)) (*.f64 eps (*.f64 #s(literal 2 binary64) x))))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 eps x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (-.f64 x (+.f64 eps x)) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps))) (+.f64 (neg.f64 eps) #s(literal 0 binary64))) |
(/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 #s(literal 0 binary64) eps)) (+.f64 #s(literal 0 binary64) eps)) |
(/.f64 (+.f64 (pow.f64 (+.f64 eps x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (*.f64 (+.f64 eps x) x)))) |
(/.f64 (+.f64 (pow.f64 (+.f64 eps x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (-.f64 x (+.f64 eps x)) (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))) |
(fma.f64 #s(literal 2 binary64) x eps) |
(-.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (+.f64 #s(literal 0 binary64) eps)) (/.f64 (*.f64 x x) (+.f64 #s(literal 0 binary64) eps))) |
(+.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal 3 binary64)) (fma.f64 x (-.f64 x (+.f64 eps x)) (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (+.f64 eps x)) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))) |
(+.f64 (*.f64 #s(literal 2 binary64) x) eps) |
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(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)))) |
(fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 (neg.f64 (neg.f64 (cos.f64 x))) #s(literal -1/2 binary64))) |
(fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
(fma.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps (*.f64 (neg.f64 (neg.f64 (cos.f64 x))) #s(literal -1/2 binary64))) |
(fma.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (neg.f64 (neg.f64 (cos.f64 x))) #s(literal -1/2 binary64))) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
(fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) |
(fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) |
(fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (neg.f64 (neg.f64 (cos.f64 x))) #s(literal -1/2 binary64))) |
(fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (*.f64 #s(literal 1/6 binary64) eps) (*.f64 (neg.f64 (neg.f64 (cos.f64 x))) #s(literal -1/2 binary64))) |
(fma.f64 (sin.f64 x) (*.f64 #s(literal 1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
(fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 (neg.f64 (neg.f64 (cos.f64 x))) #s(literal -1/2 binary64))) |
(fma.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))) (/.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))) |
(-.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) |
(-.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (neg.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) |
(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (*.f64 (neg.f64 eps) (sin.f64 x)) #s(literal 1/6 binary64))) |
(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 #s(literal -1/6 binary64) (*.f64 (sin.f64 x) eps))) |
(-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (*.f64 #s(literal 1/6 binary64) eps))) |
(+.f64 (/.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) (pow.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) #s(literal 2 binary64))))) |
(+.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (*.f64 (neg.f64 (neg.f64 (cos.f64 x))) #s(literal -1/2 binary64))) |
(+.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
(+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) |
(*.f64 (sin.f64 x) eps) |
(*.f64 eps (sin.f64 x)) |
Compiled 19 348 to 2 855 computations (85.2% saved)
26 alts after pruning (23 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 533 | 21 | 554 |
| Fresh | 1 | 2 | 3 |
| Picked | 2 | 3 | 5 |
| Done | 1 | 0 | 1 |
| Total | 537 | 26 | 563 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 53.8% | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
| 99.6% | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64)) | |
| ▶ | 99.7% | (*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.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)) |
| 53.6% | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64))) | |
| 99.5% | #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))) | |
| ✓ | 99.8% | #s(approx (- (cos (+ x eps)) (cos 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)) |
| ✓ | 99.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) |
| 98.9% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) | |
| 98.6% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) | |
| ✓ | 80.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
| ▶ | 79.1% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))) |
| 79.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) | |
| 78.9% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) | |
| 97.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) | |
| 97.4% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) | |
| ▶ | 97.4% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
| 95.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps) eps)) eps)) | |
| 54.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) | |
| 23.2% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64))))) | |
| 97.9% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) | |
| 97.5% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) | |
| 97.4% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)))) | |
| 79.1% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))) | |
| 79.0% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x))) | |
| 78.9% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))) | |
| ▶ | 78.8% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x))) |
Compiled 1 679 to 1 107 computations (34.1% saved)
| Inputs |
|---|
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.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 (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.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 #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) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x))) |
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)) |
(*.f64 (neg.f64 eps) x) |
(neg.f64 eps) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
(*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps) |
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) |
(fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) |
(-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) |
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) |
(*.f64 eps eps) |
#s(literal 1/6 binary64) |
#s(literal 1 binary64) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(literal -1/2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))) |
(*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x))) |
#s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)) |
(fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) |
(*.f64 x (*.f64 x x)) |
(*.f64 x x) |
(-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) |
(*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) |
(*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) |
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) |
#s(literal -1/5040 binary64) |
#s(literal 1/120 binary64) |
(-.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)) |
| Outputs |
|---|
(* -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)) |
(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))))))))) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
x |
(- (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))))))))) |
(* -1/2 (pow eps 2)) |
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))))))) |
(* -1/2 eps) |
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1))) |
(* 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)))) |
(pow x 3) |
(pow x 2) |
-1/6 |
(- (* 1/120 (pow x 2)) 1/6) |
(- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6) |
(* 1/120 (pow x 2)) |
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) |
(* 1/120 x) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
1/120 |
(+ 1/120 (* -1/5040 (pow x 2))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
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))) |
(* -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)) (sin (+ x (* 1/2 eps)))) |
(sin (+ x (* 1/2 eps))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(- (cos (+ eps x)) (cos x)) |
(* -1 (* eps (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)) |
(* x (- (* 1/6 (pow eps 2)) 1)) |
(* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1)) |
(sin x) |
(* -1/5040 (pow x 7)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* -1/5040 (pow x 4)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* -1/5040 (pow x 3)) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* -1/5040 (pow x 2)) |
(* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(cos (+ eps x)) |
(* x (+ 1 (/ eps x))) |
(cos 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)) (sin (- (* 1/2 eps) (* -1 x)))) |
(sin (- (* 1/2 eps) (* -1 x))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(- (cos (- eps (* -1 x))) (cos x)) |
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x))))) |
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(cos (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* 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)))))))))) |
(+ (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 (* eps (cos x))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(* -1 eps) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))) |
(* -1 (sin x)) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(* -1 x) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))) |
-1 |
(- (* 1/6 (pow eps 2)) 1) |
