
Time bar (total: 31.6s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 0 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 1 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 2 |
| 0% | 0% | 25.3% | 74.7% | 0% | 0% | 0% | 3 |
| 0% | 0% | 25.3% | 74.7% | 0% | 0% | 0% | 4 |
| 0% | 0% | 19% | 81% | 0% | 0% | 0% | 5 |
| 0% | 0% | 15.8% | 84.2% | 0% | 0% | 0% | 6 |
| 0% | 0% | 11.1% | 88.9% | 0% | 0% | 0% | 7 |
| 0% | 0% | 8.7% | 91.3% | 0% | 0% | 0% | 8 |
| 0% | 0% | 5.9% | 94.1% | 0% | 0% | 0% | 9 |
| 0% | 0% | 4.5% | 95.5% | 0% | 0% | 0% | 10 |
| 0% | 0% | 3.1% | 96.9% | 0% | 0% | 0% | 11 |
| 0% | 0% | 2.7% | 97.3% | 0% | 0% | 0% | 12 |
Compiled 28 to 18 computations (35.7% saved)
ival-sin: 18.0ms (24.8% of total)...c/correct-round.rkt:119:19: 14.0ms (19.3% of total)ival-<=: 8.0ms (11% of total)ival-<: 7.0ms (9.6% of total)ival-mult: 6.0ms (8.3% of total)ival-add: 5.0ms (6.9% of total)ival-fabs: 5.0ms (6.9% of total)ival-sub: 5.0ms (6.9% of total)ival-and: 4.0ms (5.5% of total)const: 1.0ms (1.4% of total)backward-pass: 0.0ms (0% of total)| 6.6s | 26153× | 0 | precondition |
| 2.2s | 4463× | 1 | valid |
| 995.0ms | 3793× | 0 | valid |
ival-sin: 1.7s (22.1% of total)...c/correct-round.rkt:119:19: 1.2s (15.1% of total)ival-<=: 910.0ms (11.9% of total)ival-<: 868.0ms (11.3% of total)ival-mult: 725.0ms (9.5% of total)ival-sub: 614.0ms (8% of total)ival-add: 552.0ms (7.2% of total)ival-fabs: 522.0ms (6.8% of total)ival-and: 348.0ms (4.5% of total)backward-pass: 184.0ms (2.4% of total)const: 85.0ms (1.1% of total)| 2× | egg-herbie |
| 376× | fnmadd-define |
| 344× | fnmsub-define |
| 344× | fmsub-define |
| 320× | sum3-define |
| 308× | fmm-def |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 46 |
| 1 | 43 | 42 |
| 2 | 94 | 42 |
| 3 | 198 | 42 |
| 4 | 507 | 42 |
| 5 | 917 | 42 |
| 6 | 1285 | 42 |
| 7 | 1548 | 42 |
| 8 | 1684 | 42 |
| 9 | 1711 | 42 |
| 0 | 6 | 7 |
| 1 | 9 | 7 |
| 2 | 14 | 7 |
| 3 | 21 | 7 |
| 4 | 31 | 7 |
| 5 | 63 | 7 |
| 6 | 122 | 7 |
| 7 | 210 | 7 |
| 8 | 295 | 7 |
| 9 | 401 | 7 |
| 10 | 479 | 7 |
| 11 | 485 | 7 |
| 0 | 485 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | saturated |
| Inputs |
|---|
(- (sin (+ x eps)) (sin x)) |
| Outputs |
|---|
(- (sin (+ x eps)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Inputs |
|---|
(- (sin (+ x eps)) (sin x)) |
(- (sin (+ (neg x) eps)) (sin (neg x))) |
(- (sin (+ x (neg eps))) (sin x)) |
(neg (- (sin (+ (neg x) eps)) (sin (neg x)))) |
(neg (- (sin (+ x (neg eps))) (sin x))) |
(- (sin (+ eps x)) (sin eps)) |
| Outputs |
|---|
(- (sin (+ x eps)) (sin x)) |
(- (sin (+ (neg x) eps)) (sin (neg x))) |
(+ (sin x) (sin (- eps x))) |
(- (sin (+ x (neg eps))) (sin x)) |
(- (sin (- x eps)) (sin x)) |
(neg (- (sin (+ (neg x) eps)) (sin (neg x)))) |
(- (sin (- x eps)) (sin x)) |
(neg (- (sin (+ x (neg eps))) (sin x))) |
(+ (sin x) (sin (- eps x))) |
(- (sin (+ eps x)) (sin eps)) |
(- (sin (+ x eps)) (sin eps)) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 233 | 2 | (3.545075840185958e-212 3.58034235077827e-214) | 5 | (-1.9515661030450103e-285 2.7409289292662795e-287) | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 0 | 0 | - | 0 | - | x |
| 0 | 0 | - | 0 | - | (sin.f64 x) |
| 0 | 0 | - | 0 | - | (+.f64 x eps) |
| 0 | 0 | - | 0 | - | eps |
| 0 | 0 | - | 0 | - | (sin.f64 (+.f64 x eps)) |
| 91.0ms | 280× | 1 | valid |
| 68.0ms | 232× | 0 | valid |
Compiled 51 to 20 computations (60.8% saved)
ival-add: 44.0ms (48.4% of total)ival-sin: 28.0ms (30.8% of total)ival-sub: 9.0ms (9.9% of total)backward-pass: 9.0ms (9.9% of total)const: 1.0ms (1.1% of total)Compiled 9 to 6 computations (33.3% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 60.4% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 6 computations (33.3% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sin.f64 x) |
| ✓ | cost-diff | 0 | (+.f64 x eps) |
| ✓ | cost-diff | 0 | (sin.f64 (+.f64 x eps)) |
| ✓ | cost-diff | 0 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 124× | fnmadd-define |
| 122× | sum3-define |
| 80× | fma-lowering-fma.f32 |
| 80× | fnmsub-define |
| 80× | fmsub-define |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 1 | 9 | 18 |
| 2 | 14 | 18 |
| 3 | 21 | 18 |
| 4 | 31 | 18 |
| 5 | 63 | 18 |
| 6 | 122 | 18 |
| 7 | 210 | 18 |
| 8 | 295 | 18 |
| 9 | 401 | 18 |
| 10 | 479 | 18 |
| 11 | 485 | 18 |
| 0 | 485 | 18 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(- (sin (+ x eps)) (sin x)) |
(sin (+ x eps)) |
(+ x eps) |
x |
eps |
(sin x) |
| Outputs |
|---|
(- (sin (+ x eps)) (sin x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin (+ x eps)) |
(sin.f64 (+.f64 x eps)) |
(+ x eps) |
(+.f64 x eps) |
x |
eps |
(sin x) |
(sin.f64 x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (+.f64 x eps) |
| ✓ | accuracy | 100.0% | (sin.f64 x) |
| ✓ | accuracy | 99.9% | (sin.f64 (+.f64 x eps)) |
| ✓ | accuracy | 60.5% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 45.0ms | 140× | 1 | valid |
| 30.0ms | 116× | 0 | valid |
Compiled 21 to 7 computations (66.7% saved)
ival-sin: 12.0ms (44.1% of total)ival-add: 5.0ms (18.4% of total)backward-pass: 5.0ms (18.4% of total)ival-sub: 4.0ms (14.7% of total)const: 0.0ms (0% of total)| Inputs |
|---|
#<alt (- (sin (+ x eps)) (sin x))> |
#<alt (sin (+ x eps))> |
#<alt (+ x eps)> |
#<alt (sin x)> |
| Outputs |
|---|
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (- (cos eps) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (- (sin (- eps (* -1 x))) (sin x))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (+ eps x)) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (- (sin (- x (* -1 eps))) (sin x))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (cos eps)))> |
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))> |
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin x)> |
#<alt (+ (sin x) (* eps (cos x)))> |
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))> |
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt eps> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt x> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))> |
#<alt x> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt eps> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt eps> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))> |
#<alt x> |
#<alt (* x (+ 1 (* -1/6 (pow x 2))))> |
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))> |
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
#<alt (sin x)> |
21 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | eps | @ | inf | (- (sin (+ x eps)) (sin x)) |
| 1.0ms | eps | @ | 0 | (- (sin (+ x eps)) (sin x)) |
| 1.0ms | x | @ | 0 | (- (sin (+ x eps)) (sin x)) |
| 0.0ms | x | @ | inf | (+ x eps) |
| 0.0ms | x | @ | 0 | (sin (+ x eps)) |
| 1× | batch-egg-rewrite |
| 2788× | *-lowering-*.f32 |
| 2788× | *-lowering-*.f64 |
| 2132× | /-lowering-/.f32 |
| 2132× | /-lowering-/.f64 |
| 2068× | fma-lowering-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 1 | 49 | 16 |
| 2 | 402 | 16 |
| 3 | 5232 | 16 |
| 0 | 8309 | 16 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- (sin (+ x eps)) (sin x)) |
(sin (+ x eps)) |
(+ x eps) |
(sin x) |
| Outputs |
|---|
(+.f64 (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x))) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) |
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x))) |
(+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (+.f64 x eps))) |
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))) |
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(+.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps))) |
(+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))) |
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(-.f64 #s(literal 0 binary64) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps)))) |
(-.f64 (+.f64 (sin.f64 (+.f64 x eps)) #s(literal 0 binary64)) (sin.f64 x)) |
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (sin.f64 (+.f64 x eps)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
(fma.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))) |
(fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 (sin.f64 (+.f64 x eps)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))) |
(fma.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps)))))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) |
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (sin.f64 (+.f64 x eps))) |
(fma.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) |
(fma.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3/2 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))) |
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(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 6 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 3 binary64)))) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (*.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (-.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 2 binary64)))) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps)))))) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))) |
(-.f64 (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (*.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 x eps))) (/.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 x eps)))) |
(sin.f64 (+.f64 x eps)) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps))) |
(fma.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))) (neg.f64 (*.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (sin.f64 x) (*.f64 (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))))) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) |
(/.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (sin.f64 (-.f64 x eps))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))))))) |
(/.f64 (neg.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps)))) (neg.f64 (sin.f64 (-.f64 x eps)))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps)))) |
(*.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps))))))) |
(*.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps)))) |
(+.f64 x eps) |
(+.f64 eps x) |
(+.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) |
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x))) |
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 eps eps))) (+.f64 x eps) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 x eps))) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(neg.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) |
(neg.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) (-.f64 x eps)))) |
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) |
(neg.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) (-.f64 x eps))) |
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps)) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) |
(/.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) |
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (-.f64 (*.f64 eps eps) (*.f64 x x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (*.f64 (-.f64 x eps) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x x) (*.f64 eps eps)))))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x)) |
(/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) (*.f64 (-.f64 x eps) (+.f64 (*.f64 x x) (*.f64 eps eps)))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x eps)) (*.f64 (-.f64 x eps) (*.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps))) |
(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) #s(literal 1 binary64)) (*.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x x) (*.f64 eps eps)))) (-.f64 x eps))) |
(/.f64 (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))) |
(/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) |
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) #s(literal 1 binary64)) (-.f64 x eps)) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps)))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 x eps)))) |
(/.f64 (neg.f64 (-.f64 (*.f64 eps eps) (*.f64 x x))) (neg.f64 (-.f64 eps x))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (+.f64 (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (+.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x x) (*.f64 eps eps))))) |
(/.f64 (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (*.f64 x x) (*.f64 eps eps))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64)) |
(*.f64 (+.f64 x eps) (*.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))) |
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps))) |
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) |
(*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) |
(*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) |
(*.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) |
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))) |
(*.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x eps)))) |
(*.f64 #s(literal 1 binary64) (+.f64 x eps)) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (-.f64 (*.f64 x x) (*.f64 eps eps))) |
(*.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x))) |
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 (*.f64 x x) (*.f64 eps eps))) (+.f64 x eps)) |
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x)))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x))))) |
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) |
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 x eps)))) |
(sin.f64 x) |
| 1× | egg-herbie |
| 3796× | *-lowering-*.f32 |
| 3796× | *-lowering-*.f64 |
| 2064× | +-lowering-+.f64 |
| 2064× | +-lowering-+.f32 |
| 1456× | fnmadd-define |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 107 | 488 |
| 1 | 327 | 465 |
| 2 | 963 | 459 |
| 3 | 3572 | 459 |
| 0 | 8267 | 459 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
eps |
(+ eps x) |
(+ eps x) |
(+ eps x) |
x |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
x |
(+ eps x) |
(+ eps x) |
(+ eps x) |
eps |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
| Outputs |
|---|
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (*.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(-.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (cos.f64 eps))))) x) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (+ eps x)) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (cos eps))) |
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+.f64 (*.f64 x (cos.f64 eps)) (*.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (cos.f64 eps)) x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* eps (cos x))) |
(+.f64 (sin.f64 x) (*.f64 eps (cos.f64 x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+.f64 (*.f64 eps (cos.f64 x)) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 x))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
eps |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
x |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
(* x (+ 1 (/ eps x))) |
(+.f64 eps x) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(+.f64 eps x) |
x |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
eps |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
(* eps (+ 1 (/ x eps))) |
(+.f64 eps x) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(+.f64 eps x) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x #s(literal 1/120 binary64))))))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
(sin x) |
(sin.f64 x) |
Compiled 7060 to 730 computations (89.7% saved)
10 alts after pruning (9 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 252 | 9 | 261 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 252 | 10 | 262 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 60.0% | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))) |
| 59.9% | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x #s(literal 1/120 binary64)))))))) | |
| ▶ | 59.7% | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
| ✓ | 60.4% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| ▶ | 99.9% | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
| ▶ | 100.0% | (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) |
| 100.0% | (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) | |
| 99.8% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) | |
| 99.4% | (*.f64 eps (cos.f64 x)) | |
| ▶ | 98.2% | (sin.f64 eps) |
