
Time bar (total: 8.1s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0.0% | 0.0% | 50.6% | 49.4% | 0.0% | 0.0% | 0.0% | 0 |
| 0.0% | 0.0% | 50.6% | 49.4% | 0.0% | 0.0% | 0.0% | 1 |
| 0.0% | 0.0% | 50.6% | 49.4% | 0.0% | 0.0% | 0.0% | 2 |
| 0.0% | 0.0% | 25.3% | 49.4% | 0.0% | 25.3% | 0.0% | 3 |
| 0.0% | 0.0% | 25.3% | 49.4% | 0.0% | 25.3% | 0.0% | 4 |
| 0.0% | 0.0% | 19.0% | 49.4% | 0.0% | 31.6% | 0.0% | 5 |
| 0.0% | 0.0% | 15.8% | 49.4% | 0.0% | 34.8% | 0.0% | 6 |
| 0.0% | 0.0% | 11.1% | 49.4% | 0.0% | 39.5% | 0.0% | 7 |
| 0.0% | 0.0% | 8.7% | 49.4% | 0.0% | 41.9% | 0.0% | 8 |
| 0.0% | 0.0% | 5.9% | 49.4% | 0.0% | 44.6% | 0.0% | 9 |
| 0.0% | 0.0% | 4.5% | 49.4% | 0.0% | 46.0% | 0.0% | 10 |
| 0.0% | 0.0% | 3.1% | 49.4% | 0.0% | 47.5% | 0.0% | 11 |
| 0.0% | 0.0% | 2.7% | 49.4% | 0.0% | 47.9% | 0.0% | 12 |
Compiled 27 to 19 computations (29.6% saved)
| 2.5s | 25 547× | 0 | invalid |
| 2.4s | 5 756× | 2 | valid |
| 362.0ms | 2 432× | 1 | valid |
| 20.0ms | 68× | 0 | valid |
ival-cos: 2.8s (67.6% of total)ival-fabs: 350.0ms (8.4% of total)adjust: 344.0ms (8.3% of total)ival-mult!: 170.0ms (4.1% of total)ival-<: 150.0ms (3.6% of total)ival-sub!: 128.0ms (3.1% of total)ival-add!: 125.0ms (3.0% of total)ival-and: 64.0ms (1.5% of total)ival-assert: 12.0ms (0.3% of total)Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 46 |
| 1 | 143 | 42 |
| 2 | 1851 | 42 |
| 1× | node-limit |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 50.5% | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Compiled 14 to 12 computations (14.3% saved)
| Inputs |
|---|
| Outputs |
|---|
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 141 | 506 |
| 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 |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 #s(literal -1 binary64) (*.f64 x (sin.f64 eps)))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps)))) (sin.f64 eps)))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps)))))) (sin.f64 eps)))) #s(literal 1 binary64))) |
#s(approx (cos (+ x eps)) (cos.f64 eps)) |
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 eps) (*.f64 #s(literal -1 binary64) (*.f64 x (sin.f64 eps))))) |
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (cos.f64 eps))) (sin.f64 eps))))) |
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps))))) (sin.f64 eps))))) |
#s(approx (+ x eps) eps) |
#s(approx (+ x eps) (+.f64 eps x)) |
#s(approx x x) |
#s(approx (cos x) #s(literal 1 binary64)) |
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))) |
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x))) |
#s(approx (+ x eps) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))) |
#s(approx (cos x) (cos.f64 x)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 x))) |
#s(approx (cos (+ x eps)) (cos.f64 (-.f64 eps (*.f64 #s(literal -1 binary64) x)))) |
#s(approx (+ x eps) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 eps x)) #s(literal 1 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))) |
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 x) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x))))) |
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))) |
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x))))) |
#s(approx (+ x eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))) (cos.f64 x))) |
#s(approx (cos (+ x eps)) (cos.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps)))) |
#s(approx (+ x eps) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1 binary64))))) |
6 calls:
| Time | Variable | Point |
|---|---|---|
| 1.0ms | x | 0 |
| 1.0ms | eps | inf |
| 1.0ms | eps | -inf |
| 1.0ms | x | -inf |
| 0.0ms | eps | 0 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 0 | 10 | 18 |
| 1 | 79 | 18 |
| 2 | 528 | 18 |
| 0 | 4119 | 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 #s(literal 1 binary64) (/.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x)))) (neg.f64 (cos.f64 x))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (neg.f64 (cos.f64 x))) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (neg.f64 (cos.f64 x))) (cos.f64 (+.f64 eps x)))) (cos.f64 (+.f64 eps x))) |
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 eps x)))) (cos.f64 (+.f64 eps x))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (cos.f64 (+.f64 eps x))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)) (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)) (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)) (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)) (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (fabs.f64 (+.f64 eps x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (neg.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (neg.f64 (fabs.f64 (+.f64 eps x)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (neg.f64 (fabs.f64 (+.f64 eps x)))) #s(literal 2 binary64))))) |
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(/.f64 (-.f64 (*.f64 x x) (*.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 eps)))) (-.f64 x (neg.f64 (neg.f64 eps)))) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps)) |
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (neg.f64 (neg.f64 eps)) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (*.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 eps))) (*.f64 x (neg.f64 (neg.f64 eps)))))) |
(/.f64 (-.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (fma.f64 eps eps (+.f64 (*.f64 x x) (*.f64 eps (neg.f64 x))))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (+.f64 eps (neg.f64 x))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x)) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 (neg.f64 eps) (neg.f64 eps))) (+.f64 x (neg.f64 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 x #s(literal 3 binary64)) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (neg.f64 eps) (neg.f64 eps) (*.f64 x (neg.f64 eps))))) |
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 x x (-.f64 (*.f64 eps eps) (*.f64 x eps)))) |
(neg.f64 (-.f64 (neg.f64 eps) x)) |
(-.f64 eps (neg.f64 x)) |
(-.f64 x (neg.f64 eps)) |
(+.f64 eps x) |
(+.f64 x (neg.f64 (neg.f64 eps))) |
(+.f64 x eps) |
x |
eps |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (cos.f64 x) #s(literal 1 binary64)) (*.f64 (sin.f64 x) #s(literal 0 binary64)))) (*.f64 (sin.f64 x) #s(literal 0 binary64))) |
(/.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)))))) |
(sin.f64 (+.f64 (neg.f64 (neg.f64 x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) |
(sin.f64 (+.f64 (neg.f64 (fabs.f64 x)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) |
(sin.f64 (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) |
(sin.f64 (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) |
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) |
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64))) |
(fma.f64 (sin.f64 (fabs.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))) |
(-.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) (sin.f64 (neg.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))) |
(cos.f64 (neg.f64 (neg.f64 (neg.f64 x)))) |
(cos.f64 (neg.f64 (neg.f64 (fabs.f64 x)))) |
(cos.f64 (neg.f64 (neg.f64 x))) |
(cos.f64 (neg.f64 (fabs.f64 x))) |
(cos.f64 (neg.f64 x)) |
(cos.f64 (fabs.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 (sin.f64 (fabs.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 5 792 to 1 321 computations (77.2% saved)
16 alts after pruning (15 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 244 | 15 | 259 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 244 | 16 | 260 |
| Status | Accuracy | Program |
|---|---|---|
| 50.6% | (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x)) | |
| 50.6% | (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) | |
| ▶ | 50.5% | (-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) |
| 50.5% | (-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64))))) | |
| ✓ | 50.5% | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 49.1% | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) | |
| 50.6% | (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x))) | |
| ▶ | 80.7% | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) |
| ▶ | 5.5% | (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))))) |
| 5.4% | (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 x) (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (neg.f64 x) (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64))))) | |
| 5.5% | (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 x (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 x (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64))))) | |
| ▶ | 49.0% | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
| ▶ | 99.4% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))) |
| 99.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x)))) | |
| 99.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))) | |
| 77.6% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))) |
Compiled 589 to 394 computations (33.1% saved)
| Inputs |
|---|
-1/2 |
1/24 |
-1/6 |
1 |
(PI) |
1/2 |
-2 |
2 |
| Outputs |
|---|
#s(literal -1/2 binary64) |
#s(literal 6004799503160661/144115188075855872 binary64) |
#s(literal -6004799503160661/36028797018963968 binary64) |
#s(literal 1 binary64) |
#s(literal 884279719003555/281474976710656 binary64) |
#s(literal 1/2 binary64) |
#s(literal -2 binary64) |
#s(literal 2 binary64) |
| 0.0ms | 1× | 0 | valid |
Compiled 10 to 10 computations (0.0% saved)
adjust: 0.0ms (0.0% of total)Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1107 | 8275 |
| 1× | iter-limit |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))) |
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x))) |
eps |
(-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x)) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) |
(fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))))) |
#s(literal -1/2 binary64) |
(cos.f64 x) |
x |
(*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))) |
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) |
(*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) |
#s(literal 1/24 binary64) |
(*.f64 eps (cos.f64 x)) |
(*.f64 #s(literal -1/6 binary64) (sin.f64 x)) |
#s(literal -1/6 binary64) |
(sin.f64 x) |
#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) |
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) |
(fma.f64 (PI.f64) #s(literal 1/2 binary64) x) |
(PI.f64) |
#s(literal 1/2 binary64) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) |
(*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) |
(sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) |
(*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)) |
(+.f64 (+.f64 eps x) x) |
(+.f64 eps x) |
(sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) |
(*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)) |
(-.f64 (+.f64 eps x) x) |
#s(literal -2 binary64) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))))) |
#s(literal 2 binary64) |
(*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)))) |
(sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) |
(/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)) |
(+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) |
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) |
(+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)) |
(cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) |
(/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)) |
(-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 #s(literal -1 binary64) (*.f64 x (sin.f64 eps)))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps)))) (sin.f64 eps)))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps)))))) (sin.f64 eps)))) #s(literal 1 binary64))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 x (fma.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 x (fma.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 x (fma.f64 eps (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/36 binary64) (pow.f64 eps #s(literal 2 binary64))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) #s(literal 1 binary64))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 eps (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/36 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) #s(literal 1 binary64))))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (fma.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -1/36 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) x) (*.f64 eps (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))))))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 eps x))) #s(literal 1/2 binary64))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) #s(literal 1/2 binary64))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))))) #s(literal 1/2 binary64))) |
#s(approx (cos x) #s(literal 1 binary64)) |
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))) |
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64))))) |
#s(approx x x) |
#s(approx (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)))) |
#s(approx (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))) (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)))) |
#s(approx (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))) (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -1/48 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) x) (*.f64 #s(literal 1/6 binary64) eps))))) |
#s(approx (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))) (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) eps (*.f64 x (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))))) |
#s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 #s(literal 1/24 binary64) eps)) |
#s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) |
#s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps x)))))) |
#s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x (fma.f64 #s(literal -1/36 binary64) x (*.f64 #s(literal -1/48 binary64) eps))))))) |