(* 1/6 (pow eps 2)) |
(pow eps 2) |
(+ (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 (+ 1/2 (/ x eps))) |
(* 1/6 (* (pow eps 3) (sin x))) |
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(* 1/6 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(* 1/6 (* (pow eps 2) x)) |
(* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps)))) |
(* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps)))) |
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2)))) |
(* eps (+ 1 (/ x eps))) |
(* -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 eps)) (sin (- x (* -1/2 eps)))) |
(sin (- x (* -1/2 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(- (cos (- x (* -1 eps))) (cos x)) |
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x)))) |
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x))) |
(cos (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 8.0ms | x | @ | 0 | ((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) 1/2 eps x (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg eps) x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 1 (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (* x x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x)) |
| 5.0ms | x | @ | inf | ((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) 1/2 eps x (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg eps) x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 1 (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (* x x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x)) |
| 4.0ms | x | @ | -inf | ((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) 1/2 eps x (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg eps) x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 1 (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (* x x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x)) |
| 4.0ms | eps | @ | inf | ((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) 1/2 eps x (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg eps) x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 1 (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (* x x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x)) |
| 3.0ms | eps | @ | -inf | ((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) 1/2 eps x (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg eps) x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 1 (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (* x x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 445 | 1837 |
| 1 | 1505 | 1783 |
| 2 | 5567 | 1779 |
| 0 | 8276 | 1642 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* -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)) |
(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))))))))) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
x |
(- (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))))))))) |
(* -1/2 (pow eps 2)) |
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))))))) |
(* -1/2 eps) |
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1))) |
(* 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)))) |
(pow x 3) |
(pow x 2) |
-1/6 |
(- (* 1/120 (pow x 2)) 1/6) |
(- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6) |
(* 1/120 (pow x 2)) |
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) |
(* 1/120 x) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
1/120 |
(+ 1/120 (* -1/5040 (pow x 2))) |
(cos eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
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))) |
(* -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)) (sin (+ x (* 1/2 eps)))) |
(sin (+ x (* 1/2 eps))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(- (cos (+ eps x)) (cos x)) |
(* -1 (* eps (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)) |
(* x (- (* 1/6 (pow eps 2)) 1)) |
(* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1)) |
(sin x) |
(* -1/5040 (pow x 7)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* -1/5040 (pow x 4)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* -1/5040 (pow x 3)) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* -1/5040 (pow x 2)) |
(* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(cos (+ eps x)) |
(* x (+ 1 (/ eps x))) |
(cos 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)) (sin (- (* 1/2 eps) (* -1 x)))) |
(sin (- (* 1/2 eps) (* -1 x))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(- (cos (- eps (* -1 x))) (cos x)) |
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x))))) |
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(cos (- eps (* -1 x))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* 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)))))))))) |
(+ (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 (* eps (cos x))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(* -1 eps) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))) |
(* -1 (sin x)) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(* -1 x) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))) |
-1 |
(- (* 1/6 (pow eps 2)) 1) |
(* 1/6 (pow eps 2)) |
(pow eps 2) |
(+ (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 (+ 1/2 (/ x eps))) |
(* 1/6 (* (pow eps 3) (sin x))) |
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(* 1/6 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(* 1/6 (* (pow eps 2) x)) |
(* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps)))) |
(* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps)))) |
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2)))) |
(* eps (+ 1 (/ x eps))) |
(* -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 eps)) (sin (- x (* -1/2 eps)))) |
(sin (- x (* -1/2 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(- (cos (- x (* -1 eps))) (cos x)) |
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x)))) |
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x))) |
(cos (- x (* -1 eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
| Outputs |
|---|
(* -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)) (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) |
(+ (* -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 (*.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)))) #s(literal -2 binary64) (*.f64 (*.f64 x x) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) |
(+ (* -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 (*.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)))) #s(literal -2 binary64) (*.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #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 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.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 (+ (* 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 (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x)) #s(literal 1/6 binary64) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -1/2 binary64))) x (*.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))) |
(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 #s(literal -1/2 binary64) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (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)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps))))))))) |
(fma.f64 (fma.f64 (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (sin.f64 (*.f64 #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) |
x |
(- (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 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (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 eps) x) |
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))) |
(*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) 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)) (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 (neg.f64 eps) x)) |
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 (neg.f64 eps) x)) |
(* -1/2 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) |
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))) |
(fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
(* -1/2 eps) |
(*.f64 #s(literal -1/2 binary64) eps) |
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1))) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) |
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1))) |
(fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps)) |
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1))) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps)) |
(* 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) |
(pow x 3) |
(pow.f64 x #s(literal 3 binary64)) |
(pow x 2) |
(*.f64 x x) |
-1/6 |
#s(literal -1/6 binary64) |
(- (* 1/120 (pow x 2)) 1/6) |
(fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) |
(- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6) |
(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)) |
(* 1/120 (pow x 2)) |
(*.f64 #s(literal 1/120 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) |
(*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) |
(* 1/120 x) |
(*.f64 #s(literal 1/120 binary64) x) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
(*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) |
1/120 |
#s(literal 1/120 binary64) |
(+ 1/120 (* -1/5040 (pow x 2))) |
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) |
(cos eps) |
(cos.f64 eps) |
(+ (cos eps) (* -1 (* x (sin eps)))) |
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)) |
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) |
(fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/2 binary64)) (sin.f64 eps)) x (cos.f64 eps)) |
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) |
(fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64))) x) (sin.f64 eps)) x (cos.f64 eps)) |
eps |
(+ eps x) |
(+.f64 x eps) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(fma.f64 (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)) |
(* -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)) (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 (+ 1 (* 1/2 (/ eps x)))) |
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) |
(- (cos (+ eps x)) (cos x)) |
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(* -1 (* eps (sin x))) |
(*.f64 (neg.f64 eps) (sin.f64 x)) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps) |
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)) |
(-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) |
(* x (- (* 1/6 (pow eps 2)) 1)) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x) |
(* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1)) |
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x) |
(sin x) |
(sin.f64 x) |
(* -1/5040 (pow x 7)) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/5040 binary64)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (pow.f64 x #s(literal 7 binary64))) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 7 binary64))) |
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))) (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/5040 binary64))) (pow.f64 x #s(literal 7 binary64))) |
(* -1/5040 (pow x 4)) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/5040 binary64)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64))) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64))) |
(* -1/5040 (pow x 3)) |
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/5040 binary64)) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (pow.f64 x #s(literal 3 binary64))) |
(* -1/5040 (pow x 2)) |
(*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) |
(* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) x) x) |
(cos (+ eps x)) |
(cos.f64 (+.f64 x eps)) |
(* x (+ 1 (/ eps x))) |
(fma.f64 (/.f64 eps x) x x) |
(cos x) |
(cos.f64 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)) (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 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))) |
(- (cos (- eps (* -1 x))) (cos x)) |
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x))))) |
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x) |
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(*.f64 (neg.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) |
(*.f64 (neg.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/120 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(*.f64 (neg.f64 (pow.f64 x #s(literal 7 binary64))) (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))))) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x)))) |
(cos (- eps (* -1 x))) |
(cos.f64 (+.f64 x eps)) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1 binary64) #s(literal -1 binary64))) |
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))) |
(*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (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 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) 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 #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) |
(+ (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 #s(literal -1/8 binary64) (*.f64 (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 (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (*.f64 #s(literal 1/2 binary64) eps)) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) 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 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps) |
(* -1 eps) |
(neg.f64 eps) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (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) |
(* -1 (sin x)) |
(neg.f64 (sin.f64 x)) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1 x) |
(neg.f64 x) |
(+ (* -1 x) (* -1/2 eps)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64)) eps (neg.f64 x)) |
-1 |
#s(literal -1 binary64) |
(- (* 1/6 (pow eps 2)) 1) |
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) |
(* 1/6 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) |
(pow eps 2) |
(*.f64 eps 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) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) |
(fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps (cos.f64 x)) |
(* eps (+ 1/2 (/ x eps))) |
(*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps) |
(* 1/6 (* (pow eps 3) (sin x))) |
(*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64)) (sin.f64 x)) |
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (pow.f64 eps #s(literal 3 binary64))) |
(* 1/6 (* (pow eps 2) (sin x))) |
(*.f64 (*.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal 1/6 binary64)) |
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(*.f64 (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) eps) |
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (*.f64 eps eps)) |
(* 1/6 (* (pow eps 2) x)) |
(*.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x) eps) |
(* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps)))) |
(*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)) |
(* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps)))) |
(*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1/2 binary64)) eps)) eps) eps) |
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2)))) |
(*.f64 (*.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 (/.f64 #s(literal 1 binary64) eps) eps)) eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 (/.f64 x eps) eps 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 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 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps) |
(- (cos (- x (* -1 eps))) (cos x)) |
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))))) |
(*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))))) |
(*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (pow.f64 eps #s(literal 3 binary64))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x)))) |
(*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (*.f64 eps eps)) |
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x))) |
(*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1/2 binary64)) eps)) eps) eps) |
(cos (- x (* -1 eps))) |
(cos.f64 (+.f64 x eps)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1 binary64))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 64 | 419 |
| 0 | 92 | 409 |
| 1 | 357 | 405 |
| 0 | 2958 | 395 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.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 (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.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 #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) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x))) |
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)) |
(*.f64 (neg.f64 eps) x) |
(neg.f64 eps) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
(*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps) |
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) |
(fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) |
(-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) |
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) |
(*.f64 eps eps) |
#s(literal 1/6 binary64) |
#s(literal 1 binary64) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(literal -1/2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))) |
(*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x))) |
#s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)) |
(fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) |
(*.f64 x (*.f64 x x)) |
(*.f64 x x) |
(-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) |
(*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) |
(*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) |
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) |
#s(literal -1/5040 binary64) |
#s(literal 1/120 binary64) |
(-.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)) |
| Outputs |
|---|
(*.f64 #s(literal -2 binary64) #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))) |
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64)) |
(neg.f64 (*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))) |
(neg.f64 (*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))) |
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
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(/.f64 (*.f64 x (fma.f64 #s(literal -1/128024064000 binary64) (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/1728000 binary64))) (-.f64 (+.f64 (pow.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1/14400 binary64)) (*.f64 (*.f64 x x) #s(literal -1/604800 binary64)))) |
(fma.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) x (*.f64 #s(literal 1/120 binary64) x)) |
(fma.f64 #s(literal 1/120 binary64) x (*.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) x)) |
(fma.f64 x (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) (*.f64 x #s(literal 1/120 binary64))) |
(fma.f64 x #s(literal 1/120 binary64) (*.f64 x (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))) |
(+.f64 (*.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) x) (*.f64 #s(literal 1/120 binary64) x)) |
(+.f64 (*.f64 #s(literal 1/120 binary64) x) (*.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) x)) |
(+.f64 (*.f64 x (*.f64 #s(literal -1/5040 binary64) (*.f64 x x))) (*.f64 x #s(literal 1/120 binary64))) |
(+.f64 (*.f64 x #s(literal 1/120 binary64)) (*.f64 x (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))) |