Compiled 321 to 218 computations (32.1% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 128 | (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)) |
| ✓ | cost-diff | 128 | (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) |
| ✓ | cost-diff | 128 | (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) |
| ✓ | cost-diff | 128 | (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))) |
| ✓ | cost-diff | 0 | (+.f64 x eps) |
| ✓ | cost-diff | 0 | (sin.f64 (+.f64 x eps)) |
| ✓ | cost-diff | 0 | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))) |
| ✓ | cost-diff | 0 | (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))) |
| ✓ | cost-diff | 0 | (+.f64 x eps) |
| ✓ | cost-diff | 0 | (sin.f64 (+.f64 x eps)) |
| ✓ | cost-diff | 0 | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
| ✓ | cost-diff | 0 | (sin.f64 eps) |
| ✓ | cost-diff | 0 | (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) |
| ✓ | cost-diff | 0 | (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) |
| 2008× | *-lowering-*.f32 |
| 2008× | *-lowering-*.f64 |
| 1726× | +-lowering-+.f64 |
| 1726× | +-lowering-+.f32 |
| 1564× | sum4-define |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 49 | 354 |
| 1 | 138 | 331 |
| 2 | 509 | 323 |
| 3 | 2153 | 323 |
| 4 | 5829 | 323 |
| 0 | 8256 | 323 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2)))) |
eps |
(+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2))) |
(* (+ (* (* eps eps) -1/6) 1) (cos x)) |
(+ (* (* eps eps) -1/6) 1) |
(* (* eps eps) -1/6) |
(* eps eps) |
-1/6 |
1 |
(cos x) |
x |
(* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2)) |
(* eps (sin x)) |
(sin x) |
(+ (* (* eps eps) 1/24) -1/2) |
(* (* eps eps) 1/24) |
1/24 |
-1/2 |
(sin eps) |
eps |
(- (sin (+ x eps)) (* x (+ 1 (* x (* x -1/6))))) |
(sin (+ x eps)) |
(+ x eps) |
x |
eps |
(* x (+ 1 (* x (* x -1/6)))) |
(+ 1 (* x (* x -1/6))) |
1 |
(* x (* x -1/6)) |
(* x -1/6) |
-1/6 |
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))))) |
(sin (+ x eps)) |
(+ x eps) |
x |
eps |
(* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))))) |
(+ 1 (* (* x x) (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))) |
1 |
(* (* x x) (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))) |
(* x x) |
(+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))) |
-1/6 |
(* (* x x) (+ 1/120 (* x (* x -1/5040)))) |
(+ 1/120 (* x (* x -1/5040))) |
1/120 |
(* x (* x -1/5040)) |
(* x -1/5040) |
-1/5040 |
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2) |
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) |
(sin (/ (+ eps 0) 2)) |
(/ (+ eps 0) 2) |
(+ eps 0) |
eps |
0 |
2 |
(cos (/ (+ eps (* x 2)) 2)) |
(/ (+ eps (* x 2)) 2) |
(+ eps (* x 2)) |
(* x 2) |
x |
| Outputs |
|---|
(* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2)))) |
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) |
eps |
(+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2))) |
(+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) |
(* (+ (* (* eps eps) -1/6) 1) (cos x)) |
(*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) |
(+ (* (* eps eps) -1/6) 1) |
(+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(* (* eps eps) -1/6) |
(*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) |
(* eps eps) |
(*.f64 eps eps) |
-1/6 |
#s(literal -1/6 binary64) |
1 |
#s(literal 1 binary64) |
(cos x) |
(cos.f64 x) |
x |
(* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2)) |
(*.f64 (*.f64 eps (sin.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(sin x) |
(sin.f64 x) |
(+ (* (* eps eps) 1/24) -1/2) |
(+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) |
(* (* eps eps) 1/24) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
1/24 |
#s(literal 1/24 binary64) |
-1/2 |
#s(literal -1/2 binary64) |
(sin eps) |
(sin.f64 eps) |
eps |
(- (sin (+ x eps)) (* x (+ 1 (* x (* x -1/6))))) |
(+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (-.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(sin (+ x eps)) |
(sin.f64 (+.f64 eps x)) |
(+ x eps) |
(+.f64 eps x) |
x |
eps |
(* x (+ 1 (* x (* x -1/6)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) |
(+ 1 (* x (* x -1/6))) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) |
1 |
#s(literal 1 binary64) |
(* x (* x -1/6)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 x x)) |
(* x -1/6) |
(*.f64 #s(literal -1/6 binary64) x) |
-1/6 |
#s(literal -1/6 binary64) |
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))))) |
(+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) (-.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))) |
(sin (+ x eps)) |
(sin.f64 (+.f64 eps x)) |
(+ x eps) |
(+.f64 eps x) |
x |
eps |
(* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))) |
(+ 1 (* (* x x) (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))) |
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))) |
1 |
#s(literal 1 binary64) |
(* (* x x) (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))) |
(* x x) |
(*.f64 x x) |
(+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))) |
(+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))) |
-1/6 |
#s(literal -1/6 binary64) |
(* (* x x) (+ 1/120 (* x (* x -1/5040)))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) |
(+ 1/120 (* x (* x -1/5040))) |
(+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))) |
1/120 |
#s(literal 1/120 binary64) |
(* x (* x -1/5040)) |
(*.f64 x (*.f64 x #s(literal -1/5040 binary64))) |
(* x -1/5040) |
(*.f64 x #s(literal -1/5040 binary64)) |
-1/5040 |
#s(literal -1/5040 binary64) |
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) |
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) |
(sin (/ (+ eps 0) 2)) |
(sin.f64 (/.f64 eps #s(literal 2 binary64))) |
(/ (+ eps 0) 2) |
(/.f64 eps #s(literal 2 binary64)) |
(+ eps 0) |
eps |
eps |
0 |
#s(literal 0 binary64) |
2 |
#s(literal 2 binary64) |
(cos (/ (+ eps (* x 2)) 2)) |
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
(/ (+ eps (* x 2)) 2) |
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) |
(+ eps (* x 2)) |
(+.f64 eps (*.f64 x #s(literal 2 binary64))) |
(* x 2) |
(*.f64 x #s(literal 2 binary64)) |
x |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) |
| ✓ | accuracy | 99.9% | (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
| ✓ | accuracy | 99.8% | (*.f64 x (*.f64 x #s(literal -1/5040 binary64))) |
| ✓ | accuracy | 99.8% | (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64))))))) |
| ✓ | accuracy | 60.9% | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))) |
| ✓ | accuracy | 99.9% | (sin.f64 (+.f64 x eps)) |
| ✓ | accuracy | 99.9% | (*.f64 x (*.f64 x #s(literal -1/6 binary64))) |
| ✓ | accuracy | 99.5% | (*.f64 x #s(literal -1/6 binary64)) |
| ✓ | accuracy | 61.0% | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
| ✓ | accuracy | 100.0% | (sin.f64 eps) |
| ✓ | accuracy | 100.0% | (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) |
| ✓ | accuracy | 100.0% | (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) |
| 397.0ms | 138× | 1 | valid |
| 231.0ms | 118× | 0 | valid |
Compiled 377 to 50 computations (86.7% saved)
ival-mult: 192.0ms (51.5% of total)ival-add: 46.0ms (12.3% of total)...c/correct-round.rkt:119:19: 41.0ms (11% of total)backward-pass: 36.0ms (9.6% of total)ival-sin: 22.0ms (5.9% of total)ival-cos: 14.0ms (3.8% of total)ival-div: 12.0ms (3.2% of total)ival-sub: 9.0ms (2.4% of total)const: 2.0ms (0.5% of total)| Inputs |
|---|
#<alt (* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2))))> |
#<alt (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2)))> |
#<alt (* (+ (* (* eps eps) -1/6) 1) (cos x))> |
#<alt (+ (* (* eps eps) -1/6) 1)> |
#<alt (sin eps)> |
#<alt (- (sin (+ x eps)) (* x (+ 1 (* x (* x -1/6)))))> |
#<alt (sin (+ x eps))> |
#<alt (+ x eps)> |
#<alt (* x (+ 1 (* x (* x -1/6))))> |
#<alt (- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))))))> |
#<alt (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))))> |
#<alt (* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)> |
#<alt (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))> |
#<alt (sin (/ (+ eps 0) 2))> |
#<alt (/ (+ eps 0) 2)> |
#<alt (* (* eps eps) -1/6)> |
#<alt (* (* eps eps) 1/24)> |
#<alt (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2))> |
#<alt (* x -1/6)> |
#<alt (* x (* x -1/6))> |
#<alt (* (* x x) (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))> |
#<alt (* (* x x) (+ 1/120 (* x (* x -1/5040))))> |
#<alt (* x (* x -1/5040))> |
#<alt (cos (/ (+ eps (* x 2)) 2))> |
#<alt (* x 2)> |
| Outputs |
|---|
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))> |
#<alt (* 1/24 (* (pow eps 4) (sin x)))> |
#<alt (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))> |
#<alt (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))> |
#<alt (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))> |
#<alt (* 1/24 (* (pow eps 4) (sin x)))> |
#<alt (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))> |
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))> |
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))> |
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))> |
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))> |
#<alt (* 1/24 (* (pow eps 3) (sin x)))> |
#<alt (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))> |
#<alt (* 1/24 (* (pow eps 3) (sin x)))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))) (* eps (- (* 1/24 (pow eps 2)) 1/2))))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2))))))))))> |
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))> |
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))> |
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))> |
#<alt (* -1/6 (* (pow eps 2) (cos x)))> |
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (* -1/6 (* (pow eps 2) (cos x)))> |
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2))))))))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt 1> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt eps> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))> |
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (- (cos eps) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))> |
#<alt (* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))> |
#<alt (* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))> |
#<alt (* 1/6 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))> |
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))> |
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))> |
#<alt (- (sin x) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (cos eps)))> |
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))> |
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin (- eps (* -1 x)))> |
#<alt (sin x)> |
#<alt (+ (sin x) (* eps (cos x)))> |
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))> |
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (+ eps x))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt (sin (- x (* -1 eps)))> |
#<alt eps> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt x> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt (* x (+ 1 (/ eps x)))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))> |
#<alt x> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt (+ eps x)> |
#<alt eps> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt (* eps (+ 1 (/ x eps)))> |
#<alt eps> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))> |
#<alt x> |
#<alt (* x (+ 1 (* -1/6 (pow x 2))))> |
#<alt (* x (+ 1 (* -1/6 (pow x 2))))> |
#<alt (* x (+ 1 (* -1/6 (pow x 2))))> |
#<alt (* -1/6 (pow x 3))> |
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))> |
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))> |
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))> |
#<alt (* -1/6 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))> |
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))> |
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (- (cos eps) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))> |
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))> |
#<alt (* 1/5040 (pow x 7))> |
#<alt (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))> |
#<alt (* 1/5040 (pow x 7))> |
#<alt (* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))> |
#<alt (* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))> |
#<alt (* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))> |
#<alt (- (sin x) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))> |
#<alt x> |
#<alt (* x (+ 1 (* -1/6 (pow x 2))))> |
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))> |
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (* -1/5040 (pow x 7))> |
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* -1/5040 (pow x 7))> |
#<alt (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))> |
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))> |
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 1/2 (* eps (cos x)))> |
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))> |
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))> |
#<alt (* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))> |
#<alt (* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))> |
#<alt (* 1/24 (* (pow eps 3) (sin x)))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x))))> |
#<alt (* 1/24 (* (pow eps 3) (sin x)))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2))))))> |
#<alt (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* x (+ (* -1/6 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* 1/120 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2))))))))> |
#<alt (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* (pow x 2) (+ (* -1/5040 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/120 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))))))> |
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 x)> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))> |
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))> |
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))> |
#<alt (* -1/5040 (pow x 6))> |
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* -1/5040 (pow x 6))> |
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* 1/120 (pow x 2))> |
#<alt (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))> |
#<alt (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))> |
#<alt (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))> |
#<alt (* -1/5040 (pow x 4))> |
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* -1/5040 (pow x 4))> |
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* -1/5040 (pow x 2))> |
#<alt (* -1/5040 (pow x 2))> |
#<alt (* -1/5040 (pow x 2))> |
#<alt (* -1/5040 (pow x 2))> |
#<alt (* -1/5040 (pow x 2))> |
#<alt (* -1/5040 (pow x 2))> |
#<alt (* -1/5040 (pow x 2))> |
#<alt (* -1/5040 (pow x 2))> |
#<alt (* -1/5040 (pow x 2))> |
#<alt (* -1/5040 (pow x 2))> |
#<alt (* -1/5040 (pow x 2))> |
#<alt (* -1/5040 (pow x 2))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))> |
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 eps))> |
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
108 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 7.0ms | eps | @ | inf | (* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2) |
| 6.0ms | x | @ | -inf | (* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2)))) |
| 5.0ms | x | @ | inf | (* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2)))) |
| 4.0ms | x | @ | -inf | (- (sin (+ x eps)) (* x (+ 1 (* x (* x -1/6))))) |
| 3.0ms | x | @ | inf | (* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2) |
| 1× | batch-egg-rewrite |
| 6006× | *-lowering-*.f32 |
| 6006× | *-lowering-*.f64 |
| 2754× | /-lowering-/.f32 |
| 2754× | /-lowering-/.f64 |
| 2528× | +-lowering-+.f64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 49 | 244 |
| 1 | 306 | 226 |
| 2 | 3194 | 226 |
| 0 | 10240 | 226 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2)))) |
(+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2))) |
(* (+ (* (* eps eps) -1/6) 1) (cos x)) |
(+ (* (* eps eps) -1/6) 1) |
(sin eps) |
(- (sin (+ x eps)) (* x (+ 1 (* x (* x -1/6))))) |
(sin (+ x eps)) |
(+ x eps) |
(* x (+ 1 (* x (* x -1/6)))) |
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040))))))))) |
(* x (+ 1 (* (* x x) (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))))) |