#s(approx (* 1/24 (* eps (cos x))) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) eps))) |
#s(approx (* 1/24 (* eps (cos x))) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/48 binary64) eps (*.f64 #s(literal 1/576 binary64) (*.f64 eps (pow.f64 x #s(literal 2 binary64)))))))) |
#s(approx (* 1/24 (* eps (cos x))) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/48 binary64) eps (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/17280 binary64) (*.f64 eps (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/576 binary64) eps))))))) |
#s(approx (* eps (cos x)) eps) |
#s(approx (* eps (cos x)) (+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (pow.f64 x #s(literal 2 binary64)))))) |
#s(approx (* eps (cos x)) (+.f64 eps (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal 1/24 binary64) (*.f64 eps (pow.f64 x #s(literal 2 binary64)))))))) |
#s(approx (* eps (cos x)) (+.f64 eps (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) eps (*.f64 (pow.f64 x #s(literal 2 binary64)) (fma.f64 #s(literal -1/720 binary64) (*.f64 eps (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) eps))))))) |
#s(approx (* -1/6 (sin x)) (*.f64 #s(literal -1/6 binary64) x)) |
#s(approx (* -1/6 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/6 binary64)))) |
#s(approx (* -1/6 (sin x)) (*.f64 x (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/36 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/6 binary64)))) |
#s(approx (* -1/6 (sin x)) (*.f64 x (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/36 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/30240 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/720 binary64))))) #s(literal 1/6 binary64)))) |
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/6 binary64)))))) |
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/6 binary64)))))) |
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (cos.f64 eps) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))) |
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (+.f64 (cos.f64 eps) (*.f64 #s(literal -1 binary64) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (sin.f64 eps))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))) |
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 eps)) (*.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))) (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (sin.f64 eps))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))) |
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (-.f64 (fma.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 #s(literal -1/6 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 #s(literal -1/6 binary64) (sin.f64 eps)))) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) (*.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))) (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (sin.f64 eps))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))) |
#s(approx (cos (+ x eps)) (cos.f64 eps)) |
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 eps) (*.f64 #s(literal -1 binary64) (*.f64 x (sin.f64 eps))))) |
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (cos.f64 eps))) (sin.f64 eps))))) |
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps))))) (sin.f64 eps))))) |
#s(approx (+ x eps) (+.f64 eps x)) |
#s(approx (sin (+ (* (PI) 1/2) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))) |
#s(approx (sin (+ (* (PI) 1/2) x)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
#s(approx (sin (+ (* (PI) 1/2) x)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))))))) |
#s(approx (sin (+ (* (PI) 1/2) x)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))))))))) |
#s(approx (+ (* (PI) 1/2) x) (*.f64 #s(literal 1/2 binary64) (PI.f64))) |
#s(approx (+ (* (PI) 1/2) x) (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64)))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (fma.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 (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)))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (*.f64 (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)))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))) (*.f64 (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)))) |
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))) |
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))))) |
#s(approx (* (+ (+ eps x) x) 1/2) (*.f64 #s(literal 1/2 binary64) eps)) |
#s(approx (* (+ (+ eps x) x) 1/2) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
#s(approx (+ (+ eps x) x) (+.f64 eps (*.f64 #s(literal 2 binary64) x))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 x (fma.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 x (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))) (*.f64 x (fma.f64 #s(literal -1 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))))))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) |
#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))))))) |
#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))))))))) |
#s(approx (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (+.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) |
#s(approx (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))) |
#s(approx (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (+.f64 eps (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (+ (* (PI) 1/2) (+ eps x)) (+.f64 eps (*.f64 #s(literal 1/2 binary64) (PI.f64)))) |
#s(approx (+ (* (PI) 1/2) (+ eps x)) (+.f64 eps (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64))))) |
#s(approx (+ (+ (* (PI) 1/2) x) (PI)) (+.f64 (PI.f64) (*.f64 #s(literal 1/2 binary64) (PI.f64)))) |
#s(approx (+ (+ (* (PI) 1/2) x) (PI)) (+.f64 x (+.f64 (PI.f64) (*.f64 #s(literal 1/2 binary64) (PI.f64))))) |
#s(approx (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))) |
#s(approx (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) |
#s(approx (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (-.f64 eps (PI.f64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))))))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) |
#s(approx (cos x) (cos.f64 x)) |
#s(approx (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))))) |
#s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))) |
#s(approx (* 1/24 (* eps (cos x))) (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)))) |
#s(approx (* eps (cos x)) (*.f64 eps (cos.f64 x))) |
#s(approx (* -1/6 (sin x)) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) |
#s(approx (sin x) (sin.f64 x)) |
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x))) |
#s(approx (+ x eps) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))) |
#s(approx (sin (+ (* (PI) 1/2) x)) (sin.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64))))) |
#s(approx (+ (* (PI) 1/2) x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (PI.f64) x))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) |
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x))))) |
#s(approx (* (+ (+ eps x) x) 1/2) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) |
#s(approx (+ (+ eps x) x) (*.f64 #s(literal 2 binary64) x)) |
#s(approx (+ (+ eps x) x) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))) |
#s(approx (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) x))))) |
#s(approx (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (*.f64 x (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 (PI.f64) x) (/.f64 eps x))))) |
#s(approx (+ (* (PI) 1/2) (+ eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (PI.f64) x) (/.f64 eps x))))) |
#s(approx (+ (+ (* (PI) 1/2) x) (PI)) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (PI.f64) x) (/.f64 (PI.f64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 x))) |
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (cos.f64 (-.f64 eps (*.f64 #s(literal -1 binary64) x))) (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 #s(literal -1 binary64) x))))) |
#s(approx (cos (+ x eps)) (cos.f64 (-.f64 eps (*.f64 #s(literal -1 binary64) x)))) |
#s(approx (+ x eps) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 eps x)) #s(literal 1 binary64))))) |
#s(approx (sin (+ (* (PI) 1/2) x)) (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 #s(literal -1 binary64) x)))) |
#s(approx (+ (* (PI) 1/2) x) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) x)) #s(literal 1 binary64))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) |
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))))) |
#s(approx (* (+ (+ eps x) x) 1/2) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 1 binary64))))) |
#s(approx (+ (+ eps x) x) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 eps x)) #s(literal 2 binary64))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))))) |
#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))) |
#s(approx (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) x)) #s(literal 1 binary64))))) |
#s(approx (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) x)) #s(literal 2 binary64))))) |
#s(approx (+ (* (PI) 1/2) (+ eps x)) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 eps (*.f64 #s(literal 1/2 binary64) (PI.f64))) x)) #s(literal 1 binary64))))) |
#s(approx (+ (+ (* (PI) 1/2) x) (PI)) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 (PI.f64) (*.f64 #s(literal 1/2 binary64) (PI.f64))) x)) #s(literal 1 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x)))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x)))))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x)))))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) |
#s(approx (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x)))) |
#s(approx (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))) |
#s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) |
#s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))) |
#s(approx (- (cos eps) 1) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/2 binary64)))) |
#s(approx (- (cos eps) 1) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/40320 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/720 binary64))))) #s(literal 1/2 binary64)))) |
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) |
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (cos.f64 x) (sin.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (+.f64 (cos.f64 x) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))) (sin.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))) (sin.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
#s(approx (- (cos (+ x eps)) (sin (+ (* (PI) 1/2) x))) (-.f64 (+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x)))) (sin.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64)))))) |
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 x) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x))))) |
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))))) |
#s(approx (cos (+ x eps)) (+.f64 (cos.f64 x) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -2 binary64) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x)))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -2 binary64) (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x))) (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)))))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x)))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x))))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (fma.f64 #s(literal -1/48 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x))))))))))) |
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (+.f64 (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))))) |
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (*.f64 eps (sin.f64 x)) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))))) |
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x))))))))) |
#s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) |
#s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/3840 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/48 binary64)))))) |
#s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/3840 binary64) (*.f64 #s(literal -1/645120 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/48 binary64)))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 eps (fma.f64 #s(literal 2 binary64) (*.f64 eps (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))) (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 eps (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) (*.f64 eps (fma.f64 #s(literal 2 binary64) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal -1/48 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal 1/48 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/16 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))))) (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 eps (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
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#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) |
#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))) |
#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (*.f64 eps (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))))) |
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#s(approx (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) |
#s(approx (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))) |
#s(approx (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)))) |
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#s(approx (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (+.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (*.f64 #s(literal 1/48 binary64) (*.f64 eps (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))) (*.f64 #s(literal 1/2 binary64) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)))))))) |
#s(approx (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (*.f64 #s(literal -1/2 binary64) (PI.f64))) |
#s(approx (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (fma.f64 #s(literal -1/2 binary64) (PI.f64) (*.f64 #s(literal 1/2 binary64) eps))) |