(/.f64 (-.f64 #s(literal 1/14400 binary64) (pow.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 2 binary64))) (-.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1/14400 binary64))) (neg.f64 (-.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 1/120 binary64)))) |
(/.f64 (neg.f64 (fma.f64 #s(literal -1/128024064000 binary64) (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/1728000 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1/14400 binary64)) (*.f64 (*.f64 x x) #s(literal -1/604800 binary64))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1/14400 binary64)) (-.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 1/120 binary64))) |
(/.f64 (fma.f64 #s(literal -1/128024064000 binary64) (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/1728000 binary64)) (+.f64 #s(literal 1/14400 binary64) (-.f64 (pow.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/604800 binary64))))) |
(/.f64 (fma.f64 #s(literal -1/128024064000 binary64) (pow.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 1/1728000 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1/14400 binary64)) (*.f64 (*.f64 x x) #s(literal -1/604800 binary64)))) |
(fma.f64 (*.f64 #s(literal -1/5040 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal 1/120 binary64)) |
(fma.f64 (*.f64 #s(literal -1/5040 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 1/120 binary64)) |
(fma.f64 (*.f64 #s(literal -1/5040 binary64) x) x #s(literal 1/120 binary64)) |
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) |
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) |
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) |
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) |
(fma.f64 x (*.f64 #s(literal -1/5040 binary64) x) #s(literal 1/120 binary64)) |
(-.f64 (/.f64 (pow.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 1/120 binary64))) (/.f64 #s(literal 1/14400 binary64) (-.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 1/120 binary64)))) |
(-.f64 #s(literal 1/120 binary64) (*.f64 (neg.f64 (*.f64 #s(literal -1/5040 binary64) x)) x)) |
(-.f64 #s(literal 1/120 binary64) (*.f64 #s(literal 1/5040 binary64) (*.f64 x x))) |
(-.f64 #s(literal 1/120 binary64) (*.f64 (neg.f64 (*.f64 x x)) #s(literal -1/5040 binary64))) |
(+.f64 (/.f64 (pow.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1/14400 binary64)) (*.f64 (*.f64 x x) #s(literal -1/604800 binary64)))) (/.f64 #s(literal 1/1728000 binary64) (-.f64 (+.f64 (pow.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1/14400 binary64)) (*.f64 (*.f64 x x) #s(literal -1/604800 binary64))))) |
(+.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) #s(literal 1/120 binary64)) |
(+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (*.f64 x x))) |
#s(literal -1/5040 binary64) |
#s(literal 1/120 binary64) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (neg.f64 (+.f64 #s(approx (cos x) #s(literal 1 binary64)) (cos.f64 (+.f64 x eps))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (+.f64 #s(approx (cos x) #s(literal 1 binary64)) (cos.f64 (+.f64 x eps))) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 2 binary64))) (+.f64 #s(approx (cos x) #s(literal 1 binary64)) (cos.f64 (+.f64 x eps)))) |
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (+.f64 #s(approx (cos x) #s(literal 1 binary64)) (cos.f64 (+.f64 x eps))) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64)))) |
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 #s(approx (cos x) #s(literal 1 binary64)) (cos.f64 (+.f64 x eps)))) (/.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 2 binary64)) (+.f64 #s(approx (cos x) #s(literal 1 binary64)) (cos.f64 (+.f64 x eps))))) |
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (+.f64 #s(approx (cos x) #s(literal 1 binary64)) (cos.f64 (+.f64 x eps))) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (/.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (+.f64 #s(approx (cos x) #s(literal 1 binary64)) (cos.f64 (+.f64 x eps))) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64))))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) #s(approx (cos x) #s(literal 1 binary64)))) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 eps) (sin.f64 x)))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))))) |
(fma.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))) |
(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))) |
(sin.f64 (+.f64 (neg.f64 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) |
(cos.f64 (neg.f64 (neg.f64 (+.f64 x eps)))) |
(cos.f64 (neg.f64 (+.f64 x eps))) |
(cos.f64 (+.f64 x eps)) |
(+.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))) |
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) |
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (neg.f64 (-.f64 x eps))) |
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 eps x))) (neg.f64 (-.f64 eps x))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))) |
(/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps)) |
(/.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (-.f64 eps x)) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))) |
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) |
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x))) |
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) |
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))) |
(+.f64 x eps) |
(+.f64 eps x) |
#s(approx (cos x) #s(literal 1 binary64)) |
Compiled 16 229 to 2 290 computations (85.9% saved)
27 alts after pruning (22 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 420 | 14 | 434 |
| Fresh | 10 | 8 | 18 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 3 | 3 |
| Total | 433 | 27 | 460 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 53.8% | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
| ▶ | 99.8% | (*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64)) |
| 99.7% | (*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64)) | |
| 53.6% | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64))) | |
| 99.5% | #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))) | |
| ✓ | 99.8% | #s(approx (- (cos (+ x eps)) (cos 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)) |
| ✓ | 99.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) |
| 98.9% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) | |
| ✓ | 80.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
| 79.1% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) (*.f64 x x)) x x)))) | |
| ▶ | 79.1% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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)))) |
| 79.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x)))) | |
| ▶ | 78.9% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) |
| 97.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) | |
| 97.4% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) | |
| 94.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (*.f64 eps eps))) eps)) | |
| ▶ | 54.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
| 97.4% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps)) | |
| 78.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps)) | |
| 54.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps)) | |
| 23.2% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64))))) | |
| ▶ | 97.9% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
| 97.5% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) | |
| 97.4% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))) | |
| 79.1% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))) | |
| 78.9% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))) | |
| ✓ | 78.8% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x))) |
Compiled 1 886 to 1 202 computations (36.3% saved)
| Inputs |
|---|
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64)) |
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(cos.f64 x) |
x |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
eps |
(*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin.f64 x) |
#s(literal -2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
(*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps) |
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (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) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) |
(*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) |
(neg.f64 eps) |
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) |
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(*.f64 x x) |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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)))) |
(*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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))) |
#s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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)) |
(fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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) |
(*.f64 x (*.f64 x x)) |
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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))) |
(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)) |
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) |
#s(literal -1/5040 binary64) |
#s(literal 1/120 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) |
(fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) |
(*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) |
(fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) |
#s(literal -1/36 binary64) |
(*.f64 eps eps) |
#s(literal 1/6 binary64) |
(*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) |