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2) |
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) |
(sin (/ (+ eps 0) 2)) |
(/ (+ eps 0) 2) |
(* (* eps eps) -1/6) |
(* (* eps eps) 1/24) |
(* (* eps (sin x)) (+ (* (* eps eps) 1/24) -1/2)) |
(* x -1/6) |
(* x (* x -1/6)) |
(* (* x x) (+ -1/6 (* (* x x) (+ 1/120 (* x (* x -1/5040)))))) |
(* (* x x) (+ 1/120 (* x (* x -1/5040)))) |
(* x (* x -1/5040)) |
(cos (/ (+ eps (* x 2)) 2)) |
(* x 2) |
| Outputs |
|---|
(+.f64 (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 0 binary64))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) (*.f64 #s(literal 0 binary64) (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))) |
(+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) |
(+.f64 (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps))) |
(+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 0 binary64)) (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))) |
(+.f64 (*.f64 #s(literal 0 binary64) (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))) |
(fma.f64 eps (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) |
(fma.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) eps (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) |
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (pow.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) #s(literal 3 binary64)))) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (*.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (-.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x))))))) |
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (pow.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) #s(literal 2 binary64)))) (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))) |
(/.f64 (*.f64 (*.f64 eps eps) (+.f64 (pow.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) #s(literal 3 binary64)))) (*.f64 eps (+.f64 (*.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (*.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (-.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x))))))) |
(/.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (pow.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) #s(literal 2 binary64)))) (*.f64 eps (-.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (*.f64 eps (*.f64 eps eps))) (*.f64 (+.f64 (*.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (*.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (-.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x))))) (*.f64 eps eps))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (*.f64 eps eps)) (*.f64 (+.f64 (*.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (*.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (-.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x))))) eps)) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (pow.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) #s(literal 2 binary64))) (*.f64 eps (*.f64 eps eps))) (*.f64 (-.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (*.f64 eps eps))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (pow.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) #s(literal 2 binary64))) (*.f64 eps eps)) (*.f64 (-.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) eps)) |
(/.f64 (+.f64 (pow.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (*.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) #s(literal 2 binary64))) (-.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))) |
(/.f64 (*.f64 eps (+.f64 (pow.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) #s(literal 3 binary64)))) (+.f64 (*.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (*.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (-.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)))))) |
(/.f64 (*.f64 eps (-.f64 (*.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) (pow.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) #s(literal 2 binary64)))) (-.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) |
(/.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps)) |
(/.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))) (*.f64 eps eps)) eps) |
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) (*.f64 eps eps)) |
(/.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) eps) |
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(sin.f64 (/.f64 eps #s(literal 2 binary64))) |
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(/.f64 eps #s(literal 2 binary64)) |
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(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(pow.f64 (/.f64 #s(literal 2 binary64) eps) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) eps) #s(literal 1 binary64)) #s(literal -1 binary64)) |
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(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) |
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(fma.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) |
(fma.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) (*.f64 eps (sin.f64 x)) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) |
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(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (sin.f64 x) (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (*.f64 eps eps)) |
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(+.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 x x)) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))) #s(literal 1 binary64))) |
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(fma.f64 #s(literal -1/6 binary64) (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))) |
(fma.f64 x (*.f64 #s(literal -1/6 binary64) x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))) |
(fma.f64 (*.f64 #s(literal -1/6 binary64) x) x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))) |
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))) |
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal -1/216 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))) (*.f64 (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (+.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))) |
(/.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))) |
(/.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/216 binary64) (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))) (*.f64 (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))) (+.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))) (-.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))) #s(literal -1/6 binary64))))) |
(/.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1/36 binary64) (*.f64 (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))) (-.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))) |
(/.f64 (*.f64 (+.f64 #s(literal -1/216 binary64) (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))) (*.f64 (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))) (*.f64 x x)) (+.f64 #s(literal 1/36 binary64) (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))) (-.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))) #s(literal -1/6 binary64))))) |
(/.f64 (*.f64 (-.f64 #s(literal 1/36 binary64) (*.f64 (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))) (*.f64 x x)) (-.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))) |
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))) |
(*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))) |
(*.f64 (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))) (*.f64 x x)) |
(*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))) #s(literal 1 binary64)) |
(*.f64 (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))) x) |
(*.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))) (*.f64 x x)) |
(+.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))) |
(+.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))) |
(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))) |
(fma.f64 #s(literal 1/120 binary64) (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))) |
(/.f64 (+.f64 (*.f64 #s(literal 1/1728000 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/128024064000 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (+.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))) (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))) (*.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))) |
(/.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/1728000 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/128024064000 binary64))))) (+.f64 #s(literal 1/14400 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) |
(/.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 1/14400 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/25401600 binary64)))) (-.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))) |
(/.f64 (*.f64 (+.f64 #s(literal 1/1728000 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/128024064000 binary64)))) (*.f64 x x)) (+.f64 #s(literal 1/14400 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))))) |
(/.f64 (*.f64 (-.f64 #s(literal 1/14400 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/25401600 binary64))) (*.f64 x x)) (-.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))) |
(*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))) |
(*.f64 (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))) (*.f64 x x)) |
(*.f64 (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))) x) |
(*.f64 x (*.f64 x #s(literal -1/5040 binary64))) |
(*.f64 (*.f64 x x) #s(literal -1/5040 binary64)) |
(*.f64 #s(literal -1/5040 binary64) (*.f64 x x)) |
(*.f64 (*.f64 x #s(literal -1/5040 binary64)) x) |
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal -2 binary64))) |
(*.f64 x #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) x) |
| 1× | egg-herbie |
| 4384× | *-lowering-*.f32 |
| 4384× | *-lowering-*.f64 |
| 2122× | +-lowering-+.f64 |
| 2122× | +-lowering-+.f32 |
| 1724× | sum3-define |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 488 | 4908 |
| 1 | 1674 | 4492 |
| 2 | 6169 | 4490 |
| 0 | 8122 | 4490 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* 1/24 (* (pow eps 4) (sin x))) |
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))) |
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))) |
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3)))))) |
(* 1/24 (* (pow eps 4) (sin x))) |
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x)))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x)))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))) |
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))) |
(* 1/24 (* (pow eps 3) (sin x))) |
(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3)))))) |
(* 1/24 (* (pow eps 3) (sin x))) |
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x))))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2))))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))))) |
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(cos x) |
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))) |
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))) |
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2)))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))))))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2)))))))))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
1 |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (* -1/6 (pow eps 2))) |
(* -1/6 (pow eps 2)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* -1/6 (pow eps 2)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(* 1/6 (pow x 3)) |
(* (pow x 3) (- 1/6 (/ 1 (pow x 2)))) |
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2)))) |
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2)))) |
(* 1/6 (pow x 3)) |
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6))) |
(- (sin x) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
eps |
(+ eps x) |
(+ eps x) |
(+ eps x) |
x |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
x |
(+ eps x) |
(+ eps x) |
(+ eps x) |
eps |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* -1/6 (pow x 3)) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(* -1/6 (pow x 3)) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(* 1/5040 (pow x 7)) |
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))) |
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))) |
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))) |
(* 1/5040 (pow x 7)) |
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))) |
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))) |
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))) |
(- (sin x) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(* -1/5040 (pow x 7)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* -1/5040 (pow x 7)) |
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2)))))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))) |
(* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))) |
(* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))) |
(* 1/24 (* (pow eps 3) (sin x))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x)))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x)))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x)))) |
(* 1/24 (* (pow eps 3) (sin x))) |
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2)))))) |
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2)))))) |
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2)))))) |
(* eps (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* x (+ (* -1/6 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/24 (pow eps 2)) 1/2)))) |
(* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* 1/120 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2)))))))) |
(* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* (pow x 2) (+ (* -1/5040 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/120 (* eps (- (* 1/24 (pow eps 2)) 1/2))))))))) |
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) |
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) |
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) |
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) |
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) |
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) |
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) |
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 x) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* -1/6 (pow x 2)) |
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)) |
(* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) |
(* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) |
(* -1/5040 (pow x 6)) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* -1/5040 (pow x 6)) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* 1/120 (pow x 2)) |
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) |
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) |
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) |
(* -1/5040 (pow x 4)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* -1/5040 (pow x 4)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* -1/5040 (pow x 2)) |
(* -1/5040 (pow x 2)) |
(* -1/5040 (pow x 2)) |
(* -1/5040 (pow x 2)) |
(* -1/5040 (pow x 2)) |
(* -1/5040 (pow x 2)) |
(* -1/5040 (pow x 2)) |
(* -1/5040 (pow x 2)) |
(* -1/5040 (pow x 2)) |
(* -1/5040 (pow x 2)) |
(* -1/5040 (pow x 2)) |
(* -1/5040 (pow x 2)) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 eps)) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
| Outputs |
|---|
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))))) |
(* 1/24 (* (pow eps 4) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))) |
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (*.f64 #s(literal -1/6 binary64) (/.f64 (cos.f64 x) eps)) (*.f64 (sin.f64 x) #s(literal 1/24 binary64)))) |
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (*.f64 #s(literal -1/6 binary64) (/.f64 (cos.f64 x) eps)) (+.f64 (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps)) eps)))) |
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3)))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps)) eps) (+.f64 (+.f64 (*.f64 #s(literal -1/6 binary64) (/.f64 (cos.f64 x) eps)) (*.f64 (sin.f64 x) #s(literal 1/24 binary64))) (/.f64 (cos.f64 x) (*.f64 eps (*.f64 eps eps)))))) |