#s(approx (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (*.f64 #s(literal -1 binary64) (PI.f64))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (cos.f64 x)))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps)))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps))))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (cos.f64 x)))) |
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#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps))))) |
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#s(approx (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (*.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 x eps) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) eps)))))) |
#s(approx (+ (* (PI) 1/2) (+ eps x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (PI.f64) eps) (/.f64 x eps))))) |
#s(approx (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) eps))))) |
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#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))) (cos.f64 x))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 x) eps))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x)))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x)))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x)))))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 x) eps))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) |
#s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 #s(literal -1 binary64) (*.f64 eps (fma.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x)))))) |
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#s(approx (cos (+ x eps)) (cos.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps)))) |
#s(approx (+ x eps) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1 binary64))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1 binary64) eps))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1 binary64) eps)))))) |
#s(approx (sin (* (+ (+ eps x) x) 1/2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1 binary64) eps))))) |
#s(approx (* (+ (+ eps x) x) 1/2) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64))))) |
#s(approx (+ (+ eps x) x) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 x eps)) #s(literal 1 binary64))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) eps))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) eps)))))) |
#s(approx (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) eps))))) |
#s(approx (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) eps)) #s(literal 1/2 binary64))))) |
#s(approx (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) eps)) #s(literal 1 binary64))))) |
#s(approx (+ (* (PI) 1/2) (+ eps x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (PI.f64))) eps)) #s(literal 1 binary64))))) |
#s(approx (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) eps))))) |
#s(approx (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (PI.f64) eps)) #s(literal 1/2 binary64))))) |
#s(approx (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (/.f64 (PI.f64) eps) #s(literal 1 binary64))))) |
6 calls:
| Time | Variable | Point |
|---|---|---|
| 13.0ms | x | 0 |
| 13.0ms | eps | -inf |
| 7.0ms | x | -inf |
| 7.0ms | eps | 0 |
| 6.0ms | eps | inf |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 53 | 457 |
| 0 | 92 | 420 |
| 1 | 481 | 403 |
| 2 | 2709 | 403 |
| 0 | 4050 | 389 |
| 1× | iter-limit |
| 1× | node-limit |
| 1× | iter-limit |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))) |
(*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x))) |
eps |
(-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x)) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) |
(fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))))) |
#s(literal -1/2 binary64) |
(cos.f64 x) |
x |
(*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))) |
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) |
(*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) |
#s(literal 1/24 binary64) |
(*.f64 eps (cos.f64 x)) |
(*.f64 #s(literal -1/6 binary64) (sin.f64 x)) |
#s(literal -1/6 binary64) |
(sin.f64 x) |
#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) |
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) |
(fma.f64 (PI.f64) #s(literal 1/2 binary64) x) |
(PI.f64) |
#s(literal 1/2 binary64) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) |
(*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) |
(sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) |
(*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)) |
(+.f64 (+.f64 eps x) x) |
(+.f64 eps x) |
(sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) |
(*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)) |
(-.f64 (+.f64 eps x) x) |
#s(literal -2 binary64) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))))) |
#s(literal 2 binary64) |
(*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)))) |
(sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) |
(/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)) |
(+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) |
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) |
(+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64)) |
(cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) |
(/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64)) |
(-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps) |
(*.f64 eps (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x))) |
(neg.f64 (*.f64 (-.f64 (sin.f64 x) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)) eps)) |
(neg.f64 (*.f64 eps (-.f64 (sin.f64 x) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)))) |
(fma.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps)) |
(fma.f64 eps (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (*.f64 eps (neg.f64 (sin.f64 x)))) |
(+.f64 (*.f64 eps (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)) (*.f64 eps (neg.f64 (sin.f64 x)))) |
(+.f64 (*.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) eps) (*.f64 (neg.f64 (sin.f64 x)) eps)) |
eps |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps))) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps))) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)) |
(/.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)) (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x)))) (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (neg.f64 (sin.f64 x)))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) #s(literal 3 binary64)) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x))) (*.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (neg.f64 (sin.f64 x)))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps)) (*.f64 (sin.f64 x) (sin.f64 x))) (+.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x))))) |
(neg.f64 (-.f64 (sin.f64 x) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps))) |
(fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (neg.f64 (sin.f64 x)))) |
(fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (cos.f64 x) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (sin.f64 x))) |
(fma.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (neg.f64 (sin.f64 x)))) |
(fma.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (sin.f64 x))) |
(fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps (neg.f64 (sin.f64 x))) |
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (neg.f64 (sin.f64 x)))) |
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (sin.f64 x))) |
(fma.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) eps) (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (neg.f64 (sin.f64 x)))) |
(fma.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) eps) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (sin.f64 x))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps) (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (neg.f64 (sin.f64 x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps) (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 eps eps)) (sin.f64 x))) |
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#s(literal -1/2 binary64) |
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(cos.f64 (neg.f64 (neg.f64 x))) |
(cos.f64 (neg.f64 (fabs.f64 x))) |
(cos.f64 (fabs.f64 (fabs.f64 x))) |
(cos.f64 (neg.f64 x)) |
(cos.f64 (fabs.f64 x)) |
(cos.f64 x) |
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x |
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(*.f64 eps (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))) |
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(fma.f64 (neg.f64 (sin.f64 x)) #s(literal -1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) |
(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) |
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(*.f64 (*.f64 #s(literal 1/24 binary64) (cos.f64 x)) eps) |
(*.f64 (*.f64 #s(literal 1/24 binary64) eps) (cos.f64 x)) |
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(*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps)) |
(*.f64 (cos.f64 x) (*.f64 #s(literal 1/24 binary64) eps)) |
(*.f64 eps (*.f64 (cos.f64 x) #s(literal 1/24 binary64))) |
#s(literal 1/24 binary64) |
(*.f64 (cos.f64 x) eps) |
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(*.f64 (sin.f64 x) #s(literal -1/6 binary64)) |
(*.f64 #s(literal -1/6 binary64) (sin.f64 x)) |
#s(literal -1/6 binary64) |
(sin.f64 x) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))) (cos.f64 eps)) |
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(neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 eps))) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(+.f64 #s(literal -1 binary64) (cos.f64 eps)) |
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(sin.f64 (+.f64 (neg.f64 eps) (*.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(sin.f64 (+.f64 (fabs.f64 eps) (*.f64 #s(literal 1/2 binary64) (PI.f64)))) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps)) |
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(cos.f64 (neg.f64 (neg.f64 eps))) |
(cos.f64 (neg.f64 (fabs.f64 eps))) |
(cos.f64 (fabs.f64 (fabs.f64 eps))) |
(cos.f64 (neg.f64 eps)) |
(cos.f64 (fabs.f64 eps)) |
(cos.f64 eps) |
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#s(literal 1 binary64) |
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(-.f64 eps #s(literal 0 binary64)) |
(-.f64 x (-.f64 (neg.f64 eps) (neg.f64 x))) |
(-.f64 x (+.f64 (neg.f64 eps) x)) |
(+.f64 #s(literal 0 binary64) eps) |
(+.f64 (neg.f64 x) (+.f64 eps x)) |
(+.f64 (+.f64 eps x) (neg.f64 x)) |
(+.f64 eps #s(literal 0 binary64)) |
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(+.f64 x (-.f64 eps x)) |
#s(literal -2 binary64) |
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#s(literal 2 binary64) |
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(-.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 eps x)) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) |
(-.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 eps x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) (+.f64 (PI.f64) x)) |
(-.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 eps x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (PI.f64)) |
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (-.f64 (neg.f64 eps) x) (-.f64 (neg.f64 (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))) |
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (+.f64 (-.f64 (neg.f64 eps) x) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) (PI.f64)))) |
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (neg.f64 (-.f64 (-.f64 (+.f64 eps x) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))) |
(-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 eps x)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) (PI.f64))) |
(+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps) (+.f64 x (-.f64 (neg.f64 (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))) |
(+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) eps) (-.f64 x (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) (PI.f64)))) |
(+.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 eps x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (neg.f64 (PI.f64))) |
(+.f64 (-.f64 (-.f64 (+.f64 eps x) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (*.f64 #s(literal 1/2 binary64) (PI.f64))) |
(+.f64 (-.f64 (neg.f64 (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 eps x))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (-.f64 (-.f64 (+.f64 eps x) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) |
(+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (+.f64 eps x)) (-.f64 (neg.f64 (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x))) |
(+.f64 (+.f64 eps x) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (-.f64 (neg.f64 (PI.f64)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) x)))) |
(+.f64 (+.f64 eps x) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (+.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) x) (PI.f64)))) |
Compiled 37 463 to 5 705 computations (84.8% saved)
22 alts after pruning (20 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 913 | 17 | 930 |
| Fresh | 7 | 3 | 10 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 1 | 1 |
| Total | 924 | 22 | 946 |
| Status | Accuracy | Program |
|---|---|---|
| 50.6% | (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) | |
| 50.5% | (-.f64 (sin.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 #s(literal 1/2 binary64) (PI.f64)))) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) | |
| ✓ | 50.5% | (-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) |
| ✓ | 50.5% | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 49.1% | (-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) | |
| 50.6% | (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x))) | |
| 36.5% | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 #s(literal 0 binary64) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 eps #s(literal 0 binary64))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) | |