#s(literal 1/4 binary64) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) |
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) |
| Outputs |
|---|
(* -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)) |
(sin (* 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 |
(+ 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))) |
x |
(* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(* x (+ (* -1/6 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(* x (+ (* (cos (* 1/2 eps)) (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/6 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/120 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))) |
(* x (+ (* (cos (* 1/2 eps)) (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/6 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* 1/120 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))))) |
(* x (cos (* 1/2 eps))) |
(* x (+ (cos (* 1/2 eps)) (* -1/6 (* (pow x 2) (cos (* 1/2 eps)))))) |
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* 1/120 (* (pow x 2) (cos (* 1/2 eps)))))))) |
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/120 (cos (* 1/2 eps))))))))) |
(* 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) 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)) |
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))))))) |
(* -1/2 eps) |
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 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 (* -1/6 (pow x 2))) |
(pow x 2) |
(pow x 3) |
-1/6 |
(- (* 1/120 (pow x 2)) 1/6) |
(- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6) |
1/120 |
(+ 1/120 (* -1/5040 (pow x 2))) |
(* eps (- (* 1/6 (pow eps 2)) 1)) |
(+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))) |
(+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))))) |
(* 1/4 (pow eps 2)) |
(+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))) |
(* x (+ 1/6 (* -1/36 (pow eps 2)))) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))) |
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) |
(* (cos x) (sin (* 1/2 eps))) |
(cos x) |
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 eps)) (sin x)) |
(sin x) |
(- (cos (+ eps x)) (cos x)) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)) |
(* -1 (* eps (sin x))) |
(* -1/6 (pow x 3)) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(* -1/6 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6)) |
(* -1/5040 (pow x 7)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* -1/5040 (pow x 4)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* -1/5040 (pow x 2)) |
(* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* eps (* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))) |
(* (pow x 3) (+ (* 1/4 (/ (pow eps 2) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2)))))) |
(* (pow x 3) (+ (* 1/4 (/ (pow eps 2) x)) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))) |
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/4 (/ (pow eps 2) x)) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))) |
(* eps (* (pow x 2) (+ 1/6 (* -1/36 (pow eps 2))))) |
(* (pow x 2) (+ (* 1/4 (/ (pow eps 2) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2)))))) |
(* (pow x 2) (+ (* 1/4 (/ (pow eps 2) x)) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))) |
(* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) |
(* x (+ (* 1/4 (/ (pow eps 2) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2)))))) |
(* -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)) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1/4 (/ (pow eps 2) x))))) |
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x))))) |
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) (* -1/4 (pow eps 2))) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2)))))) |
(* -1 (* x (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1/4 (/ (pow 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)))))))))) |
(* 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)))))))) |
(* 1/2 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)))) |
eps |
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))) |
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* 1/3840 (sin x)) (+ (* 1/768 (sin x)) (* 1/384 (sin x)))))))))) |
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* 1/3840 (sin x)) (+ (* 1/768 (sin x)) (+ (* 1/384 (sin x)) (* (pow eps 2) (+ (* -1/18432 (sin x)) (+ (* -1/30720 (sin x)) (+ (* -1/92160 (sin x)) (* -1/645120 (sin x))))))))))))))) |
(+ (sin x) (* -1/8 (* (pow eps 2) (sin x)))) |
(+ (sin x) (* (pow eps 2) (+ (* -1/8 (sin x)) (* 1/384 (* (pow eps 2) (sin x)))))) |
(+ (sin x) (* (pow eps 2) (+ (* -1/8 (sin x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (sin x))) (* 1/384 (sin x))))))) |
(+ 1 (* -1/8 (pow eps 2))) |
(+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8))) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8))) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))) |
(* -1 (sin x)) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(* -1 eps) |
(* eps (* x (- (* 1/6 (pow x 2)) 1))) |
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))) |
(* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))) |
(* eps (- (* 1/6 (pow x 2)) 1)) |
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)) |
(* eps (- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1)) |
(* 1/6 (* eps x)) |
(* eps (+ (* 1/6 x) (* 1/4 eps))) |
(* eps (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))) |
(* 1/6 x) |
(+ (* -1/36 (* (pow eps 2) x)) (* 1/6 x)) |
1/6 |
(+ 1/6 (* -1/36 (pow eps 2))) |
(pow eps 2) |
-1 |
(- (* 1/6 (pow eps 2)) 1) |
(cos (* 1/2 eps)) |
(* 1/6 (* (pow eps 3) (sin x))) |
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(* 1/6 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(* (pow eps 3) (* x (+ 1/6 (* -1/36 (pow x 2))))) |
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps)))) |
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps)))) |
(* (pow eps 3) (+ 1/6 (* -1/36 (pow x 2)))) |
(* (pow eps 3) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps))))) |
(* (pow eps 3) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2)))) |
(* -1/36 (* (pow eps 3) x)) |
(* (pow eps 3) (+ (* -1/36 x) (* 1/4 (/ 1 eps)))) |
(* (pow eps 3) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps))))) |
(* -1/36 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1/36 x) (* 1/6 (/ x (pow eps 2))))) |
(* -1/36 (pow eps 2)) |
(* (pow eps 2) (- (* 1/6 (/ 1 (pow eps 2))) 1/36)) |
(* 1/6 (pow eps 3)) |
(* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))) |
(* 1/6 (pow eps 2)) |
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 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)) |
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x)))) |
(* -1 (* (pow eps 3) (* x (- (* 1/36 (pow x 2)) 1/6)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6))))) |
(* -1 (* (pow eps 3) (- (* 1/36 (pow x 2)) 1/6))) |
(* -1 (* (pow eps 3) (- (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2))) 1/6))) |
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2))) 1/6))) |
(* -1 (* (pow eps 3) (- (* 1/36 x) (* 1/4 (/ 1 eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/4 (* 1/6 (/ x eps))) eps)) (* 1/36 x)))) |
(* -1 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 12.0ms | eps | @ | inf | ((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (+ (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps)))) (* (cos x) (sin (* 1/2 eps))) (cos x) x (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)) (cos (* 1/2 eps)) (sin x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (+ (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) -1/6) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) (* (+ (* -1/36 (* eps eps)) 1/6) x) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* 1/4 (* eps eps)) 1/4 (* (+ (* (* eps eps) 1/6) -1) eps) (+ (* (* eps eps) 1/6) -1) -1 (* (* eps eps) -1/2)) |
| 7.0ms | x | @ | inf | ((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (+ (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps)))) (* (cos x) (sin (* 1/2 eps))) (cos x) x (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)) (cos (* 1/2 eps)) (sin x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (+ (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) -1/6) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) (* (+ (* -1/36 (* eps eps)) 1/6) x) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* 1/4 (* eps eps)) 1/4 (* (+ (* (* eps eps) 1/6) -1) eps) (+ (* (* eps eps) 1/6) -1) -1 (* (* eps eps) -1/2)) |
| 6.0ms | x | @ | -inf | ((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (+ (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps)))) (* (cos x) (sin (* 1/2 eps))) (cos x) x (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)) (cos (* 1/2 eps)) (sin x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (+ (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) -1/6) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) (* (+ (* -1/36 (* eps eps)) 1/6) x) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* 1/4 (* eps eps)) 1/4 (* (+ (* (* eps eps) 1/6) -1) eps) (+ (* (* eps eps) 1/6) -1) -1 (* (* eps eps) -1/2)) |
| 5.0ms | eps | @ | -inf | ((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (+ (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps)))) (* (cos x) (sin (* 1/2 eps))) (cos x) x (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)) (cos (* 1/2 eps)) (sin x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (+ (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) -1/6) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) (* (+ (* -1/36 (* eps eps)) 1/6) x) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* 1/4 (* eps eps)) 1/4 (* (+ (* (* eps eps) 1/6) -1) eps) (+ (* (* eps eps) 1/6) -1) -1 (* (* eps eps) -1/2)) |