(* 1/24 (* (pow eps 4) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))) |
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))) |
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(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
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(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
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(cos x) |
(cos.f64 x) |
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(* 1/24 (* (pow eps 3) (sin x))) |
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(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))) |
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(* 1/24 (* (pow eps 3) (sin x))) |
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(cos x) |
(cos.f64 x) |
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(* -1/6 (* (pow eps 2) (cos x))) |
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(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
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(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
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(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
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(* -1/6 (* (pow eps 2) (cos x))) |
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(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
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(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
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(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
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(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
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(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
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(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
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(*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
1 |
#s(literal 1 binary64) |
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(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/120 binary64) (*.f64 eps (*.f64 eps #s(literal -1/5040 binary64))))))))))) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (cos.f64 eps) (*.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))))))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (+.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 eps)))))) #s(literal -1 binary64))))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(* (pow x 3) (- 1/6 (/ 1 (pow x 2)))) |
(*.f64 (*.f64 x x) (*.f64 x (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2)))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (*.f64 x x))) (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2)))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (*.f64 x x))) (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64))) |
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))) |
(*.f64 (*.f64 x (*.f64 x x)) (neg.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6))) |
(*.f64 (+.f64 #s(literal -1/6 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x)))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6))) |
(*.f64 (+.f64 #s(literal -1/6 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x)))) |
(- (sin x) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(+.f64 (*.f64 eps (cos.f64 x)) (-.f64 (sin.f64 x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))))) |
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(+.f64 (sin.f64 x) (-.f64 (*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))))) |
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) (-.f64 (sin.f64 x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (cos eps))) |
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (*.f64 x (*.f64 #s(literal -1/6 binary64) (cos.f64 eps)))))))) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* eps (cos x))) |
(+.f64 (*.f64 eps (cos.f64 x)) (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+.f64 (sin.f64 x) (*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(+.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
(sin (- x (* -1 eps))) |
(sin.f64 (+.f64 eps x)) |
eps |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
x |
(* x (+ 1 (/ eps x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x))) |
(* x (+ 1 (/ eps x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x))) |
(* x (+ 1 (/ eps x))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 eps x))) #s(literal -1 binary64))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 eps x))) #s(literal -1 binary64))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(*.f64 x (*.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 eps x))) #s(literal -1 binary64))) |
x |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
eps |
(* eps (+ 1 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(* eps (+ 1 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
(* eps (+ 1 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 x (-.f64 #s(literal 0 binary64) eps))))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 x (-.f64 #s(literal 0 binary64) eps))))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 x (-.f64 #s(literal 0 binary64) eps))))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) |
(* -1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(*.f64 (*.f64 x x) (*.f64 x (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(*.f64 (*.f64 x x) (*.f64 x (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(*.f64 (*.f64 x x) (*.f64 x (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(* -1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 x (*.f64 x x)) (*.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64))) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 x (*.f64 x x)) (*.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64))) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 x (*.f64 x x)) (*.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (cos.f64 eps) (*.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))))))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) (+.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (*.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 eps)))))) #s(literal -1 binary64))))) |
(* 1/5040 (pow x 7)) |
(*.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64))) |
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x)))) |
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))))) |
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/5040 binary64) (+.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))))))) |
(* 1/5040 (pow x 7)) |
(*.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64))) |
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) #s(literal -1 binary64))) |
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))) |
(*.f64 (-.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64)))) |
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 4 binary64))))) (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64)))) |
(- (sin x) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))) |
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (+.f64 (*.f64 eps (cos.f64 x)) (sin.f64 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))) |
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (+.f64 (sin.f64 x) (*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))) |
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(+.f64 (sin.f64 x) (-.f64 (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))) |
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))))))))))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
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(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))) |
(* -1/5040 (pow x 7)) |
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 7 binary64))) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x)))) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
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(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
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(* -1/5040 (pow x 7)) |
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 7 binary64))) |
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
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(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
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(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
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(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2)))))))) |
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(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
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(* 1/2 (* eps (cos x))) |
(*.f64 (*.f64 eps (cos.f64 x)) #s(literal 1/2 binary64)) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (*.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/4 binary64)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/12 binary64))) (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (sin.f64 x) #s(literal -1/4 binary64)) (*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64))))))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
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(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
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(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
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(-.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
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(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
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(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
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(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
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(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
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(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
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(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
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(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
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(+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64)))))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64))) (*.f64 (cos.f64 x) #s(literal -1/8 binary64))))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 eps)) |
(cos.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(-.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (-.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
Compiled 32427 to 2288 computations (92.9% saved)
15 alts after pruning (15 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 909 | 13 | 922 |
| Fresh | 2 | 2 | 4 |
| Picked | 5 | 0 | 5 |
| Done | 1 | 0 | 1 |
| Total | 917 | 15 | 932 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) |
| ▶ | 98.2% | (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps x)))) |
| 98.9% | (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) | |
| ▶ | 99.9% | (*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
| 99.8% | (*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| 98.8% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) | |
| ▶ | 98.8% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))))) |
| 98.2% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) | |
| 99.5% | (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps #s(literal -1/6 binary64))) (*.f64 x (*.f64 x (+.f64 (*.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 eps (*.f64 x x))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps #s(literal 1/120 binary64)))))))))))) | |
| 99.5% | (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) | |
| 100.0% | (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) | |
| 99.8% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) | |
| 98.2% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) | |
| 99.4% | (*.f64 eps (cos.f64 x)) | |
| ▶ | 98.2% | eps |
Compiled 772 to 462 computations (40.2% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
| ✓ | cost-diff | 384 | (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
| ✓ | cost-diff | 384 | (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
| ✓ | cost-diff | 384 | (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))) |
| ✓ | cost-diff | 384 | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))))) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
| ✓ | cost-diff | 256 | (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps x)))) |
| ✓ | cost-diff | 0 | (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) |
| ✓ | cost-diff | 0 | (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) |
| ✓ | cost-diff | 128 | (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) |
| 5604× | +-lowering-+.f64 |
| 5604× | +-lowering-+.f32 |
| 3628× | *-lowering-*.f32 |
| 3628× | *-lowering-*.f64 |
| 1810× | sum5-define |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 54 | 529 |
| 1 | 184 | 510 |
| 2 | 740 | 484 |
| 3 | 3420 | 484 |
| 0 | 8205 | 484 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ (* (+ (* eps (* eps -1/6)) 1) (* (cos x) eps)) (* eps (* (sin x) (* eps (+ (* eps (* eps 1/24)) -1/2))))) |
(* (+ (* eps (* eps -1/6)) 1) (* (cos x) eps)) |
(+ (* eps (* eps -1/6)) 1) |
(* eps (* eps -1/6)) |
eps |
(* eps -1/6) |
-1/6 |
1 |
(* (cos x) eps) |
(cos x) |
x |
(* eps (* (sin x) (* eps (+ (* eps (* eps 1/24)) -1/2)))) |
(* (sin x) (* eps (+ (* eps (* eps 1/24)) -1/2))) |
(sin x) |
(* eps (+ (* eps (* eps 1/24)) -1/2)) |
(+ (* eps (* eps 1/24)) -1/2) |
(* eps (* eps 1/24)) |
(* eps 1/24) |
1/24 |
-1/2 |
eps |
(+ (* eps (+ 1 (* -1/6 (* eps eps)))) (* (+ -1/2 (* 1/24 (* eps eps))) (* eps (* eps x)))) |
(* eps (+ 1 (* -1/6 (* eps eps)))) |
eps |
(+ 1 (* -1/6 (* eps eps))) |
1 |
(* -1/6 (* eps eps)) |
-1/6 |
(* eps eps) |
(* (+ -1/2 (* 1/24 (* eps eps))) (* eps (* eps x))) |
(+ -1/2 (* 1/24 (* eps eps))) |
-1/2 |
(* 1/24 (* eps eps)) |
1/24 |
(* eps (* eps x)) |
(* eps x) |
x |
(* eps (+ (+ 1 (* -1/6 (* eps eps))) (* x (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps)))))))))) |
eps |
(+ (+ 1 (* -1/6 (* eps eps))) (* x (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps))))))))) |
(+ 1 (* -1/6 (* eps eps))) |
1 |
(* -1/6 (* eps eps)) |
-1/6 |
(* eps eps) |
(* x (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps)))))))) |
x |
(+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps))))))) |
(* eps (+ -1/2 (* 1/24 (* eps eps)))) |
(+ -1/2 (* 1/24 (* eps eps))) |
-1/2 |
(* 1/24 (* eps eps)) |
1/24 |
(* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps)))))) |
(+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps))))) |
(+ -1/2 (* (* eps eps) 1/12)) |
(* (* eps eps) 1/12) |
1/12 |
(* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps)))) |
(* -1/6 (* eps x)) |
(* eps x) |
(* (* (* eps (+ 1/2 (* (* eps eps) -1/48))) (cos (/ (+ eps (* x 2)) 2))) 2) |
(* (* eps (+ 1/2 (* (* eps eps) -1/48))) (cos (/ (+ eps (* x 2)) 2))) |
(* eps (+ 1/2 (* (* eps eps) -1/48))) |
eps |
(+ 1/2 (* (* eps eps) -1/48)) |
1/2 |
(* (* eps eps) -1/48) |
(* eps eps) |
-1/48 |
(cos (/ (+ eps (* x 2)) 2)) |
(/ (+ eps (* x 2)) 2) |
(+ eps (* x 2)) |
(* x 2) |
x |
2 |
| Outputs |
|---|
(+ (* (+ (* eps (* eps -1/6)) 1) (* (cos x) eps)) (* eps (* (sin x) (* eps (+ (* eps (* eps 1/24)) -1/2))))) |
(*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) (*.f64 eps (sin.f64 x))) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))) |
(* (+ (* eps (* eps -1/6)) 1) (* (cos x) eps)) |
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) (*.f64 eps (cos.f64 x))) |
(+ (* eps (* eps -1/6)) 1) |
(+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) |
(* eps (* eps -1/6)) |
(*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) |
eps |
(* eps -1/6) |
(*.f64 eps #s(literal -1/6 binary64)) |
-1/6 |
#s(literal -1/6 binary64) |
1 |
#s(literal 1 binary64) |
(* (cos x) eps) |
(*.f64 eps (cos.f64 x)) |
(cos x) |
(cos.f64 x) |
x |