| 99.3% | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) #s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) #s(literal -2 binary64)) | |
| ▶ | 99.6% | (*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) #s(literal -2 binary64)) |
| 77.6% | (*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x)))) #s(literal -2 binary64)) | |
| ▶ | 5.7% | (*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))))) |
| 49.0% | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64))) | |
| 99.4% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps)) | |
| 41.6% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x))))))) | |
| 99.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps #s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))) | |
| 98.5% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (sin.f64 x)))) | |
| 99.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))) | |
| 97.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))))) | |
| 50.3% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) | |
| ▶ | 77.6% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))))) |
| ▶ | 50.3% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) |
| ▶ | 97.9% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) |
Compiled 1 437 to 893 computations (37.9% saved)
| Inputs |
|---|
1/2 |
-2 |
-1/2 |
2 |
-1 |
1/6 |
1 |
1/24 |
(PI) |
(* 2 (PI)) |
| Outputs |
|---|
#s(literal 1/2 binary64) |
#s(literal -2 binary64) |
#s(literal -1/2 binary64) |
#s(literal 2 binary64) |
#s(literal -1 binary64) |
#s(literal 6004799503160661/36028797018963968 binary64) |
#s(literal 1 binary64) |
#s(literal 6004799503160661/144115188075855872 binary64) |
#s(literal 884279719003555/281474976710656 binary64) |
#s(literal 884279719003555/140737488355328 binary64) |
| 0.0ms | 1× | 0 | valid |
Compiled 14 to 12 computations (14.3% saved)
adjust: 0.0ms (0.0% of total)Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 950 | 7050 |
| 1× | iter-limit |
| Inputs |
|---|
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) #s(literal -2 binary64)) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
eps |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))) |
(*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))) |
(-.f64 eps (*.f64 #s(literal -2 binary64) x)) |
(*.f64 #s(literal -2 binary64) x) |
#s(literal -2 binary64) |
x |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) |
#s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))) |
(*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))) |
#s(literal -1/2 binary64) |
(pow.f64 eps #s(literal 2 binary64)) |
#s(literal 2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))))) |
(*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x)))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))) |
(*.f64 #s(literal -1 binary64) (sin.f64 x)) |
#s(literal -1 binary64) |
(sin.f64 x) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
(fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
(*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) |
(-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) |
#s(literal 1/6 binary64) |
#s(literal 1 binary64) |
(*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) |
#s(literal 1/24 binary64) |
(*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))))) |
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) |
(*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))) |
(-.f64 eps (PI.f64)) |
(PI.f64) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))) |
(*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))) |
(-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)) |
(+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
| Outputs |
|---|
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (fma.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 (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)))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (*.f64 (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)))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))) (*.f64 (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)))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))))) |
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 #s(literal 1/2 binary64) eps)) |
#s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
#s(approx (- eps (* -2 x)) eps) |
#s(approx (- eps (* -2 x)) (+.f64 eps (*.f64 #s(literal 2 binary64) x))) |
#s(approx (* -2 x) (*.f64 #s(literal -2 binary64) x)) |
#s(approx x x) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 #s(literal -1 binary64) (*.f64 x (sin.f64 eps)))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps)))) (sin.f64 eps)))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps)))))) (sin.f64 eps)))) #s(literal 1 binary64))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 x (fma.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 x (fma.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 x (fma.f64 eps (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/36 binary64) (pow.f64 eps #s(literal 2 binary64))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) #s(literal 1 binary64))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 eps (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/36 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) #s(literal 1 binary64))))) |
#s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x)) |
#s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))) |
#s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/120 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1 binary64)))) |
#s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/120 binary64))))) #s(literal 1 binary64)))) |
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/6 binary64)))))) |
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/6 binary64)))))) |
#s(approx (* x (- (* 1/6 (pow eps 2)) 1)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 x (fma.f64 #s(literal -1 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 x (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))) (*.f64 x (fma.f64 #s(literal -1 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/3 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))))))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) |
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))))))) |
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))))))))))) |
#s(approx (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))) (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))))) |
#s(approx (- (+ eps (* 2 (PI))) (* -2 x)) (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64)))) |
#s(approx (- (+ eps (* 2 (PI))) (* -2 x)) (+.f64 eps (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x))))) |
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) |
#s(approx (- eps (* -2 x)) (*.f64 #s(literal 2 binary64) x)) |
#s(approx (- eps (* -2 x)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x))) |
#s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))) |
#s(approx (sin x) (sin.f64 x)) |
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))) |
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 x (fma.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))) x)))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))) |
#s(approx (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) x))))) |
#s(approx (- (+ eps (* 2 (PI))) (* -2 x)) (*.f64 x (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 (PI.f64) x) (/.f64 eps x))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))))) |
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 1 binary64))))) |
#s(approx (- eps (* -2 x)) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 eps x)) #s(literal 2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 x))) |
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal -1 binary64) (*.f64 x (fma.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))) x)))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))))) |
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))) |
#s(approx (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) x)) #s(literal 1 binary64))))) |
#s(approx (- (+ eps (* 2 (PI))) (* -2 x)) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) x)) #s(literal 2 binary64))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -2 binary64) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x)))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -2 binary64) (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x))) (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)))))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x)))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x))))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (fma.f64 #s(literal -1/48 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x))))))))))) |
#s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) |
#s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/3840 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/48 binary64)))))) |
#s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/3840 binary64) (*.f64 #s(literal -1/645120 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/48 binary64)))))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (*.f64 eps (sin.f64 x)) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x))))))))) |
#s(approx (- eps (* -2 x)) (-.f64 eps (*.f64 #s(literal -2 binary64) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x)))) |
#s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))) |
#s(approx (- (cos eps) 1) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/2 binary64)))) |
#s(approx (- (cos eps) 1) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/40320 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/720 binary64))))) #s(literal 1/2 binary64)))) |
#s(approx (pow eps 2) (pow.f64 eps #s(literal 2 binary64))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x)))))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x))) |
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal -1 binary64) (*.f64 eps x))) |
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps)))) |
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64)))))) |
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal 1/6 binary64) x))) #s(literal 1/2 binary64)))))) |
#s(approx (* x (- (* 1/6 (pow eps 2)) 1)) (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) x)))) |
#s(approx (- (* 1/6 (pow eps 2)) 1) #s(literal -1 binary64)) |
#s(approx (- (* 1/6 (pow eps 2)) 1) (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) |
#s(approx (* 1/6 (pow eps 2)) (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)))) |
#s(approx (- (* 1/24 (pow eps 2)) 1/2) #s(literal -1/2 binary64)) |
#s(approx (- (* 1/24 (pow eps 2)) 1/2) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
#s(approx (* 1/24 (pow eps 2)) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 eps (fma.f64 #s(literal 2 binary64) (*.f64 eps (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))) (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (fma.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 eps (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) (*.f64 eps (fma.f64 #s(literal 2 binary64) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal -1/48 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal 1/48 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/16 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))))))) (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 eps (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 eps (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)))) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal -1/48 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (fma.f64 #s(literal 1/48 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))) (*.f64 #s(literal 1/16 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))))))))))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64)))))))) |
#s(approx (* (cos (* 1/2 (- eps (PI)))) (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)))))) |
#s(approx (* (cos (* 1/2 (- eps (PI)))) (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))))) |
#s(approx (* (cos (* 1/2 (- eps (PI)))) (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))) (*.f64 eps (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))) (*.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))))) |
#s(approx (* (cos (* 1/2 (- eps (PI)))) (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))))) (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))) (*.f64 eps (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)))) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))) (fma.f64 #s(literal -1/48 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))) (fma.f64 #s(literal 1/48 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))) (*.f64 #s(literal 1/16 binary64) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))))))))))))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))))) |
#s(approx (cos (* 1/2 (- eps (PI)))) (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)))) |
#s(approx (cos (* 1/2 (- eps (PI)))) (+.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))) |
#s(approx (cos (* 1/2 (- eps (PI)))) (+.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (*.f64 eps (-.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))) (*.f64 #s(literal 1/2 binary64) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)))))))) |
#s(approx (cos (* 1/2 (- eps (PI)))) (+.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (cos.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))) (*.f64 #s(literal 1/48 binary64) (*.f64 eps (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64))))))) (*.f64 #s(literal 1/2 binary64) (sin.f64 (*.f64 #s(literal -1/2 binary64) (PI.f64)))))))) |
#s(approx (* 1/2 (- eps (PI))) (*.f64 #s(literal -1/2 binary64) (PI.f64))) |