| 4.0ms | eps | @ | 0 | ((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (+ (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps)))) (* (cos x) (sin (* 1/2 eps))) (cos x) x (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)) (cos (* 1/2 eps)) (sin x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (+ (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) -1/6) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) (* (+ (* -1/36 (* eps eps)) 1/6) x) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* 1/4 (* eps eps)) 1/4 (* (+ (* (* eps eps) 1/6) -1) eps) (+ (* (* eps eps) 1/6) -1) -1 (* (* eps eps) -1/2)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 673 | 3037 |
| 1 | 2436 | 2889 |
| 0 | 8941 | 2675 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* -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)) |
(sin (* 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 |
(+ 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))) |
x |
(* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(* x (+ (* -1/6 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(* x (+ (* (cos (* 1/2 eps)) (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/6 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/120 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))) |
(* x (+ (* (cos (* 1/2 eps)) (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/6 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* 1/120 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))))) |
(* x (cos (* 1/2 eps))) |
(* x (+ (cos (* 1/2 eps)) (* -1/6 (* (pow x 2) (cos (* 1/2 eps)))))) |
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* 1/120 (* (pow x 2) (cos (* 1/2 eps)))))))) |
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/120 (cos (* 1/2 eps))))))))) |
(* 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) 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)) |
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))) |
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))))))) |
(* -1/2 eps) |
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1))) |
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 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 (* -1/6 (pow x 2))) |
(pow x 2) |
(pow x 3) |
-1/6 |
(- (* 1/120 (pow x 2)) 1/6) |
(- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6) |
1/120 |
(+ 1/120 (* -1/5040 (pow x 2))) |
(* eps (- (* 1/6 (pow eps 2)) 1)) |
(+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))) |
(+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))))) |
(* 1/4 (pow eps 2)) |
(+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))) |
(* x (+ 1/6 (* -1/36 (pow eps 2)))) |
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))) |
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))) |
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))) |
(* (cos x) (sin (* 1/2 eps))) |
(cos x) |
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 eps)) (sin x)) |
(sin x) |
(- (cos (+ eps x)) (cos x)) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))) |
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)) |
(* -1 (* eps (sin x))) |
(* -1/6 (pow x 3)) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(* -1/6 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6)) |
(* -1/5040 (pow x 7)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* -1/5040 (pow x 4)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* -1/5040 (pow x 2)) |
(* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* eps (* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2))))) |
(* (pow x 3) (+ (* 1/4 (/ (pow eps 2) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2)))))) |
(* (pow x 3) (+ (* 1/4 (/ (pow eps 2) x)) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))) |
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/4 (/ (pow eps 2) x)) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))) |
(* eps (* (pow x 2) (+ 1/6 (* -1/36 (pow eps 2))))) |
(* (pow x 2) (+ (* 1/4 (/ (pow eps 2) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2)))))) |
(* (pow x 2) (+ (* 1/4 (/ (pow eps 2) x)) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))) |
(* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) |
(* x (+ (* 1/4 (/ (pow eps 2) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2)))))) |
(* -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)) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1/4 (/ (pow eps 2) x))))) |
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x))))) |
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) (* -1/4 (pow eps 2))) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2)))))) |
(* -1 (* x (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1/4 (/ (pow 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)))))))))) |
(* 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)))))))) |
(* 1/2 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)))) |
eps |
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (* -1/48 (sin x)))))) |
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* 1/3840 (sin x)) (+ (* 1/768 (sin x)) (* 1/384 (sin x)))))))))) |
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* 1/3840 (sin x)) (+ (* 1/768 (sin x)) (+ (* 1/384 (sin x)) (* (pow eps 2) (+ (* -1/18432 (sin x)) (+ (* -1/30720 (sin x)) (+ (* -1/92160 (sin x)) (* -1/645120 (sin x))))))))))))))) |
(+ (sin x) (* -1/8 (* (pow eps 2) (sin x)))) |
(+ (sin x) (* (pow eps 2) (+ (* -1/8 (sin x)) (* 1/384 (* (pow eps 2) (sin x)))))) |
(+ (sin x) (* (pow eps 2) (+ (* -1/8 (sin x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (sin x))) (* 1/384 (sin x))))))) |
(+ 1 (* -1/8 (pow eps 2))) |
(+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8))) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8))) |
(* eps (- (* -1/2 (* eps (cos x))) (sin x))) |
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) |
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))) |
(* -1 (sin x)) |
(- (* -1/2 (* eps (cos x))) (sin x)) |
(* -1 eps) |
(* eps (* x (- (* 1/6 (pow x 2)) 1))) |
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))) |
(* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))) |
(* eps (- (* 1/6 (pow x 2)) 1)) |
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)) |
(* eps (- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1)) |
(* 1/6 (* eps x)) |
(* eps (+ (* 1/6 x) (* 1/4 eps))) |
(* eps (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))) |
(* 1/6 x) |
(+ (* -1/36 (* (pow eps 2) x)) (* 1/6 x)) |
1/6 |
(+ 1/6 (* -1/36 (pow eps 2))) |
(pow eps 2) |
-1 |
(- (* 1/6 (pow eps 2)) 1) |
(cos (* 1/2 eps)) |
(* 1/6 (* (pow eps 3) (sin x))) |
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(* 1/6 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))) |
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))) |
(* (pow eps 3) (* x (+ 1/6 (* -1/36 (pow x 2))))) |
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps)))) |
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps)))) |
(* (pow eps 3) (+ 1/6 (* -1/36 (pow x 2)))) |
(* (pow eps 3) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps))))) |
(* (pow eps 3) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2)))) |
(* -1/36 (* (pow eps 3) x)) |
(* (pow eps 3) (+ (* -1/36 x) (* 1/4 (/ 1 eps)))) |
(* (pow eps 3) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps))))) |
(* -1/36 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1/36 x) (* 1/6 (/ x (pow eps 2))))) |
(* -1/36 (pow eps 2)) |
(* (pow eps 2) (- (* 1/6 (/ 1 (pow eps 2))) 1/36)) |
(* 1/6 (pow eps 3)) |
(* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))) |
(* 1/6 (pow eps 2)) |
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 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)) |
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x)))) |
(* -1 (* (pow eps 3) (* x (- (* 1/36 (pow x 2)) 1/6)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6))))) |
(* -1 (* (pow eps 3) (- (* 1/36 (pow x 2)) 1/6))) |
(* -1 (* (pow eps 3) (- (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2))) 1/6))) |
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2))) 1/6))) |
(* -1 (* (pow eps 3) (- (* 1/36 x) (* 1/4 (/ 1 eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/4 (* 1/6 (/ x eps))) eps)) (* 1/36 x)))) |
(* -1 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))) |
| Outputs |
|---|
(* -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 #s(literal -2 binary64) (*.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))))) |
(+ (* -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 #s(literal -2 binary64) (*.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)))) (*.f64 (*.f64 x x) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) |
(+ (* -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 #s(literal -2 binary64) (*.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)))) (*.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #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 (*.f64 x (*.f64 #s(literal -1/2 binary64) x)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.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 (+ (* 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 x #s(literal -1/2 binary64)) (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))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(+ (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 (fma.f64 (*.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 x x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) (*.f64 x x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(fma.f64 (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)) |