(* eps (* (sin x) (* eps (+ (* eps (* eps 1/24)) -1/2)))) |
(*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))))) |
(* (sin x) (* eps (+ (* eps (* eps 1/24)) -1/2))) |
(*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) (*.f64 eps (sin.f64 x))) |
(sin x) |
(sin.f64 x) |
(* eps (+ (* eps (* eps 1/24)) -1/2)) |
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))))) |
(+ (* eps (* eps 1/24)) -1/2) |
(+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) |
(* eps (* eps 1/24)) |
(*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) |
(* eps 1/24) |
(*.f64 eps #s(literal 1/24 binary64)) |
1/24 |
#s(literal 1/24 binary64) |
-1/2 |
#s(literal -1/2 binary64) |
eps |
(+ (* eps (+ 1 (* -1/6 (* eps eps)))) (* (+ -1/2 (* 1/24 (* eps eps))) (* eps (* eps x)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))))))))) |
(* eps (+ 1 (* -1/6 (* eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
eps |
(+ 1 (* -1/6 (* eps eps))) |
(+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) |
1 |
#s(literal 1 binary64) |
(* -1/6 (* eps eps)) |
(*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) |
-1/6 |
#s(literal -1/6 binary64) |
(* eps eps) |
(*.f64 eps eps) |
(* (+ -1/2 (* 1/24 (* eps eps))) (* eps (* eps x))) |
(*.f64 (*.f64 eps eps) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))))) |
(+ -1/2 (* 1/24 (* eps eps))) |
(+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) |
-1/2 |
#s(literal -1/2 binary64) |
(* 1/24 (* eps eps)) |
(*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) |
1/24 |
#s(literal 1/24 binary64) |
(* eps (* eps x)) |
(*.f64 eps (*.f64 eps x)) |
(* eps x) |
(*.f64 eps x) |
x |
(* eps (+ (+ 1 (* -1/6 (* eps eps))) (* x (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps)))))))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/12 binary64))))) (*.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))))) (+.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) x) x) #s(literal 1 binary64)))))))) |
eps |
(+ (+ 1 (* -1/6 (* eps eps))) (* x (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps))))))))) |
(+.f64 #s(literal 1 binary64) (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/12 binary64))))) (*.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))))) (+.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) x) x) #s(literal 1 binary64))))))) |
(+ 1 (* -1/6 (* eps eps))) |
(+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) |
1 |
#s(literal 1 binary64) |
(* -1/6 (* eps eps)) |
(*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) |
-1/6 |
#s(literal -1/6 binary64) |
(* eps eps) |
(*.f64 eps eps) |
(* x (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps)))))))) |
(*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/12 binary64))))) (*.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))))) (+.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) x) x) #s(literal 1 binary64))))) |
x |
(+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps))))))) |
(+.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/12 binary64))))) (*.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))))) (+.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) x) x) #s(literal 1 binary64)))) |
(* eps (+ -1/2 (* 1/24 (* eps eps)))) |
(*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))))) |
(+ -1/2 (* 1/24 (* eps eps))) |
(+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) |
-1/2 |
#s(literal -1/2 binary64) |
(* 1/24 (* eps eps)) |
(*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) |
1/24 |
#s(literal 1/24 binary64) |
(* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps)))))) |
(*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/144 binary64))) x) (*.f64 eps #s(literal 1/12 binary64)))))) |
(+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps))))) |
(+.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 (*.f64 (+.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/144 binary64))) x) (*.f64 eps #s(literal 1/12 binary64))))) |
(+ -1/2 (* (* eps eps) 1/12)) |
(+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/12 binary64)))) |
(* (* eps eps) 1/12) |
(*.f64 eps (*.f64 eps #s(literal 1/12 binary64))) |
1/12 |
#s(literal 1/12 binary64) |
(* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps)))) |
(*.f64 (*.f64 eps x) (+.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/144 binary64)))) |
(* -1/6 (* eps x)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) |
(* eps x) |
(*.f64 eps x) |
(* (* (* eps (+ 1/2 (* (* eps eps) -1/48))) (cos (/ (+ eps (* x 2)) 2))) 2) |
(*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) #s(literal 2 binary64))) |
(* (* eps (+ 1/2 (* (* eps eps) -1/48))) (cos (/ (+ eps (* x 2)) 2))) |
(*.f64 eps (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(* eps (+ 1/2 (* (* eps eps) -1/48))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) |
eps |
(+ 1/2 (* (* eps eps) -1/48)) |
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))) |
1/2 |
#s(literal 1/2 binary64) |
(* (* eps eps) -1/48) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* eps eps) |
(*.f64 eps eps) |
-1/48 |
#s(literal -1/48 binary64) |
(cos (/ (+ eps (* x 2)) 2)) |
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
(/ (+ eps (* x 2)) 2) |
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) |
(+ eps (* x 2)) |
(+.f64 eps (*.f64 x #s(literal 2 binary64))) |
(* x 2) |
(*.f64 x #s(literal 2 binary64)) |
x |
2 |
#s(literal 2 binary64) |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 eps eps) |
| ✓ | accuracy | 100.0% | (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) |
| ✓ | accuracy | 99.9% | (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) |
| ✓ | accuracy | 99.7% | (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) |
| ✓ | accuracy | 99.7% | (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
| ✓ | accuracy | 99.7% | (*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) |
| ✓ | accuracy | 100.0% | (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps x))) |
| ✓ | accuracy | 99.8% | (*.f64 eps (*.f64 eps x)) |
| ✓ | accuracy | 99.7% | (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) |
| ✓ | accuracy | 99.7% | (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
| ✓ | accuracy | 99.8% | (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) |
| ✓ | accuracy | 99.8% | (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) |
| ✓ | accuracy | 99.4% | (*.f64 eps #s(literal 1/24 binary64)) |
| ✓ | accuracy | 99.4% | (*.f64 eps #s(literal -1/6 binary64)) |
| 407.0ms | 254× | 0 | valid |
| 7.0ms | 1× | 3 | valid |
| 3.0ms | 1× | 1 | valid |
Compiled 574 to 55 computations (90.4% saved)
ival-mult: 127.0ms (59.9% of total)ival-add: 37.0ms (17.4% of total)...c/correct-round.rkt:119:19: 27.0ms (12.7% of total)ival-cos: 9.0ms (4.2% of total)ival-div: 4.0ms (1.9% of total)ival-sin: 4.0ms (1.9% of total)const: 2.0ms (0.9% of total)backward-pass: 1.0ms (0.5% of total)| Inputs |
|---|
#<alt (+ (* (+ (* eps (* eps -1/6)) 1) (* (cos x) eps)) (* eps (* (sin x) (* eps (+ (* eps (* eps 1/24)) -1/2)))))> |
#<alt (* (+ (* eps (* eps -1/6)) 1) (* (cos x) eps))> |
#<alt (+ (* eps (* eps -1/6)) 1)> |
#<alt (* eps (* eps -1/6))> |
#<alt (+ (* eps (+ 1 (* -1/6 (* eps eps)))) (* (+ -1/2 (* 1/24 (* eps eps))) (* eps (* eps x))))> |
#<alt (* eps (+ 1 (* -1/6 (* eps eps))))> |
#<alt (+ 1 (* -1/6 (* eps eps)))> |
#<alt (* -1/6 (* eps eps))> |
#<alt (* eps (+ (+ 1 (* -1/6 (* eps eps))) (* x (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps))))))))))> |
#<alt (+ (+ 1 (* -1/6 (* eps eps))) (* x (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps)))))))))> |
#<alt (* x (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps))))))))> |
#<alt (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps)))))))> |
#<alt (* (* (* eps (+ 1/2 (* (* eps eps) -1/48))) (cos (/ (+ eps (* x 2)) 2))) 2)> |
#<alt (* (* eps (+ 1/2 (* (* eps eps) -1/48))) (cos (/ (+ eps (* x 2)) 2)))> |
#<alt (* eps (+ 1/2 (* (* eps eps) -1/48)))> |
#<alt (+ 1/2 (* (* eps eps) -1/48))> |
#<alt (* eps -1/6)> |
#<alt (* eps 1/24)> |
#<alt (* eps (* eps 1/24))> |
#<alt (* 1/24 (* eps eps))> |
#<alt (* eps (* eps x))> |
#<alt (* (+ -1/2 (* 1/24 (* eps eps))) (* eps (* eps x)))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* (* eps eps) 1/12)> |
#<alt (* (* eps eps) -1/48)> |
#<alt (cos (/ (+ eps (* x 2)) 2))> |
#<alt (* eps eps)> |
| Outputs |
|---|
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))> |
#<alt (* 1/24 (* (pow eps 4) (sin x)))> |
#<alt (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))> |
#<alt (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))> |
#<alt (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))> |
#<alt (* 1/24 (* (pow eps 4) (sin x)))> |
#<alt (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))> |
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))> |
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))> |
#<alt (+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))> |
#<alt (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))> |
#<alt (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (+ (* -1/2 (* eps (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* eps (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (* eps (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* (pow x 2) (+ (* -1/720 (* eps (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* 1/24 (* eps (+ 1 (* -1/6 (pow eps 2))))))))))> |
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt 1> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt eps> |
#<alt (* eps (+ 1 (* -1/2 (* eps x))))> |
#<alt (* eps (+ 1 (* eps (+ (* -1/2 x) (* -1/6 eps)))))> |
#<alt (* eps (+ 1 (* eps (+ (* -1/2 x) (* eps (- (* 1/24 (* eps x)) 1/6))))))> |
#<alt (* 1/24 (* (pow eps 4) x))> |
#<alt (* (pow eps 4) (- (* 1/24 x) (* 1/6 (/ 1 eps))))> |
#<alt (* (pow eps 4) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)) (* 1/6 (/ 1 eps))))> |
#<alt (* (pow eps 4) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (/ 1 (pow eps 3)))) (* 1/6 (/ 1 eps))))> |
#<alt (* 1/24 (* (pow eps 4) x))> |
#<alt (* (pow eps 4) (- (* 1/24 x) (* 1/6 (/ 1 eps))))> |
#<alt (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* 1/2 (/ x eps))) eps)) (* 1/24 x)))> |
#<alt (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* -1 (/ (+ (* -1/2 x) (/ 1 eps)) eps))) eps)) (* 1/24 x)))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* x (+ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)))> |
#<alt (* x (+ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)))> |
#<alt (* x (+ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)))> |
#<alt (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* -1 (* x (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)))))> |
#<alt (* -1 (* x (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)))))> |
#<alt (* -1 (* x (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)))))> |
#<alt eps> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* -1/6 (pow eps 3))> |
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#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))> |
#<alt 1> |
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#<alt (* -1/6 (pow eps 2))> |
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#<alt (* -1/6 (pow eps 2))> |
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#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
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#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2)))))))> |
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (+ (* 1/12 (pow x 2)) (* eps (* x (+ 1/24 (* -1/144 (pow x 2)))))) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2)))))))> |
#<alt (* (pow eps 4) (* x (+ 1/24 (* -1/144 (pow x 2)))))> |
#<alt (* (pow eps 4) (- (+ (* 1/12 (/ (pow x 2) eps)) (* x (+ 1/24 (* -1/144 (pow x 2))))) (* 1/6 (/ 1 eps))))> |
#<alt (* (pow eps 4) (- (+ (* 1/12 (/ (pow x 2) eps)) (+ (* x (+ 1/24 (* -1/144 (pow x 2)))) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (pow eps 2)))) (* 1/6 (/ 1 eps))))> |
#<alt (* (pow eps 4) (- (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/12 (/ (pow x 2) eps)) (+ (* x (+ 1/24 (* -1/144 (pow x 2)))) (+ (/ 1 (pow eps 3)) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (pow eps 2)))))) (* 1/6 (/ 1 eps))))> |
#<alt (* -1 (* (pow eps 4) (* x (- (* 1/144 (pow x 2)) 1/24))))> |
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#<alt (* (pow eps 4) (+ (* -1 (* x (- (* 1/144 (pow x 2)) 1/24))) (* -1 (/ (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))) eps))) eps))))> |
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#<alt (* (pow x 3) (+ (* -1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (+ (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 3)) (+ (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2))))))> |
#<alt (* -1/6 (* (pow eps 2) (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
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#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)) x)) (* 1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))) x)) (* 1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))))> |
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#<alt (* (pow eps 3) (- (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/12 (/ (pow x 2) eps)) (+ (* x (+ 1/24 (* -1/144 (pow x 2)))) (+ (/ 1 (pow eps 3)) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (pow eps 2)))))) (* 1/6 (/ 1 eps))))> |
#<alt (* -1 (* (pow eps 3) (* x (- (* 1/144 (pow x 2)) 1/24))))> |
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#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* x (- (* 1/144 (pow x 2)) 1/24)))))> |
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#<alt (* (pow x 3) (- (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (+ (* 1/12 (/ (pow eps 2) x)) (+ (/ 1 (pow x 3)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))))) (* 1/2 (/ 1 x))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
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#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2) x)) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x))) x)) (* 1/12 (pow eps 2))) 1/2) x)) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))))))> |
#<alt (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
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#<alt (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2))))> |
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#<alt (* (pow x 3) (- (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* 1/12 (/ (pow eps 2) x)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))) (* 1/2 (/ 1 x))))> |
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#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2) x)) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2) x)) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))))))> |
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#<alt (* (pow eps 3) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/12 (/ (pow x 2) eps)) (+ (* x (+ 1/24 (* -1/144 (pow x 2)))) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (pow eps 2))))))> |
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#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) eps)) (* 1/12 (pow x 2))) eps)) (* x (- (* 1/144 (pow x 2)) 1/24)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))) eps)) (* 1/12 (pow x 2))) eps)) (* x (- (* 1/144 (pow x 2)) 1/24)))))> |
#<alt (* -1/2 x)> |
#<alt (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))> |
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#<alt (* (pow eps 3) (+ 1/24 (* -1/144 (pow x 2))))> |
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#<alt (* (pow eps 3) (- (+ 1/24 (+ (* -1/2 (/ x (pow eps 3))) (+ (* -1/144 (pow x 2)) (+ (* 1/12 (/ x eps)) (* 1/12 (/ (pow x 2) (pow eps 2))))))) (/ 1/2 (pow eps 2))))> |
#<alt (* -1 (* (pow eps 3) (- (* 1/144 (pow x 2)) 1/24)))> |
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#<alt (* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/12 (pow x 2))) eps)) (* 1/12 x)) eps)) (* 1/144 (pow x 2))) 1/24)))> |
#<alt (* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/12 x)) eps)) (* 1/144 (pow x 2))) 1/24)))> |
#<alt (* eps (- (* 1/24 (pow eps 2)) 1/2))> |