#s(approx (* 1/2 (- eps (PI))) (fma.f64 #s(literal -1/2 binary64) (PI.f64) (*.f64 #s(literal 1/2 binary64) eps))) |
#s(approx (- eps (PI)) (*.f64 #s(literal -1 binary64) (PI.f64))) |
#s(approx (- eps (PI)) (-.f64 eps (PI.f64))) |
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))) |
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)))))))) |
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)))) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (*.f64 eps (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))))))) |
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)))) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)))) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)))) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)))))))))))) |
#s(approx (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)))) |
#s(approx (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))))) |
#s(approx (- (+ eps (* 2 (PI))) (* -2 x)) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x))) |
#s(approx (- (+ eps (* 2 (PI))) (* -2 x)) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))) |
#s(approx (+ eps (* 2 (PI))) (*.f64 #s(literal 2 binary64) (PI.f64))) |
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
#s(approx (- eps (* -2 x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 x eps))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (cos.f64 x)))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps)))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps))))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (cos.f64 x)))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))) (*.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps))))) |
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))) |
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps))))) |
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps))) (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))) |
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (+.f64 #s(literal 1/24 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 x (pow.f64 eps #s(literal 3 binary64))) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))))) |
#s(approx (* x (- (* 1/6 (pow eps 2)) 1)) (*.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) x))) |
#s(approx (* x (- (* 1/6 (pow eps 2)) 1)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 x (pow.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 1/6 binary64) x)))) |
#s(approx (- (* 1/6 (pow eps 2)) 1) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 2 binary64)))))) |
#s(approx (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 2 binary64))))))) |
#s(approx (- (* 1/24 (pow eps 2)) 1/2) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 2 binary64))))))) |
#s(approx (cos (* 1/2 (- eps (PI)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))))) |
#s(approx (* 1/2 (- eps (PI))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (PI.f64) eps))))) |
#s(approx (- eps (PI)) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (PI.f64) eps))))) |
#s(approx (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)) eps))))) |
#s(approx (- (+ eps (* 2 (PI))) (* -2 x)) (*.f64 eps (-.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) eps))) (*.f64 #s(literal -2 binary64) (/.f64 x eps))))) |
#s(approx (+ eps (* 2 (PI))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) eps))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1 binary64) eps))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1 binary64) eps)))))) |
#s(approx (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal -2 binary64) x (*.f64 #s(literal -1 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal -2 binary64) x (*.f64 #s(literal -1 binary64) eps))))) |
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64))))) |
#s(approx (- eps (* -2 x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 x eps)) #s(literal 1 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))) (cos.f64 x))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 x) eps))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x)))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x)))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x)))))) |
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))) eps))))) |
#s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)) eps) (*.f64 #s(literal -1/6 binary64) x)) eps))))) |
#s(approx (* 2 (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)))) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) eps))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) eps)))))) |
#s(approx (* (cos (* 1/2 (- eps (PI)))) (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 #s(literal -2 binary64) x (*.f64 #s(literal -1 binary64) eps))))))) |
#s(approx (cos (* 1/2 (- eps (PI)))) (cos.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (PI.f64) (*.f64 #s(literal -1 binary64) eps))))) |
#s(approx (* 1/2 (- eps (PI))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (PI.f64) eps)) #s(literal 1/2 binary64))))) |
#s(approx (- eps (PI)) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (/.f64 (PI.f64) eps) #s(literal 1 binary64))))) |
#s(approx (sin (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (fma.f64 #s(literal -2 binary64) x (*.f64 #s(literal -1 binary64) eps)))))) |
#s(approx (* 1/2 (- (+ eps (* 2 (PI))) (* -2 x))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)) eps)) #s(literal 1/2 binary64))))) |
#s(approx (- (+ eps (* 2 (PI))) (* -2 x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (*.f64 #s(literal -2 binary64) x)) eps)) #s(literal 1 binary64))))) |
#s(approx (+ eps (* 2 (PI))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) eps)) #s(literal 1 binary64))))) |
6 calls:
| Time | Variable | Point |
|---|---|---|
| 11.0ms | eps | 0 |
| 5.0ms | eps | inf |
| 5.0ms | x | -inf |
| 5.0ms | x | inf |
| 4.0ms | eps | -inf |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 87 | 615 |
| 0 | 120 | 611 |
| 1 | 643 | 607 |
| 2 | 3358 | 607 |
| 0 | 4021 | 556 |
| 1× | iter-limit |
| 1× | node-limit |
| 1× | iter-limit |
| Inputs |
|---|
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) #s(literal -2 binary64)) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
eps |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))) |
(*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))) |
(-.f64 eps (*.f64 #s(literal -2 binary64) x)) |
(*.f64 #s(literal -2 binary64) x) |
#s(literal -2 binary64) |
x |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) |
#s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))) |
(*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))) |
#s(literal -1/2 binary64) |
(pow.f64 eps #s(literal 2 binary64)) |
#s(literal 2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))))) |
(*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x)))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))) |
(*.f64 #s(literal -1 binary64) (sin.f64 x)) |
#s(literal -1 binary64) |
(sin.f64 x) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
(fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
(*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) |
(-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) |
#s(literal 1/6 binary64) |
#s(literal 1 binary64) |
(*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) |
#s(literal 1/24 binary64) |
(*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))))) |
#s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))))) |
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) |
(*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))) |
(-.f64 eps (PI.f64)) |
(PI.f64) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)))) |
(*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))) |
(-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x)) |
(+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
| Outputs |
|---|
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 #s(literal -2 binary64) #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(neg.f64 (*.f64 #s(literal 2 binary64) #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))) |
(neg.f64 (*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (-.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 #s(literal 2 binary64) x eps)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 #s(literal 2 binary64) x eps))))) #s(literal 1/2 binary64)) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
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(*.f64 eps #s(literal 1/2 binary64)) |
(/.f64 (*.f64 eps #s(literal 1 binary64)) #s(literal 2 binary64)) |
(/.f64 (*.f64 #s(literal 1 binary64) eps) #s(literal 2 binary64)) |
(/.f64 eps #s(literal 2 binary64)) |
#s(literal 1/2 binary64) |
eps |
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(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) |
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)) |
(/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 2 binary64)) |
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(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) |
(neg.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal -2 binary64) x) eps))) |
(neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
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(fma.f64 #s(literal 1/2 binary64) (+.f64 x eps) (*.f64 #s(literal 1/2 binary64) x)) |
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(fma.f64 (+.f64 x eps) #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (+.f64 x eps) #s(literal 1/2 binary64))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 x x))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) |
(fma.f64 eps #s(literal 1/2 binary64) (/.f64 (+.f64 x x) #s(literal 2 binary64))) |
(-.f64 (/.f64 (+.f64 x eps) #s(literal 2 binary64)) (/.f64 (neg.f64 x) #s(literal 2 binary64))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) (+.f64 x eps))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x eps)) (*.f64 #s(literal 1/2 binary64) x)) |
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (+.f64 x eps) #s(literal 1/2 binary64))) |
(+.f64 (*.f64 (+.f64 x eps) #s(literal 1/2 binary64)) (*.f64 x #s(literal 1/2 binary64))) |
(+.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 (+.f64 x eps) #s(literal 2 binary64))) |
(+.f64 (/.f64 (+.f64 x eps) #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64))) |
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(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) |
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(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x x) eps)) eps) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x eps) x)) x) |
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(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 x eps)) eps x) |
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps x)) x x) |
(fma.f64 (neg.f64 x) #s(literal -2 binary64) eps) |
(fma.f64 #s(literal 2 binary64) x eps) |
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(fma.f64 x #s(literal 2 binary64) eps) |
(-.f64 (+.f64 x x) (neg.f64 eps)) |
(-.f64 (+.f64 x eps) (neg.f64 x)) |
(-.f64 x (-.f64 (neg.f64 x) eps)) |
(-.f64 eps (-.f64 (neg.f64 x) x)) |
(-.f64 eps (+.f64 (neg.f64 x) (neg.f64 x))) |
(-.f64 eps (*.f64 #s(literal -2 binary64) x)) |
(+.f64 (+.f64 x x) eps) |
(+.f64 (+.f64 x eps) (neg.f64 (neg.f64 x))) |
(+.f64 (+.f64 x eps) x) |
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(*.f64 #s(literal -2 binary64) x) |
(*.f64 x #s(literal -2 binary64)) |
(neg.f64 (+.f64 x x)) |
#s(literal -2 binary64) |
x |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
#s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps) |
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) |
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(neg.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 eps eps))) |
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#s(literal -1/2 binary64) |
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(*.f64 (pow.f64 eps #s(literal 1 binary64)) eps) |
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(*.f64 (neg.f64 eps) (neg.f64 eps)) |
(*.f64 (fabs.f64 eps) (fabs.f64 eps)) |
(*.f64 eps eps) |
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#s(literal 2 binary64) |
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#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) |
(*.f64 #s(literal -1 binary64) (sin.f64 x)) |
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(neg.f64 (sin.f64 x)) |
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(sin.f64 (neg.f64 x)) |
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#s(literal -1 binary64) |
(sin.f64 x) |
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(/.f64 (+.f64 (sin.f64 (-.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 1/2 binary64)) (*.f64 (-.f64 eps (PI.f64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 1/2 binary64) (*.f64 (-.f64 eps (PI.f64)) #s(literal 1/2 binary64))))) #s(literal 2 binary64)) |
(sin.f64 (fma.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) |
(sin.f64 (fma.f64 (fabs.f64 (-.f64 eps (PI.f64))) #s(literal 1/2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) |
(sin.f64 (fma.f64 (-.f64 eps (PI.f64)) #s(literal 1/2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) |
(fma.f64 (sin.f64 (*.f64 (-.f64 eps (PI.f64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 (-.f64 eps (PI.f64)) #s(literal -1/2 binary64))) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))) |
(cos.f64 (neg.f64 (fabs.f64 (*.f64 (-.f64 eps (PI.f64)) #s(literal -1/2 binary64))))) |
(cos.f64 (fabs.f64 (fabs.f64 (*.f64 (-.f64 eps (PI.f64)) #s(literal -1/2 binary64))))) |
(cos.f64 (*.f64 (-.f64 eps (PI.f64)) #s(literal -1/2 binary64))) |
(cos.f64 (fabs.f64 (*.f64 (-.f64 eps (PI.f64)) #s(literal -1/2 binary64)))) |
(cos.f64 (*.f64 (-.f64 eps (PI.f64)) #s(literal 1/2 binary64))) |
(+.f64 (*.f64 (sin.f64 (*.f64 (-.f64 eps (PI.f64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (*.f64 (cos.f64 (*.f64 (-.f64 eps (PI.f64)) #s(literal -1/2 binary64))) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))) |