x |
(* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(* x (+ (* -1/6 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(*.f64 (*.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) |
(* x (+ (* (cos (* 1/2 eps)) (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/6 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/120 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))) |
(*.f64 (fma.f64 (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (*.f64 x x) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x) |
(* x (+ (* (cos (* 1/2 eps)) (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/6 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* 1/120 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))))) |
(*.f64 (fma.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))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))))) x) |
(* x (cos (* 1/2 eps))) |
(*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x) |
(* x (+ (cos (* 1/2 eps)) (* -1/6 (* (pow x 2) (cos (* 1/2 eps)))))) |
(*.f64 (*.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) |
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* 1/120 (* (pow x 2) (cos (* 1/2 eps)))))))) |
(*.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (*.f64 x x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) x) |
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/120 (cos (* 1/2 eps))))))))) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (*.f64 x x) (*.f64 #s(literal -1/6 binary64) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (*.f64 x x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) x) |
(* x (+ 1 (* -1/6 (pow x 2)))) |
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(*.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/6 binary64))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (- (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2))) 1/6))) |
(*.f64 (neg.f64 (fma.f64 (/.f64 x eps) #s(literal -1/4 binary64) (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/6 binary64)))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2))) 1/6))) |
(*.f64 (neg.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) (neg.f64 eps))) eps) #s(literal -1 binary64) (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/6 binary64)))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (- (* 1/36 x) (* 1/4 (/ 1 eps))))) |
(*.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (-.f64 (*.f64 #s(literal 1/36 binary64) x) (/.f64 #s(literal 1/4 binary64) eps))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/4 (* 1/6 (/ x eps))) eps)) (* 1/36 x)))) |
(*.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) x (/.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)) (neg.f64 eps)))) (pow.f64 eps #s(literal 3 binary64))) |
(* -1 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))) |
(*.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 1/6 binary64))) (pow.f64 eps #s(literal 3 binary64))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 82 | 721 |
| 0 | 126 | 699 |
| 1 | 484 | 663 |
| 0 | 3948 | 648 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64)) |
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(cos.f64 x) |
x |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
eps |
(*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin.f64 x) |
#s(literal -2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
(*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps) |
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (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) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) |
(*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) |
(neg.f64 eps) |
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) |
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
(*.f64 x x) |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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)))) |
(*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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))) |
#s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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)) |
(fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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) |
(*.f64 x (*.f64 x x)) |
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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))) |
(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)) |
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) |
#s(literal -1/5040 binary64) |
#s(literal 1/120 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) |
(fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) |
(*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) |
(fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) |
#s(literal -1/36 binary64) |
(*.f64 eps eps) |
#s(literal 1/6 binary64) |
(*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) |
#s(literal 1/4 binary64) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) |
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) |
| Outputs |
|---|
(*.f64 #s(literal -2 binary64) #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.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)) |
(neg.f64 (*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.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))) |
(neg.f64 (*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))) |
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.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 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (*.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)))) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (-.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x))) (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (-.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x))) (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64)))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 x) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x))) |
(fma.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x) (*.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(fma.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) |
(fma.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x))) |
(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 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x))) |
(fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) |
(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 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x))) |
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
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(/.f64 (fma.f64 (pow.f64 (*.f64 eps eps) #s(literal 3 binary64)) #s(literal 1/216 binary64) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))) |
(/.f64 (fma.f64 (pow.f64 (*.f64 eps eps) #s(literal 3 binary64)) #s(literal 1/216 binary64) #s(literal -1 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
(fma.f64 (*.f64 #s(literal 1/6 binary64) (fabs.f64 eps)) (fabs.f64 eps) #s(literal -1 binary64)) |
(fma.f64 (*.f64 #s(literal 1/6 binary64) (neg.f64 eps)) (neg.f64 eps) #s(literal -1 binary64)) |
(fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64)) |
(fma.f64 (fabs.f64 eps) (*.f64 (fabs.f64 eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) |
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) |
(fma.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) |
(fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) |
(fma.f64 eps (*.f64 #s(literal 1/6 binary64) eps) #s(literal -1 binary64)) |
(-.f64 (/.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))) |
(-.f64 #s(literal -1 binary64) (*.f64 (*.f64 (neg.f64 eps) eps) #s(literal 1/6 binary64))) |
(-.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) |
(-.f64 #s(literal -1 binary64) (*.f64 (neg.f64 eps) (*.f64 #s(literal 1/6 binary64) eps))) |
(+.f64 (/.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))) |
(+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)) |
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) |
#s(literal -1 binary64) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (fabs.f64 eps)) (fabs.f64 eps)) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (neg.f64 eps)) (neg.f64 eps)) |
(*.f64 (fabs.f64 eps) (*.f64 (fabs.f64 eps) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) |
(*.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps) |
(*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps)) |
Compiled 41 516 to 4 065 computations (90.2% saved)
26 alts after pruning (19 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 741 | 8 | 749 |
| Fresh | 6 | 11 | 17 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 5 | 5 |
| Total | 750 | 26 | 776 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 53.8% | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
| 99.6% | (*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64)) | |
| 99.7% | (*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64)) | |
| 53.6% | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64))) | |
| 99.5% | #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))) | |
| ✓ | 99.8% | #s(approx (- (cos (+ x eps)) (cos 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)) |
| ✓ | 99.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) |
| 98.9% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) | |