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#<alt (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2)))> |
#<alt (* -1/6 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2))))> |
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#<alt (* (pow x 2) (- (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* 1/12 (/ (pow eps 2) x)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))) (* 1/2 (/ 1 x))))> |
#<alt (* (pow x 2) (- (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* 1/12 (/ (pow eps 2) x)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))) (* 1/2 (/ 1 x))))> |
#<alt (* -1/6 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2))))> |
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#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
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#<alt (* -1/24 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x))))))> |
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#<alt (* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))> |
#<alt (* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))> |
#<alt (* -1/24 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))> |
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))> |
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 1/2 (* eps (cos x)))> |
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))> |
#<alt (* -1/48 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))> |
#<alt (* -1/48 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))> |
#<alt (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))> |
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))))> |
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* -1/48 (pow eps 3))> |
#<alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))> |
#<alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))> |
#<alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))> |
#<alt (* -1/48 (pow eps 3))> |
#<alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))> |
#<alt 1/2> |
#<alt (+ 1/2 (* -1/48 (pow eps 2)))> |
#<alt (+ 1/2 (* -1/48 (pow eps 2)))> |
#<alt (+ 1/2 (* -1/48 (pow eps 2)))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))> |
#<alt (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))> |
#<alt (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))> |
#<alt (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))> |
#<alt (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* -1/6 eps)> |
#<alt (* 1/24 eps)> |
#<alt (* 1/24 eps)> |
#<alt (* 1/24 eps)> |
#<alt (* 1/24 eps)> |
#<alt (* 1/24 eps)> |
#<alt (* 1/24 eps)> |
#<alt (* 1/24 eps)> |
#<alt (* 1/24 eps)> |
#<alt (* 1/24 eps)> |
#<alt (* 1/24 eps)> |
#<alt (* 1/24 eps)> |
#<alt (* 1/24 eps)> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* (pow eps 2) x)> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (* 1/24 (* (pow eps 2) x))))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (* 1/24 (* (pow eps 2) x))))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (* 1/24 (* (pow eps 2) x))))> |
#<alt (* 1/24 (* (pow eps 4) x))> |
#<alt (* (pow eps 4) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)))> |
#<alt (* (pow eps 4) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)))> |
#<alt (* (pow eps 4) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)))> |
#<alt (* 1/24 (* (pow eps 4) x))> |
#<alt (* (pow eps 4) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)))> |
#<alt (* (pow eps 4) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)))> |
#<alt (* (pow eps 4) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)))> |
#<alt (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* -1/6 (* eps x))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* 1/12 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))> |
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))> |
#<alt (cos (* 1/2 eps))> |
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
120 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 15.0ms | eps | @ | -inf | (* eps (+ (+ 1 (* -1/6 (* eps eps))) (* x (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps)))))))))) |
| 5.0ms | x | @ | inf | (+ (+ 1 (* -1/6 (* eps eps))) (* x (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps))))))))) |
| 3.0ms | x | @ | inf | (* (* (* eps (+ 1/2 (* (* eps eps) -1/48))) (cos (/ (+ eps (* x 2)) 2))) 2) |
| 3.0ms | eps | @ | inf | (* (* (* eps (+ 1/2 (* (* eps eps) -1/48))) (cos (/ (+ eps (* x 2)) 2))) 2) |
| 2.0ms | x | @ | -inf | (* (* (* eps (+ 1/2 (* (* eps eps) -1/48))) (cos (/ (+ eps (* x 2)) 2))) 2) |
| 1× | batch-egg-rewrite |
| 3560× | *-lowering-*.f32 |
| 3560× | *-lowering-*.f64 |
| 1894× | pow-lowering-pow.f64 |
| 1894× | pow-lowering-pow.f32 |
| 1390× | fma-lowering-fma.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 54 | 336 |
| 1 | 344 | 319 |
| 2 | 3463 | 319 |
| 0 | 8210 | 319 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ (* (+ (* eps (* eps -1/6)) 1) (* (cos x) eps)) (* eps (* (sin x) (* eps (+ (* eps (* eps 1/24)) -1/2))))) |
(* (+ (* eps (* eps -1/6)) 1) (* (cos x) eps)) |
(+ (* eps (* eps -1/6)) 1) |
(* eps (* eps -1/6)) |
(+ (* eps (+ 1 (* -1/6 (* eps eps)))) (* (+ -1/2 (* 1/24 (* eps eps))) (* eps (* eps x)))) |
(* eps (+ 1 (* -1/6 (* eps eps)))) |
(+ 1 (* -1/6 (* eps eps))) |
(* -1/6 (* eps eps)) |
(* eps (+ (+ 1 (* -1/6 (* eps eps))) (* x (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps)))))))))) |
(+ (+ 1 (* -1/6 (* eps eps))) (* x (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps))))))))) |
(* x (+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps)))))))) |
(+ (* eps (+ -1/2 (* 1/24 (* eps eps)))) (* x (+ (+ -1/2 (* (* eps eps) 1/12)) (* (* -1/6 (* eps x)) (+ -1/2 (* 1/24 (* eps eps))))))) |
(* (* (* eps (+ 1/2 (* (* eps eps) -1/48))) (cos (/ (+ eps (* x 2)) 2))) 2) |
(* (* eps (+ 1/2 (* (* eps eps) -1/48))) (cos (/ (+ eps (* x 2)) 2))) |
(* eps (+ 1/2 (* (* eps eps) -1/48))) |
(+ 1/2 (* (* eps eps) -1/48)) |
(* eps -1/6) |
(* eps 1/24) |
(* eps (* eps 1/24)) |
(* 1/24 (* eps eps)) |
(* eps (* eps x)) |
(* (+ -1/2 (* 1/24 (* eps eps))) (* eps (* eps x))) |
(* -1/6 (* eps x)) |
(* (* eps eps) 1/12) |
(* (* eps eps) -1/48) |
(cos (/ (+ eps (* x 2)) 2)) |
(* eps eps) |
| Outputs |
|---|
(+.f64 (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(+.f64 (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))) (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) #s(literal 2 binary64)) (*.f64 eps (-.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) (/.f64 (pow.f64 (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))) #s(literal 2 binary64)) (*.f64 eps (-.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (sin.f64 x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))) |
(fma.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))) (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))) |
(fma.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(fma.f64 (*.f64 (sin.f64 x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))) eps (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))) |
(fma.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) (*.f64 eps (cos.f64 x)) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(fma.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) eps (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(fma.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))) |
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(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) (-.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/110592 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/2304 binary64))))) |
(/.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/110592 binary64)))) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) (-.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))) |
(/.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/110592 binary64)))) (+.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/2304 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/96 binary64) (*.f64 eps eps))))) |
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/2304 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))))) |
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/110592 binary64))))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) (-.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/2304 binary64)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/2304 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) #s(literal 1/2 binary64))) |
(pow.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) (-.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/110592 binary64))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/2304 binary64)))) #s(literal -1 binary64)) |
(*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/110592 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) (-.f64 (*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))))) |
(*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/2304 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))))) |
(*.f64 eps #s(literal -1/6 binary64)) |
(*.f64 #s(literal -1/6 binary64) eps) |
(*.f64 eps #s(literal 1/24 binary64)) |
(*.f64 #s(literal 1/24 binary64) eps) |
(*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) |
(*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 eps #s(literal 1/24 binary64)) eps) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) |
(*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 eps #s(literal 1/24 binary64)) eps) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(*.f64 eps (*.f64 eps x)) |
(*.f64 x (*.f64 eps eps)) |
(*.f64 (*.f64 eps eps) x) |
(*.f64 (*.f64 eps x) eps) |
(+.f64 (*.f64 (*.f64 x (*.f64 eps eps)) #s(literal -1/2 binary64)) (*.f64 (*.f64 x (*.f64 eps eps)) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) |
(+.f64 (*.f64 (*.f64 x (*.f64 eps eps)) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 eps eps)) #s(literal -1/2 binary64))) |
(+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps))) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 eps eps)))) |
(+.f64 (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 eps eps))) (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps eps)))) |
(/.f64 (*.f64 (*.f64 x (*.f64 eps eps)) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/13824 binary64))))) (+.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/576 binary64)))) |
(/.f64 (*.f64 (*.f64 x (*.f64 eps eps)) (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/13824 binary64))))) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))))) |
(/.f64 (*.f64 (*.f64 x (*.f64 eps eps)) (+.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/576 binary64)) #s(literal -1/4 binary64))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (*.f64 x (*.f64 eps eps)) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/576 binary64)))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/24 binary64) (*.f64 eps eps)))) |
(/.f64 (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/13824 binary64)))) (*.f64 x (*.f64 eps eps))) (+.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 eps (*.f64 eps #s(literal -1/48 binary64)))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/576 binary64)))) |
(/.f64 (*.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/13824 binary64)))) (*.f64 x (*.f64 eps eps))) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))))) |
(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/576 binary64)) #s(literal -1/4 binary64)) (*.f64 x (*.f64 eps eps))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/576 binary64))) (*.f64 x (*.f64 eps eps))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/24 binary64) (*.f64 eps eps)))) |
(*.f64 eps (*.f64 eps (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))) |
(*.f64 (*.f64 eps eps) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))) |
(*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 eps eps))) |
(*.f64 (*.f64 eps x) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))) |
(*.f64 (*.f64 x (*.f64 eps eps)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) |
(*.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 eps x)) |
(*.f64 (*.f64 eps (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))) eps) |
(*.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps eps)) x) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) eps) x) |
(*.f64 eps (*.f64 x #s(literal -1/6 binary64))) |
(*.f64 eps (*.f64 #s(literal -1/6 binary64) x)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) x) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(*.f64 (*.f64 eps x) #s(literal -1/6 binary64)) |
(*.f64 (*.f64 #s(literal -1/6 binary64) x) eps) |
(*.f64 eps (*.f64 eps #s(literal 1/12 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) |
(*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 eps #s(literal 1/12 binary64)) eps) |
(*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) |
(*.f64 eps (*.f64 (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) |
(*.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 eps #s(literal 1/24 binary64)) (*.f64 eps #s(literal -1/2 binary64))) |
(*.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(*.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)) |
(*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal 1/24 binary64))) |
(*.f64 (*.f64 eps #s(literal -1/48 binary64)) eps) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps #s(literal 1/24 binary64))) eps) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) |
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) |
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal -2 binary64))) |
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64))) |
(pow.f64 eps #s(literal 2 binary64)) |
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64)) |
(*.f64 eps eps) |
(*.f64 #s(literal 1 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 eps eps) #s(literal 1 binary64)) |
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps))) |
| 1× | egg-herbie |
| 7938× | *-lowering-*.f32 |
| 7938× | *-lowering-*.f64 |
| 4352× | +-lowering-+.f64 |
| 4352× | +-lowering-+.f32 |
| 1604× | associate-*r* |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 694 | 6691 |
| 1 | 2480 | 6360 |
| 0 | 8717 | 6360 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* 1/24 (* (pow eps 4) (sin x))) |
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))) |
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))) |
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3)))))) |
(* 1/24 (* (pow eps 4) (sin x))) |
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x)))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x)))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) |
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) |
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x))))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(+ (* -1/2 (* eps (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (* eps (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* (pow x 2) (+ (* -1/720 (* eps (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* 1/24 (* eps (+ 1 (* -1/6 (pow eps 2)))))))))) |
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
1 |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (* -1/6 (pow eps 2))) |
(* -1/6 (pow eps 2)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* -1/6 (pow eps 2)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
eps |
(* eps (+ 1 (* -1/2 (* eps x)))) |
(* eps (+ 1 (* eps (+ (* -1/2 x) (* -1/6 eps))))) |
(* eps (+ 1 (* eps (+ (* -1/2 x) (* eps (- (* 1/24 (* eps x)) 1/6)))))) |
(* 1/24 (* (pow eps 4) x)) |
(* (pow eps 4) (- (* 1/24 x) (* 1/6 (/ 1 eps)))) |
(* (pow eps 4) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)) (* 1/6 (/ 1 eps)))) |
(* (pow eps 4) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (/ 1 (pow eps 3)))) (* 1/6 (/ 1 eps)))) |
(* 1/24 (* (pow eps 4) x)) |
(* (pow eps 4) (- (* 1/24 x) (* 1/6 (/ 1 eps)))) |
(* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* 1/2 (/ x eps))) eps)) (* 1/24 x))) |
(* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* -1 (/ (+ (* -1/2 x) (/ 1 eps)) eps))) eps)) (* 1/24 x))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* x (+ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x))) |