(*.f64 (-.f64 eps (PI.f64)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64))) |
(/.f64 (*.f64 (-.f64 eps (PI.f64)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 eps (PI.f64))) #s(literal 2 binary64)) |
(/.f64 (-.f64 eps (PI.f64)) #s(literal 2 binary64)) |
(neg.f64 (*.f64 (-.f64 eps (PI.f64)) #s(literal -1/2 binary64))) |
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (neg.f64 (PI.f64)))) |
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (neg.f64 (PI.f64)))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) (neg.f64 (PI.f64)))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 (neg.f64 (PI.f64)) #s(literal 1/2 binary64))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (PI.f64)) eps)) eps) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (PI.f64) eps)) eps) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (neg.f64 (PI.f64)) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 eps (neg.f64 (PI.f64)))))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (PI.f64) (PI.f64))) (+.f64 eps (PI.f64))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (PI.f64) (PI.f64))) (-.f64 eps (neg.f64 (PI.f64)))) |
(/.f64 (-.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64))) (fma.f64 eps eps (fma.f64 (PI.f64) (PI.f64) (*.f64 eps (PI.f64))))) |
(neg.f64 (-.f64 (PI.f64) eps)) |
(fma.f64 (neg.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) (cbrt.f64 (PI.f64)) eps) |
(fma.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (neg.f64 (cbrt.f64 (PI.f64))) eps) |
(-.f64 eps (neg.f64 (neg.f64 (PI.f64)))) |
(-.f64 eps (PI.f64)) |
(+.f64 (neg.f64 (PI.f64)) eps) |
(+.f64 eps (neg.f64 (PI.f64))) |
(PI.f64) |
(sin.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) |
(/.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 1 binary64)) #s(literal 2 binary64)) |
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(literal 2 binary64)) |
(/.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #s(literal 2 binary64)) |
(neg.f64 (*.f64 (-.f64 (*.f64 #s(literal -2 binary64) x) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) #s(literal 1/2 binary64))) |
(neg.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal -2 binary64) x) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)))) |
(fma.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 1/2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (*.f64 #s(literal 1/2 binary64) (+.f64 x x))) |
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)))) |
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) #s(literal 1/2 binary64))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) #s(literal 1/2 binary64))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (+.f64 x x))) |
(+.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (*.f64 (+.f64 x x) #s(literal 1/2 binary64))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) #s(literal 1/2 binary64))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x x) (fma.f64 (PI.f64) #s(literal 2 binary64) eps))) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) eps)) eps) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) x) (fma.f64 (PI.f64) #s(literal 2 binary64) eps))) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) |
(/.f64 (-.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) (*.f64 (+.f64 x x) (+.f64 x x))) (-.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (+.f64 x x))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)))) (-.f64 eps (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)))) |
(/.f64 (+.f64 (pow.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) #s(literal 3 binary64)) (pow.f64 (+.f64 x x) #s(literal 3 binary64))) (fma.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (-.f64 (*.f64 (+.f64 x x) (+.f64 x x)) (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (+.f64 x x))))) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x))) (*.f64 eps (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)))))) |
(/.f64 (-.f64 (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) (*.f64 (*.f64 #s(literal -2 binary64) x) (*.f64 #s(literal -2 binary64) x))) (+.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (*.f64 #s(literal -2 binary64) x))) |
(/.f64 (-.f64 (pow.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 3 binary64))) (fma.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (fma.f64 (*.f64 #s(literal -2 binary64) x) (*.f64 #s(literal -2 binary64) x) (*.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (*.f64 #s(literal -2 binary64) x))))) |
(neg.f64 (-.f64 (*.f64 #s(literal -2 binary64) x) (fma.f64 (PI.f64) #s(literal 2 binary64) eps))) |
(fma.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) (cbrt.f64 (PI.f64)) (fma.f64 #s(literal 2 binary64) x eps)) |
(fma.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) x eps)) |
(fma.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (+.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (fma.f64 #s(literal 2 binary64) x eps)) |
(fma.f64 (cbrt.f64 (PI.f64)) (+.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) (fma.f64 #s(literal 2 binary64) x eps)) |
(fma.f64 (neg.f64 x) #s(literal -2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) |
(fma.f64 (PI.f64) #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) |
(fma.f64 #s(literal 2 binary64) (PI.f64) (fma.f64 #s(literal 2 binary64) x eps)) |
(fma.f64 #s(literal 2 binary64) x (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) |
(fma.f64 #s(literal -2 binary64) (neg.f64 x) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) |
(fma.f64 x #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) |
(-.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (*.f64 #s(literal -2 binary64) x)) |
(-.f64 eps (-.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (+.f64 x x))) |
(-.f64 eps (fma.f64 (PI.f64) #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) x))) |
(-.f64 eps (neg.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)))) |
(+.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x)) eps) |
(+.f64 (+.f64 x x) (fma.f64 (PI.f64) #s(literal 2 binary64) eps)) |
(+.f64 (fma.f64 (PI.f64) #s(literal 2 binary64) eps) (+.f64 x x)) |
(+.f64 (+.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal 2 binary64) x eps)) |
(+.f64 eps (fma.f64 (PI.f64) #s(literal 2 binary64) (+.f64 x x))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps (+.f64 (PI.f64) (PI.f64)))) (+.f64 (PI.f64) (PI.f64))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) eps)) eps) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (PI.f64) (PI.f64)) eps)) eps) |
(/.f64 (-.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (PI.f64))) (*.f64 eps eps)) (-.f64 (+.f64 (PI.f64) (PI.f64)) eps)) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 (PI.f64) #s(literal -2 binary64)))) (+.f64 eps (*.f64 (PI.f64) #s(literal -2 binary64)))) |
(/.f64 (+.f64 (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (+.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (PI.f64)) (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (PI.f64) (PI.f64)) eps)))) |
(/.f64 (-.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) #s(literal 3 binary64))) (fma.f64 eps eps (fma.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 (PI.f64) #s(literal -2 binary64)) (*.f64 eps (*.f64 (PI.f64) #s(literal -2 binary64)))))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (PI.f64)))) (-.f64 eps (+.f64 (PI.f64) (PI.f64)))) |
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (+.f64 (PI.f64) (PI.f64)) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 (+.f64 (PI.f64) (PI.f64)) (+.f64 (PI.f64) (PI.f64))) (*.f64 eps (+.f64 (PI.f64) (PI.f64)))))) |
(neg.f64 (-.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) eps)) |
(fma.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) (cbrt.f64 (PI.f64)) eps) |
(fma.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) eps) |
(fma.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (+.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) eps) |
(fma.f64 (cbrt.f64 (PI.f64)) (+.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) eps) |
(fma.f64 (PI.f64) #s(literal 2 binary64) eps) |
(fma.f64 #s(literal 2 binary64) (PI.f64) eps) |
(-.f64 (+.f64 (PI.f64) (PI.f64)) (neg.f64 eps)) |
(-.f64 eps (*.f64 (PI.f64) #s(literal -2 binary64))) |
(+.f64 (+.f64 eps (PI.f64)) (PI.f64)) |
(+.f64 (+.f64 (PI.f64) (PI.f64)) eps) |
(+.f64 (PI.f64) (+.f64 (PI.f64) eps)) |
(+.f64 eps (+.f64 (PI.f64) (PI.f64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cbrt.f64 (*.f64 (PI.f64) (PI.f64)))) (cbrt.f64 (PI.f64))) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (PI.f64))) (PI.f64)) |
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) |
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (+.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64)))) |
(*.f64 (cbrt.f64 (PI.f64)) (+.f64 (cbrt.f64 (*.f64 (PI.f64) (PI.f64))) (cbrt.f64 (*.f64 (PI.f64) (PI.f64))))) |
(*.f64 (PI.f64) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (PI.f64)) |
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) (-.f64 (PI.f64) (PI.f64))) |
(/.f64 (+.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))) |
(neg.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) |
(fma.f64 (PI.f64) #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal 1 binary64))) |
(fma.f64 #s(literal 1 binary64) (PI.f64) (*.f64 #s(literal 1 binary64) (PI.f64))) |
(-.f64 (PI.f64) (neg.f64 (PI.f64))) |
(+.f64 (*.f64 (PI.f64) #s(literal 1 binary64)) (*.f64 (PI.f64) #s(literal 1 binary64))) |
(+.f64 (*.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 #s(literal 1 binary64) (PI.f64))) |
(+.f64 (PI.f64) (PI.f64)) |
(log.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 2 binary64))) |
(log.f64 (*.f64 (exp.f64 (PI.f64)) (exp.f64 (PI.f64)))) |
Compiled 33 014 to 3 557 computations (89.2% saved)
30 alts after pruning (28 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 543 | 19 | 562 |
| Fresh | 6 | 9 | 15 |
| Picked | 5 | 0 | 5 |
| Done | 0 | 2 | 2 |
| Total | 554 | 30 | 584 |
| Status | Accuracy | Program |
|---|---|---|
| 50.6% | (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) | |
| 50.5% | (-.f64 (sin.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 #s(literal 1/2 binary64) (PI.f64)))) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) | |
| ✓ | 50.5% | (-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) |
| ✓ | 50.5% | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 50.6% | (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x))) | |
| 99.3% | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) #s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) #s(literal -2 binary64)) | |
| 99.4% | (*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (+.f64 x eps))) (+.f64 x eps)))))) #s(literal -2 binary64)) | |
| ▶ | 99.6% | (*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64)) |
| 99.4% | (*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x))))))))))) #s(literal -2 binary64)) | |
| 99.3% | (*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) #s(literal -2 binary64)) | |
| 5.7% | (*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -2 binary64) x))))))) | |
| ▶ | 49.0% | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64))) |
| 99.4% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps)) | |
| 77.6% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) eps)) | |
| 99.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps #s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))) | |
| 98.5% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (sin.f64 x)))) | |
| ▶ | 99.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))) |
| ▶ | 9.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x))))) |
| 9.3% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))) | |
| 76.9% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))))))) | |
| 77.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x))))) | |
| ▶ | 50.3% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
| 50.3% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))))) | |
| 97.9% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)))) | |
| 48.7% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps))))))) | |
| 24.0% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)) eps) (*.f64 #s(literal -1/6 binary64) x)) eps))))))) | |
| 97.7% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64)))))))) | |
| 97.7% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps)))))) | |
| 77.0% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))))) | |
| 49.1% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))))) |
Compiled 2 407 to 1 579 computations (34.4% saved)
| Inputs |
|---|
1/2 |
-2 |
-1/2 |
1 |
2 |
(PI) |
| Outputs |
|---|
#s(literal 1/2 binary64) |
#s(literal -2 binary64) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
#s(literal 2 binary64) |
#s(literal 884279719003555/281474976710656 binary64) |
| 0.0ms | 1× | 0 | valid |
Compiled 8 to 8 computations (0.0% saved)
adjust: 0.0ms (0.0% of total)Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 614 | 3872 |
| 1× | iter-limit |
| Inputs |
|---|
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64)) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
eps |
(sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps)) |
x |
#s(literal -2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
#s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) |
(*.f64 eps eps) |
#s(literal -1/2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64))) |
(-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64)) |
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))) |
#s(literal 1 binary64) |
(*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))) |
(pow.f64 eps #s(literal 2 binary64)) |
#s(literal 2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x))))) |
(*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x)))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x))) |