| ✓ | 80.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
| 79.1% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x)))) | |
| 79.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x)))) | |
| ✓ | 78.9% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) |
| 53.3% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))) | |
| 97.4% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) | |
| ✓ | 54.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
| 97.4% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps)) | |
| 78.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps)) | |
| 54.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps)) | |
| 97.4% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))) | |
| 97.9% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) | |
| 97.9% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) | |
| 97.8% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) eps (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)) x)) x) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) | |
| 97.8% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)) eps)))) | |
| 79.1% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))) | |
| 78.9% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))) | |
| ✓ | 78.8% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x))) |
Compiled 3 133 to 1 087 computations (65.3% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (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 (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) (*.f64 x x)) x x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) eps (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)) x)) x) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#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))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.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)) (cos.f64 x)) |
#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 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.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 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (*.f64 eps eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos 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)) |
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64))))) |
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (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 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64)) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos 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)) |
3 calls:
| 12.0ms | eps |
| 11.0ms | x |
| 9.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
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 eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (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 (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) (*.f64 x x)) x x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) eps (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)) x)) x) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#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))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.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)) (cos.f64 x)) |
#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 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.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 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (*.f64 eps eps))) eps)) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) |
3 calls:
| 11.0ms | eps |
| 11.0ms | x |
| 8.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 99.7% | 1 | x |
| 99.7% | 1 | eps |
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 eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (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 (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) (*.f64 x x)) x x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) eps (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)) x)) x) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#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))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.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)) (cos.f64 x)) |
#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 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.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 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))))) |
| Outputs |
|---|
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64)) |
3 calls:
| 11.0ms | eps |
| 11.0ms | x |
| 8.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 99.7% | 1 | x |
| 99.7% | 1 | eps |
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 eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (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 (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) (*.f64 x x)) x x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) eps (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)) x)) x) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#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))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
3 calls:
| 9.0ms | x |
| 9.0ms | eps |
| 6.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 98.9% | 1 | x |
| 98.9% | 1 | eps |
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 eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (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 (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) (*.f64 x x)) x x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) eps (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)) x)) x) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#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))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
3 calls:
| 8.0ms | x |
| 8.0ms | eps |
| 6.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.9% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 97.9% | 1 | x |
| 97.9% | 1 | eps |
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 eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (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 (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) (*.f64 x x)) x x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
3 calls:
| 7.0ms | x |
| 7.0ms | eps |
| 5.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.9% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 97.9% | 1 | x |
| 97.9% | 1 | eps |
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 eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (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 (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (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)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) (*.f64 x x)) x x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
3 calls:
| 7.0ms | eps |
| 7.0ms | x |
| 5.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.9% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 97.9% | 1 | x |
| 97.9% | 1 | eps |
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 eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (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 (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
3 calls:
| 5.0ms | eps |
| 5.0ms | x |
| 4.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.9% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 97.9% | 1 | x |
| 97.9% | 1 | eps |
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 eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (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 (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps)) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
3 calls:
| 3.0ms | x |
| 3.0ms | eps |
| 2.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.4% | 1 | eps |
| 97.4% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 97.4% | 1 | 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 eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (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 (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps)) |
3 calls:
| 3.0ms | eps |
| 2.0ms | x |
| 2.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.4% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 97.4% | 1 | x |
| 97.4% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
Total -15.4b remaining (-113.7%)
Threshold costs -15.4b (-113.7%)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (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 eps) x))) |
3 calls:
| 1.0ms | eps |
| 1.0ms | x |
| 1.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 78.8% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 78.8% | 1 | x |
| 78.8% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 141 | 509 |
| 1 | 243 | 503 |
| 2 | 521 | 501 |
| 3 | 1512 | 494 |
| 4 | 5756 | 494 |
| 1× | node limit |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos 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)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (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 eps) x))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos 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)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (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 eps) x))) |
| 1× | fuel |
Compiled 509 to 149 computations (70.7% saved)
Compiled 1 066 to 340 computations (68.1% saved)
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