(* x (+ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x))) |
(* x (+ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* -1 (* x (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x))))) |
(* -1 (* x (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x))))) |
(* -1 (* x (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x))))) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* -1/6 (pow eps 3)) |
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)) |
(* -1/6 (pow eps 3)) |
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))) |
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))) |
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))) |
1 |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (* -1/6 (pow eps 2))) |
(* -1/6 (pow eps 2)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* -1/6 (pow eps 2)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))) |
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2))))))) |
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (+ (* 1/12 (pow x 2)) (* eps (* x (+ 1/24 (* -1/144 (pow x 2)))))) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2))))))) |
(* (pow eps 4) (* x (+ 1/24 (* -1/144 (pow x 2))))) |
(* (pow eps 4) (- (+ (* 1/12 (/ (pow x 2) eps)) (* x (+ 1/24 (* -1/144 (pow x 2))))) (* 1/6 (/ 1 eps)))) |
(* (pow eps 4) (- (+ (* 1/12 (/ (pow x 2) eps)) (+ (* x (+ 1/24 (* -1/144 (pow x 2)))) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (pow eps 2)))) (* 1/6 (/ 1 eps)))) |
(* (pow eps 4) (- (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/12 (/ (pow x 2) eps)) (+ (* x (+ 1/24 (* -1/144 (pow x 2)))) (+ (/ 1 (pow eps 3)) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (pow eps 2)))))) (* 1/6 (/ 1 eps)))) |
(* -1 (* (pow eps 4) (* x (- (* 1/144 (pow x 2)) 1/24)))) |
(* (pow eps 4) (- (+ (* -1 (* x (- (* 1/144 (pow x 2)) 1/24))) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps)))) |
(* (pow eps 4) (+ (* -1 (* x (- (* 1/144 (pow x 2)) 1/24))) (* -1 (/ (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) eps)) eps)))) |
(* (pow eps 4) (+ (* -1 (* x (- (* 1/144 (pow x 2)) 1/24))) (* -1 (/ (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))) eps))) eps)))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/12 (pow eps 2)) 1/2)))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))) |
(* -1/6 (* (pow eps 2) (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* (pow x 3) (+ (* -1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x))) |
(* (pow x 3) (+ (* -1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (+ (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2))))) |
(* (pow x 3) (+ (* -1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (+ (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 3)) (+ (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))))) |
(* -1/6 (* (pow eps 2) (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (* eps (- (* 1/12 (pow eps 2)) 1/2)) x)) (* 1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)) x)) (* 1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))) x)) (* 1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (* 1/12 (pow x 2)) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2)))))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* eps (- (+ (* 1/12 (pow x 2)) (* eps (* x (+ 1/24 (* -1/144 (pow x 2)))))) 1/6)) (* x (- (* 1/12 (pow x 2)) 1/2)))))) |
(* (pow eps 3) (* x (+ 1/24 (* -1/144 (pow x 2))))) |
(* (pow eps 3) (- (+ (* 1/12 (/ (pow x 2) eps)) (* x (+ 1/24 (* -1/144 (pow x 2))))) (* 1/6 (/ 1 eps)))) |
(* (pow eps 3) (- (+ (* 1/12 (/ (pow x 2) eps)) (+ (* x (+ 1/24 (* -1/144 (pow x 2)))) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (pow eps 2)))) (* 1/6 (/ 1 eps)))) |
(* (pow eps 3) (- (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/12 (/ (pow x 2) eps)) (+ (* x (+ 1/24 (* -1/144 (pow x 2)))) (+ (/ 1 (pow eps 3)) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (pow eps 2)))))) (* 1/6 (/ 1 eps)))) |
(* -1 (* (pow eps 3) (* x (- (* 1/144 (pow x 2)) 1/24)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* x (- (* 1/144 (pow x 2)) 1/24))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* x (- (* 1/144 (pow x 2)) 1/24))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* x (- (* 1/144 (pow x 2)) 1/24))))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2))))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2)))))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2)))))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* (pow x 3) (- (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(* (pow x 3) (- (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* 1/12 (/ (pow eps 2) x)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))) (* 1/2 (/ 1 x)))) |
(* (pow x 3) (- (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (+ (* 1/12 (/ (pow eps 2) x)) (+ (/ 1 (pow x 3)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))))) (* 1/2 (/ 1 x)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2) x)) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x))) x)) (* 1/12 (pow eps 2))) 1/2) x)) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))) |
(* eps (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2)))) |
(* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2)))) |
(* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* (pow x 3) (- (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(* (pow x 3) (- (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* 1/12 (/ (pow eps 2) x)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))) (* 1/2 (/ 1 x)))) |
(* (pow x 3) (- (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* 1/12 (/ (pow eps 2) x)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))) (* 1/2 (/ 1 x)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* 1/12 (pow eps 2)) 1/2) x)) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2) x)) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2) x)) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))) |
(* -1/2 (pow x 2)) |
(+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))) |
(+ (* -1/2 (pow x 2)) (* eps (+ (* 1/12 (* eps (pow x 2))) (* x (- (* 1/12 (pow x 2)) 1/2))))) |
(+ (* -1/2 (pow x 2)) (* eps (+ (* eps (+ (* 1/12 (pow x 2)) (* eps (* x (+ 1/24 (* -1/144 (pow x 2))))))) (* x (- (* 1/12 (pow x 2)) 1/2))))) |
(* (pow eps 3) (* x (+ 1/24 (* -1/144 (pow x 2))))) |
(* (pow eps 3) (+ (* 1/12 (/ (pow x 2) eps)) (* x (+ 1/24 (* -1/144 (pow x 2)))))) |
(* (pow eps 3) (+ (* 1/12 (/ (pow x 2) eps)) (+ (* x (+ 1/24 (* -1/144 (pow x 2)))) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/12 (/ (pow x 2) eps)) (+ (* x (+ 1/24 (* -1/144 (pow x 2)))) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (pow eps 2)))))) |
(* -1 (* (pow eps 3) (* x (- (* 1/144 (pow x 2)) 1/24)))) |
(* -1 (* (pow eps 3) (+ (* -1/12 (/ (pow x 2) eps)) (* x (- (* 1/144 (pow x 2)) 1/24))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) eps)) (* 1/12 (pow x 2))) eps)) (* x (- (* 1/144 (pow x 2)) 1/24))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (/ (pow x 2) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))) eps)) (* 1/12 (pow x 2))) eps)) (* x (- (* 1/144 (pow x 2)) 1/24))))) |
(* -1/2 x) |
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2))) |
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2))) |
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (pow x 2)) (* eps (+ (* 1/12 x) (* eps (+ 1/24 (* -1/144 (pow x 2))))))) 1/2))) |
(* (pow eps 3) (+ 1/24 (* -1/144 (pow x 2)))) |
(* (pow eps 3) (+ 1/24 (+ (* -1/144 (pow x 2)) (* 1/12 (/ x eps))))) |
(* (pow eps 3) (- (+ 1/24 (+ (* -1/144 (pow x 2)) (+ (* 1/12 (/ x eps)) (* 1/12 (/ (pow x 2) (pow eps 2)))))) (/ 1/2 (pow eps 2)))) |
(* (pow eps 3) (- (+ 1/24 (+ (* -1/2 (/ x (pow eps 3))) (+ (* -1/144 (pow x 2)) (+ (* 1/12 (/ x eps)) (* 1/12 (/ (pow x 2) (pow eps 2))))))) (/ 1/2 (pow eps 2)))) |
(* -1 (* (pow eps 3) (- (* 1/144 (pow x 2)) 1/24))) |
(* -1 (* (pow eps 3) (- (+ (* -1/12 (/ x eps)) (* 1/144 (pow x 2))) 1/24))) |
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (* -1/12 (pow x 2))) eps)) (* 1/12 x)) eps)) (* 1/144 (pow x 2))) 1/24))) |
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/12 x)) eps)) (* 1/144 (pow x 2))) 1/24))) |
(* eps (- (* 1/24 (pow eps 2)) 1/2)) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2))) |
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/12 (pow eps 2))) 1/2))) |
(* -1/6 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* (pow x 2) (- (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(* (pow x 2) (- (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* 1/12 (/ (pow eps 2) x)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))) (* 1/2 (/ 1 x)))) |
(* (pow x 2) (- (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* 1/12 (/ (pow eps 2) x)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (pow x 2)))) (* 1/2 (/ 1 x)))) |
(* -1/6 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* (pow x 2) (- (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* -1 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) x)) (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(* -1/24 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x)))))) |
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))) |
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))) |
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))) |
(* -1/24 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(* -1/48 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x)))))) |
(* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))) |
(* -1/48 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) |
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))))) |
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* -1/48 (pow eps 3)) |
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) |
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) |
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) |
(* -1/48 (pow eps 3)) |
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2)))))) |
1/2 |
(+ 1/2 (* -1/48 (pow eps 2))) |
(+ 1/2 (* -1/48 (pow eps 2))) |
(+ 1/2 (* -1/48 (pow eps 2))) |
(* -1/48 (pow eps 2)) |
(* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) |
(* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) |
(* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) |
(* -1/48 (pow eps 2)) |
(* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) |
(* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) |
(* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* -1/6 eps) |
(* 1/24 eps) |
(* 1/24 eps) |
(* 1/24 eps) |
(* 1/24 eps) |
(* 1/24 eps) |
(* 1/24 eps) |
(* 1/24 eps) |
(* 1/24 eps) |
(* 1/24 eps) |
(* 1/24 eps) |
(* 1/24 eps) |
(* 1/24 eps) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* (pow eps 2) x) |
(* -1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1/2 x) (* 1/24 (* (pow eps 2) x)))) |
(* (pow eps 2) (+ (* -1/2 x) (* 1/24 (* (pow eps 2) x)))) |
(* (pow eps 2) (+ (* -1/2 x) (* 1/24 (* (pow eps 2) x)))) |
(* 1/24 (* (pow eps 4) x)) |
(* (pow eps 4) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x))) |
(* (pow eps 4) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x))) |
(* (pow eps 4) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x))) |
(* 1/24 (* (pow eps 4) x)) |
(* (pow eps 4) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x))) |
(* (pow eps 4) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x))) |
(* (pow eps 4) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* -1/6 (* eps x)) |
(* 1/12 (pow eps 2)) |
(* 1/12 (pow eps 2)) |
(* 1/12 (pow eps 2)) |
(* 1/12 (pow eps 2)) |
(* 1/12 (pow eps 2)) |
(* 1/12 (pow eps 2)) |
(* 1/12 (pow eps 2)) |
(* 1/12 (pow eps 2)) |
(* 1/12 (pow eps 2)) |
(* 1/12 (pow eps 2)) |
(* 1/12 (pow eps 2)) |
(* 1/12 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* 1/2 eps)) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
| Outputs |
|---|
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (+.f64 (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))))) |
(* 1/24 (* (pow eps 4) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))) |
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (/.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps) (*.f64 (sin.f64 x) #s(literal 1/24 binary64)))) |
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (/.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps) (+.f64 (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps eps))))) |
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3)))))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (+.f64 (/.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps) (*.f64 (sin.f64 x) #s(literal 1/24 binary64))) (+.f64 (/.f64 (cos.f64 x) (*.f64 eps (*.f64 eps eps))) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps eps))))) |
(* 1/24 (* (pow eps 4) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))) |
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (/.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps) (*.f64 (sin.f64 x) #s(literal 1/24 binary64)))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x)))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (/.f64 (+.f64 (*.f64 (cos.f64 x) #s(literal 1/6 binary64)) (/.f64 (*.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)) eps))) |
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x)))) |
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (/.f64 (-.f64 (*.f64 (cos.f64 x) #s(literal 1/6 binary64)) (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps)) eps)) eps))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (*.f64 eps eps) (*.f64 x (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 x (+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) (*.f64 x (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))))))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+.f64 (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+.f64 (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+.f64 (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+.f64 (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+.f64 (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+.f64 (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+.f64 (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+ (* eps (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 2) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) |
(+.f64 (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) |
(*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) |
(*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) |
(*.f64 (*.f64 eps (cos.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) |
(* -1/6 (* (pow eps 3) (cos x))) |
(*.f64 (cos.f64 x) (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps)))) |
(* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (/.f64 (cos.f64 x) (*.f64 eps eps)))) |
(* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (/.f64 (cos.f64 x) (*.f64 eps eps)))) |
(* (pow eps 3) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
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(* 1/2 (* eps (cos x))) |
(*.f64 (*.f64 eps (cos.f64 x)) #s(literal 1/2 binary64)) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
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(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
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(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(*.f64 (*.f64 eps eps) (*.f64 x (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))) |
(* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))) |
(*.f64 (*.f64 eps eps) (*.f64 x (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* -1/6 (* eps x)) |
(*.f64 x (*.f64 eps #s(literal -1/6 binary64))) |
(* 1/12 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) |
(* 1/12 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) |
(* 1/12 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) |
(* 1/12 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) |
(* 1/12 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) |
(* 1/12 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) |
(* 1/12 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) |