(sin.f64 (+.f64 (PI.f64) x)) |
(+.f64 (PI.f64) x) |
(PI.f64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))) |
(*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x))) |
(-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)) |
(*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
(*.f64 #s(literal -1/2 binary64) (cos.f64 x)) |
(cos.f64 x) |
(sin.f64 x) |
| Outputs |
|---|
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (fma.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (fma.f64 #s(literal 1/3 binary64) (*.f64 x (*.f64 (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)))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (*.f64 (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)))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))) (*.f64 (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)))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (+.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))))) |
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 #s(literal 1/2 binary64) eps)) |
#s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
#s(approx x x) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 #s(literal -1 binary64) (*.f64 x (sin.f64 eps)))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps)))) (sin.f64 eps)))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (+.f64 (cos.f64 eps) (*.f64 x (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x (sin.f64 eps)))))) (sin.f64 eps)))) #s(literal 1 binary64))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 x (fma.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 x (fma.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64)) (*.f64 x (fma.f64 eps (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/36 binary64) (pow.f64 eps #s(literal 2 binary64))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) #s(literal 1 binary64))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 eps (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/36 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) #s(literal 1 binary64))))) |
#s(approx (sin (+ (PI) x)) (sin.f64 (PI.f64))) |
#s(approx (sin (+ (PI) x)) (+.f64 (sin.f64 (PI.f64)) (*.f64 x (cos.f64 (PI.f64))))) |
#s(approx (sin (+ (PI) x)) (+.f64 (sin.f64 (PI.f64)) (*.f64 x (+.f64 (cos.f64 (PI.f64)) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (PI.f64)))))))) |
#s(approx (sin (+ (PI) x)) (+.f64 (sin.f64 (PI.f64)) (*.f64 x (+.f64 (cos.f64 (PI.f64)) (*.f64 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (PI.f64)) (*.f64 #s(literal -1/6 binary64) (*.f64 x (cos.f64 (PI.f64)))))))))) |
#s(approx (+ (PI) x) (PI.f64)) |
#s(approx (+ (PI) x) (+.f64 x (PI.f64))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (fma.f64 #s(literal 1/6 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal -1/36 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) x) (*.f64 eps (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))))))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 eps x))) #s(literal 1/2 binary64))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))))) #s(literal 1/2 binary64))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (fma.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64)) (*.f64 x (fma.f64 #s(literal 1/6 binary64) eps (*.f64 x (+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))))) #s(literal 1/2 binary64))) |
#s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64))) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/1440 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/48 binary64))))) #s(literal 1/2 binary64))) |
#s(approx (cos x) #s(literal 1 binary64)) |
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 2 binary64))))) |
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (cos x) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/2 binary64))))) |
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (pow.f64 x #s(literal 2 binary64)))))) |
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/6 binary64)))))) |
#s(approx (sin x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1/120 binary64) (*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 2 binary64))))) #s(literal 1/6 binary64)))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x))))) |
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x))) |
#s(approx (sin (+ (PI) x)) (sin.f64 (+.f64 x (PI.f64)))) |
#s(approx (+ (PI) x) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) x)))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))))))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) |
#s(approx (* -1/2 (cos x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
#s(approx (cos x) (cos.f64 x)) |
#s(approx (sin x) (sin.f64 x)) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x))))) |
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) #s(literal 1 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 eps (*.f64 #s(literal -1 binary64) x))) (cos.f64 x))) |
#s(approx (sin (+ (PI) x)) (sin.f64 (-.f64 (PI.f64) (*.f64 #s(literal -1 binary64) x)))) |
#s(approx (+ (PI) x) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (PI.f64) x)) #s(literal 1 binary64))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -2 binary64) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x)))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -2 binary64) (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x))) (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)))))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x)))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (sin.f64 x))))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/16 binary64) (sin.f64 x) (fma.f64 #s(literal -1/48 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x))))))))))) |
#s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) |
#s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/3840 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/48 binary64)))))) |
#s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/3840 binary64) (*.f64 #s(literal -1/645120 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/48 binary64)))))) |
#s(approx eps eps) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (*.f64 eps (sin.f64 x)) (*.f64 #s(literal 1/2 binary64) (cos.f64 x)))))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x))))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x)))) |
#s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))) |
#s(approx (- (cos eps) 1) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/2 binary64)))) |
#s(approx (- (cos eps) 1) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/40320 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/720 binary64))))) #s(literal 1/2 binary64)))) |
#s(approx (* eps eps) (pow.f64 eps #s(literal 2 binary64))) |
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) |
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64))))) |
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1/2 binary64))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x)))))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x)))))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))))))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) |
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) |
#s(approx (cos eps) (cos.f64 eps)) |
#s(approx (+ 1 (* -1/2 (pow eps 2))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (cos.f64 x)))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps)))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps))))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (cos.f64 x)))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) (cos.f64 x)))) (*.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps))))) |
#s(approx (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps)))))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (cos.f64 x)))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (/.f64 (sin.f64 x) eps))))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps))))) |
#s(approx (* (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) -2) (*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1 binary64) eps))))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 2 binary64) x) (*.f64 #s(literal -1 binary64) eps)))))) |
#s(approx (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal -2 binary64) x (*.f64 #s(literal -1 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (sin (* 1/2 (- eps (* -2 x)))) (sin.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal -2 binary64) x (*.f64 #s(literal -1 binary64) eps))))) |
#s(approx (* 1/2 (- eps (* -2 x))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))) (cos.f64 x))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 x) eps))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) |
#s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 #s(literal -1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x)))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (cos.f64 x) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x)))))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) (*.f64 #s(literal -1/24 binary64) (cos.f64 x)))))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 x) eps))) eps) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))))) |
6 calls:
| Time | Variable | Point |
|---|---|---|
| 5.0ms | eps | 0 |
| 3.0ms | eps | inf |
| 3.0ms | eps | -inf |
| 2.0ms | x | -inf |
| 2.0ms | x | inf |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 68 | 490 |
| 0 | 91 | 490 |
| 1 | 467 | 482 |
| 2 | 2025 | 482 |
| 0 | 4062 | 447 |
| 1× | iter-limit |
| 1× | node-limit |
| 1× | iter-limit |
| Inputs |
|---|
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64)) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
eps |
(sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) |
#s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps))) |
(+.f64 x (*.f64 #s(literal 1/2 binary64) eps)) |
x |
#s(literal -2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
#s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) |
(*.f64 eps eps) |
#s(literal -1/2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64))) |
(-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64)) |
#s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64)))) |
#s(literal 1 binary64) |
(*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))) |
(pow.f64 eps #s(literal 2 binary64)) |
#s(literal 2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x))))) |
(*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x)))) |
#s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x))) |
(sin.f64 (+.f64 (PI.f64) x)) |
(+.f64 (PI.f64) x) |
(PI.f64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))) |
(*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x))) |
(-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)) |
(*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
(*.f64 #s(literal -1/2 binary64) (cos.f64 x)) |
(cos.f64 x) |
(sin.f64 x) |
| Outputs |
|---|
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) |
(*.f64 #s(literal -2 binary64) #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
#s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(*.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 1/2 binary64)) |
(*.f64 (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (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 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))))) #s(literal -2 binary64)) |
(/.f64 (-.f64 (cos.f64 (-.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 2 binary64)) |
(/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))))))) |
(neg.f64 (/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal -2 binary64))) |
(-.f64 (/.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) (/.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(neg.f64 (*.f64 #s(literal -1/2 binary64) eps)) |
#s(literal 1/2 binary64) |
eps |
(sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x))) |
#s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 #s(literal 1/2 binary64) eps x)) |
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x |
#s(literal -2 binary64) |
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#s(literal -1/2 binary64) |
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#s(literal 1 binary64) |
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#s(literal 2 binary64) |
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(PI.f64) |
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(*.f64 (-.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps) |
(*.f64 eps (-.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))) |
(neg.f64 (*.f64 (-.f64 (sin.f64 x) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)) eps)) |
(neg.f64 (*.f64 eps (-.f64 (sin.f64 x) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)))) |
(fma.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps (*.f64 (neg.f64 (sin.f64 x)) eps)) |
(fma.f64 eps (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 eps (neg.f64 (sin.f64 x)))) |
(+.f64 (*.f64 eps (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)) (*.f64 eps (neg.f64 (sin.f64 x)))) |
(+.f64 (*.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) eps) (*.f64 (neg.f64 (sin.f64 x)) eps)) |
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sin.f64 x)) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)) |
(/.f64 (-.f64 (*.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)) (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x)))) (-.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (neg.f64 (sin.f64 x)))) |
(/.f64 (+.f64 (pow.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x))) (*.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (neg.f64 (sin.f64 x)))))) |
(/.f64 (-.f64 (*.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)) (*.f64 (sin.f64 x) (sin.f64 x))) (+.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))) |
(/.f64 (-.f64 (pow.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.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 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))))) |
(neg.f64 (-.f64 (sin.f64 x) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps))) |
(fma.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) |
(fma.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))) |
(-.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (neg.f64 (neg.f64 (sin.f64 x)))) |
(-.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) |
(+.f64 (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (neg.f64 (sin.f64 x))) |
(+.f64 (neg.f64 (sin.f64 x)) (*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)) |
(*.f64 #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) |
(*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) |
#s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
(*.f64 #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 (cos.f64 x) #s(literal -1/2 binary64)) |
(neg.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64))) |
(neg.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) |
(sin.f64 (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) |
(sin.f64 (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) |
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) |
(fma.f64 (sin.f64 x) (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))) |
(cos.f64 (neg.f64 (neg.f64 x))) |
(cos.f64 (neg.f64 (fabs.f64 x))) |
(cos.f64 (fabs.f64 (fabs.f64 x))) |
(cos.f64 (neg.f64 x)) |
(cos.f64 (fabs.f64 x)) |
(cos.f64 x) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))) |
(sin.f64 x) |
Compiled 12 218 to 1 756 computations (85.6% saved)
31 alts after pruning (26 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 287 | 8 | 295 |
| Fresh | 5 | 18 | 23 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 2 | 2 |
| Total | 294 | 31 | 325 |
| Status | Accuracy | Program |
|---|---|---|
| 50.6% | (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) | |
| 50.5% | (-.f64 (sin.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 #s(literal 1/2 binary64) (PI.f64)))) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) | |
| ✓ | 50.5% | (-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) |
| ✓ | 50.5% | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 50.6% | (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x))) | |
| 99.4% | (*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (+.f64 x eps))) (+.f64 x eps)))))) #s(literal -2 binary64)) | |
| 99.6% | (*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal -2 binary64)) | |
| 99.4% | (*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x))))))))))) #s(literal -2 binary64)) | |
| 99.3% | (*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64)) | |
| 5.7% | (*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -2 binary64) x))))))) | |
| 49.0% | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) | |
| 99.4% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps)) | |
| 77.6% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) eps)) | |
| 99.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps #s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))) | |
| ✓ | 99.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))) |
| 98.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (sin.f64 x)))) | |
| 98.5% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)))) (sin.f64 x)))) | |
| 9.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 x x)) (-.f64 (PI.f64) x)))))) | |
| ✓ | 9.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x))))) |
| 9.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) x)) x))))) | |
| 9.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (PI.f64))) (PI.f64)))))) | |
| 9.3% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))) | |
| 76.9% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))))))) | |
| 77.0% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x))))) | |
| ✓ | 50.3% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
| 97.9% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)))) | |
| 48.7% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps))))))) | |
| 97.7% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64)))))))) | |
| 97.7% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps)))))) | |
| 77.0% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))))) | |
| 49.1% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))))) |
Compiled 1 260 to 819 computations (35.0% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x))))) |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps)))))) |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64)))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps))))))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64)))))))) |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64)))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) eps)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)))) |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64)))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) eps)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)))) (sin.f64 x)))) |
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x)))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (PI.f64))) (PI.f64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) x)) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)) eps) (*.f64 #s(literal -1/6 binary64) x)) eps))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 x x)) (-.f64 (PI.f64) x)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (sin.f64 x)))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)))) (sin.f64 x)))) |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64)))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) eps)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)))) (sin.f64 x)))) |
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x)))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (PI.f64))) (PI.f64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) x)) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)) eps) (*.f64 #s(literal -1/6 binary64) x)) eps))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 x x)) (-.f64 (PI.f64) x)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (sin.f64 x)))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (sin.f64 x)))) |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64)))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) eps)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)))) (sin.f64 x)))) |
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x)))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (PI.f64))) (PI.f64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) x)) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)) eps) (*.f64 #s(literal -1/6 binary64) x)) eps))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 x x)) (-.f64 (PI.f64) x)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (sin.f64 x)))) |
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #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)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) #s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) #s(literal -2 binary64)) |
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) #s(literal -2 binary64)) |
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))) |
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64))))) |
| Outputs |
|---|
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64)) |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 #s(literal -1 binary64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1/2 binary64) eps)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (fma.f64 #s(literal -1 binary64) x (*.f64 eps (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps x)) #s(literal 1/2 binary64)))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (*.f64 #s(literal -1/2 binary64) (exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 2 binary64))))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) #s(approx (* -1 (sin x)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (/.f64 x eps))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) x) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (neg.f64 (sin.f64 x))) eps)) |
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (+.f64 (PI.f64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (*.f64 #s(literal -1 binary64) (sin.f64 x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)))) (sin.f64 x)))) |
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(literal 1/2 binary64) (*.f64 eps (sin.f64 x)))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (PI.f64))) (PI.f64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (PI.f64) x)) x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) #s(approx (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1/2 binary64)) eps) (*.f64 #s(literal -1/6 binary64) x)) eps))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (sin.f64 (/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 x x)) (-.f64 (PI.f64) x)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps #s(approx (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)) (fma.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (sin.f64 x)))) |
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #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)) #s(approx (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))) (fma.f64 eps (*.f64 x (-.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (-.f64 (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) #s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64))))))) #s(literal -2 binary64)) |
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 #s(approx (sin (* 1/2 eps)) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 2 binary64)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) #s(literal -2 binary64)) |
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps #s(approx (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))) |
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64))))) |
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal -2 binary64)) |
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (+.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))) #s(literal -2 binary64)) |
(-.f64 (sin.f64 (+.f64 (-.f64 (neg.f64 eps) x) (*.f64 #s(literal 1/2 binary64) (PI.f64)))) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) |
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (*.f64 #s(literal -2 binary64) x)))))) #s(literal -2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) |
(*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps #s(literal 884279719003555/140737488355328 binary64)) (*.f64 #s(literal -2 binary64) x))))))) |
(*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2)) (cos (/ (- (+ (* (PI) 1/2) (+ eps x)) (+ (+ (* (PI) 1/2) x) (PI))) 2))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -2 binary64) x))))))) |
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (+.f64 x eps))) (+.f64 x eps)))))) #s(literal -2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 x (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 x (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 x) (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 (neg.f64 x) (PI.f64)) (+.f64 eps x)) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (+.f64 eps x)) (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (PI.f64))) #s(literal 2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 eps (sin.f64 x))))) (sin.f64 x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps #s(approx (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 #s(literal 0 binary64) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (*.f64 eps #s(literal 0 binary64))))) #s(literal 1/2 binary64)))) #s(literal -2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (-.f64 (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (*.f64 eps (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))))) (sin.f64 x)))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) |
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(approx (sin (* 1/2 (- eps (* -2 x)))) (+.f64 (sin.f64 x) (*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (*.f64 #s(literal -1/48 binary64) (*.f64 eps (cos.f64 x))))))))))) #s(literal -2 binary64)) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 x)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 eps (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x))))))) |
| Outputs |
|---|
(*.f64 #s(approx (* (sin (* (+ (+ eps x) x) 1/2)) (sin (* (- (+ eps x) x) 1/2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx (* 1/2 (- eps (* -2 x))) (fma.f64 eps #s(literal 1/2 binary64) x))))) #s(literal -2 binary64)) |
27 calls:
| 16.0ms | x |
| 14.0ms | eps |
| 10.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 10.0ms | eps |
| 10.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 50.3% | 1 | x |
| 50.3% | 1 | eps |
| 50.3% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 77.0% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 77.0% | 1 | x |
| 77.0% | 1 | eps |
| 97.7% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 97.7% | 1 | x |
| 97.7% | 1 | eps |
| 97.7% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 97.7% | 1 | eps |
| 97.7% | 1 | x |
| 97.9% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 97.9% | 1 | x |
| 97.9% | 1 | eps |
| 98.5% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 98.5% | 1 | x |
| 98.5% | 1 | eps |
| 98.5% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 98.5% | 1 | x |
| 98.5% | 1 | eps |
| 99.3% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 99.3% | 1 | x |
| 99.3% | 1 | eps |
| 99.6% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 99.6% | 1 | x |
| 99.6% | 1 | eps |
Compiled 2 318 to 546 computations (76.4% saved)
| 1× | fuel |
Compiled 420 to 124 computations (70.5% saved)
Compiled 457 to 155 computations (66.1% saved)
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