(* 1/12 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) |
(* 1/12 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) |
(* 1/12 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) |
(* 1/12 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) |
(* 1/12 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 (sin.f64 x) (*.f64 eps #s(literal 1/48 binary64))) (*.f64 (cos.f64 x) #s(literal -1/8 binary64)))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 eps)) |
(cos.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(-.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (-.f64 (*.f64 (*.f64 x #s(literal -1/2 binary64)) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (-.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
Compiled 41187 to 2309 computations (94.4% saved)
18 alts after pruning (16 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1025 | 13 | 1038 |
| Fresh | 7 | 3 | 10 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 0 | 0 |
| Total | 1035 | 18 | 1053 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | (+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) |
| 98.9% | (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 (*.f64 eps x) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) | |
| 99.8% | (+.f64 (*.f64 eps (cos.f64 x)) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) | |
| 99.8% | (*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| ▶ | 99.9% | (*.f64 (*.f64 eps (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))) #s(literal 2 binary64)) |
| 98.8% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) | |
| 98.8% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 eps (+.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))))) | |
| 98.7% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/6 binary64))) (/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) x))))) | |
| ▶ | 98.2% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
| 98.8% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))))) | |
| 98.8% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 eps x))) #s(literal -1/2 binary64))))))) | |
| ▶ | 100.0% | (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
| 99.8% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) | |
| ▶ | 98.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
| ▶ | 27.2% | (*.f64 eps (*.f64 (-.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/144 binary64))) #s(literal -1/24 binary64))) (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) (/.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps)) #s(literal -1/6 binary64)) eps)) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
| 29.7% | (*.f64 eps (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 #s(literal -1/6 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x x))))) (+.f64 (+.f64 (/.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) x))) (/.f64 #s(literal -1/2 binary64) x))))) | |
| 99.4% | (*.f64 eps (cos.f64 x)) | |
| ✓ | 98.2% | eps |
Compiled 918 to 564 computations (38.6% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 eps (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 eps (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))) #s(literal 2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/144 binary64))) #s(literal -1/24 binary64))) |
| ✓ | cost-diff | 0 | (-.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/144 binary64))) #s(literal -1/24 binary64))) (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) (/.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps)) #s(literal -1/6 binary64)) eps)) |
| ✓ | cost-diff | 0 | (*.f64 (-.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/144 binary64))) #s(literal -1/24 binary64))) (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) (/.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps)) #s(literal -1/6 binary64)) eps)) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps)))) |
| ✓ | cost-diff | 0 | (*.f64 eps (*.f64 (-.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/144 binary64))) #s(literal -1/24 binary64))) (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) (/.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps)) #s(literal -1/6 binary64)) eps)) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) |
| ✓ | cost-diff | 128 | (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) |
| ✓ | cost-diff | 256 | (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))) |
| ✓ | cost-diff | 256 | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
| ✓ | cost-diff | 0 | (*.f64 x #s(literal -1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
| ✓ | cost-diff | 0 | (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
| ✓ | cost-diff | 0 | (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) |
| ✓ | cost-diff | 0 | (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
| ✓ | cost-diff | 0 | (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
| 4852× | *-lowering-*.f32 |
| 4852× | *-lowering-*.f64 |
| 3134× | +-lowering-+.f64 |
| 3134× | +-lowering-+.f32 |
| 1478× | sum5-define |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 66 | 629 |
| 1 | 211 | 596 |
| 2 | 689 | 587 |
| 3 | 2823 | 587 |
| 4 | 6563 | 587 |
| 0 | 8369 | 587 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* -1/2 (* eps (sin x))))) |
eps |
(+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* -1/2 (* eps (sin x)))) |
(* (+ (* (* eps eps) -1/6) 1) (cos x)) |
(+ (* (* eps eps) -1/6) 1) |
(* (* eps eps) -1/6) |
(* eps eps) |
-1/6 |
1 |
(cos x) |
x |
(* -1/2 (* eps (sin x))) |
-1/2 |
(* eps (sin x)) |
(sin x) |
(* eps (+ 1 (* x (* x -1/2)))) |
eps |
(+ 1 (* x (* x -1/2))) |
1 |
(* x (* x -1/2)) |
x |
(* x -1/2) |
-1/2 |
(* eps (+ (+ 1 (* -1/6 (* eps eps))) (* (* -1/6 (* eps (* x (* x x)))) (+ (* 1/24 (* eps eps)) -1/2)))) |
eps |
(+ (+ 1 (* -1/6 (* eps eps))) (* (* -1/6 (* eps (* x (* x x)))) (+ (* 1/24 (* eps eps)) -1/2))) |
(+ 1 (* -1/6 (* eps eps))) |
1 |
(* -1/6 (* eps eps)) |
-1/6 |
(* eps eps) |
(* (* -1/6 (* eps (* x (* x x)))) (+ (* 1/24 (* eps eps)) -1/2)) |
(* -1/6 (* eps (* x (* x x)))) |
(* eps (* x (* x x))) |
(* x (* x x)) |
x |
(* x x) |
(+ (* 1/24 (* eps eps)) -1/2) |
(* 1/24 (* eps eps)) |
1/24 |
-1/2 |
(* eps (* (- (* x (+ (* x (* x 1/144)) -1/24)) (/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps)) (* -1 (* eps (* eps eps))))) |
eps |
(* (- (* x (+ (* x (* x 1/144)) -1/24)) (/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps)) (* -1 (* eps (* eps eps)))) |
(- (* x (+ (* x (* x 1/144)) -1/24)) (/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps)) |
(* x (+ (* x (* x 1/144)) -1/24)) |
x |
(+ (* x (* x 1/144)) -1/24) |
(* x (* x 1/144)) |
(* x 1/144) |
1/144 |
-1/24 |
(/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps) |
(+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) |
(- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) |
(* (* x x) 1/12) |
(* x x) |
1/12 |
(/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps) |
(- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) |
(* x (+ 1/2 (* (* x x) -1/12))) |
(+ 1/2 (* (* x x) -1/12)) |
1/2 |
(* (* x x) -1/12) |
-1/12 |
(/ (+ 1 (* x (* x -1/2))) eps) |
(+ 1 (* x (* x -1/2))) |
1 |
(* x (* x -1/2)) |
(* x -1/2) |
-1/2 |
-1/6 |
(* -1 (* eps (* eps eps))) |
-1 |
(* eps (* eps eps)) |
(* eps eps) |
(* (* eps (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) -1/48)))) 2) |
(* eps (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) -1/48)))) |
eps |
(* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) -1/48))) |
(cos (+ x (* eps 1/2))) |
(+ x (* eps 1/2)) |
x |
(* eps 1/2) |
1/2 |
(+ 1/2 (* (* eps eps) -1/48)) |
(* (* eps eps) -1/48) |
(* eps eps) |
-1/48 |
2 |
| Outputs |
|---|
(* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
eps |
(+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* -1/2 (* eps (sin x)))) |
(+.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(* (+ (* (* eps eps) -1/6) 1) (cos x)) |
(*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
(+ (* (* eps eps) -1/6) 1) |
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) |
(* (* eps eps) -1/6) |
(*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) |
(* eps eps) |
(*.f64 eps eps) |
-1/6 |
#s(literal -1/6 binary64) |
1 |
#s(literal 1 binary64) |
(cos x) |
(cos.f64 x) |
x |
(* -1/2 (* eps (sin x))) |
(*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) |
-1/2 |
#s(literal -1/2 binary64) |
(* eps (sin x)) |
(*.f64 eps (sin.f64 x)) |
(sin x) |
(sin.f64 x) |
(* eps (+ 1 (* x (* x -1/2)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
eps |
(+ 1 (* x (* x -1/2))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
1 |
#s(literal 1 binary64) |
(* x (* x -1/2)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
x |
(* x -1/2) |
(*.f64 x #s(literal -1/2 binary64)) |
-1/2 |
#s(literal -1/2 binary64) |
(* eps (+ (+ 1 (* -1/6 (* eps eps))) (* (* -1/6 (* eps (* x (* x x)))) (+ (* 1/24 (* eps eps)) -1/2)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/144 binary64)))))))) |
eps |
(+ (+ 1 (* -1/6 (* eps eps))) (* (* -1/6 (* eps (* x (* x x)))) (+ (* 1/24 (* eps eps)) -1/2))) |
(+.f64 #s(literal 1 binary64) (*.f64 eps (+.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/144 binary64))))))) |
(+ 1 (* -1/6 (* eps eps))) |
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) |
1 |
#s(literal 1 binary64) |
(* -1/6 (* eps eps)) |
(*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) |
-1/6 |
#s(literal -1/6 binary64) |
(* eps eps) |
(*.f64 eps eps) |
(* (* -1/6 (* eps (* x (* x x)))) (+ (* 1/24 (* eps eps)) -1/2)) |
(*.f64 (*.f64 x x) (*.f64 (*.f64 eps x) (+.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/144 binary64))))) |
(* -1/6 (* eps (* x (* x x)))) |
(*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)))) |
(* eps (* x (* x x))) |
(*.f64 eps (*.f64 x (*.f64 x x))) |
(* x (* x x)) |
(*.f64 x (*.f64 x x)) |
x |
(* x x) |
(*.f64 x x) |
(+ (* 1/24 (* eps eps)) -1/2) |
(+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) |
(* 1/24 (* eps eps)) |
(*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) |
1/24 |
#s(literal 1/24 binary64) |
-1/2 |
#s(literal -1/2 binary64) |
(* eps (* (- (* x (+ (* x (* x 1/144)) -1/24)) (/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps)) (* -1 (* eps (* eps eps))))) |
(-.f64 #s(literal 0 binary64) (*.f64 (+.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/144 binary64)) #s(literal -1/24 binary64))) (/.f64 (+.f64 (/.f64 (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/12 binary64)) #s(literal 1/6 binary64))) eps)) (*.f64 eps (*.f64 eps (*.f64 eps eps))))) |
eps |
(* (- (* x (+ (* x (* x 1/144)) -1/24)) (/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps)) (* -1 (* eps (* eps eps)))) |
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/144 binary64)) #s(literal -1/24 binary64))) (/.f64 (+.f64 (/.f64 (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/12 binary64)) #s(literal 1/6 binary64))) eps))))) |
(- (* x (+ (* x (* x 1/144)) -1/24)) (/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps)) |
(+.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/144 binary64)) #s(literal -1/24 binary64))) (/.f64 (+.f64 (/.f64 (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps) (+.f64 (*.f64 (*.f64 x x) #s(literal -1/12 binary64)) #s(literal 1/6 binary64))) eps)) |
(* x (+ (* x (* x 1/144)) -1/24)) |
(*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/144 binary64)) #s(literal -1/24 binary64))) |
x |
(+ (* x (* x 1/144)) -1/24) |
(+.f64 (*.f64 (*.f64 x x) #s(literal 1/144 binary64)) #s(literal -1/24 binary64)) |
(* x (* x 1/144)) |
(*.f64 (*.f64 x x) #s(literal 1/144 binary64)) |
(* x 1/144) |
(*.f64 x #s(literal 1/144 binary64)) |
1/144 |
#s(literal 1/144 binary64) |
-1/24 |
#s(literal -1/24 binary64) |
(/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps) |
(/.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps))) eps) |
(+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) |
(+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps))) |
(- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) |
(-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) (/.f64 (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps)) |
(* (* x x) 1/12) |
(*.f64 (*.f64 x x) #s(literal 1/12 binary64)) |
(* x x) |
(*.f64 x x) |
1/12 |
#s(literal 1/12 binary64) |
(/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps) |
(/.f64 (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps) |
(- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) |
(+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) |
(* x (+ 1/2 (* (* x x) -1/12))) |
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) |
(+ 1/2 (* (* x x) -1/12)) |
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64))) |
1/2 |
#s(literal 1/2 binary64) |
(* (* x x) -1/12) |
(*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
-1/12 |
#s(literal -1/12 binary64) |
(/ (+ 1 (* x (* x -1/2))) eps) |
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps) |
(+ 1 (* x (* x -1/2))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
1 |
#s(literal 1 binary64) |
(* x (* x -1/2)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
(* x -1/2) |
(*.f64 x #s(literal -1/2 binary64)) |
-1/2 |
#s(literal -1/2 binary64) |
-1/6 |
#s(literal -1/6 binary64) |
(* -1 (* eps (* eps eps))) |
(-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps))) |
-1 |
#s(literal -1 binary64) |
(* eps (* eps eps)) |
(*.f64 eps (*.f64 eps eps)) |
(* eps eps) |
(*.f64 eps eps) |
(* (* eps (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) -1/48)))) 2) |
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))))) |
(* eps (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) -1/48)))) |
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))) |
eps |
(* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) -1/48))) |
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) |
(cos (+ x (* eps 1/2))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(+ x (* eps 1/2)) |
(+.f64 x (*.f64 eps #s(literal 1/2 binary64))) |
x |
(* eps 1/2) |
(*.f64 eps #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* (* eps eps) -1/48)) |
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))) |
(* (* eps eps) -1/48) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* eps eps) |
(*.f64 eps eps) |
-1/48 |
#s(literal -1/48 binary64) |
2 |
#s(literal 2 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 eps #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 eps (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))) |
| ✓ | accuracy | 99.9% | (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
| ✓ | accuracy | 99.5% | (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/144 binary64))) #s(literal -1/24 binary64))) |
| ✓ | accuracy | 99.5% | (*.f64 x #s(literal 1/144 binary64)) |
| ✓ | accuracy | 30.6% | (*.f64 (-.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/144 binary64))) #s(literal -1/24 binary64))) (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) (/.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps)) #s(literal -1/6 binary64)) eps)) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps)))) |
| ✓ | accuracy | 99.8% | (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) |
| ✓ | accuracy | 99.8% | (*.f64 x (*.f64 x x)) |
| ✓ | accuracy | 99.7% | (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) |
| ✓ | accuracy | 99.7% | (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
| ✓ | accuracy | 100.0% | (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
| ✓ | accuracy | 100.0% | (*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal -1/2 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
| ✓ | accuracy | 100.0% | (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) |
| ✓ | accuracy | 100.0% | (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) |
| ✓ | accuracy | 99.7% | (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) |
| 511.0ms | 256× | 0 | valid |
Compiled 690 to 67 computations (90.3% saved)
ival-mult: 142.0ms (55.1% of total)...c/correct-round.rkt:119:19: 45.0ms (17.5% of total)ival-add: 34.0ms (13.2% of total)ival-div: 13.0ms (5% of total)ival-cos: 9.0ms (3.5% of total)ival-sub: 8.0ms (3.1% of total)ival-sin: 4.0ms (1.6% of total)const: 2.0ms (0.8% of total)backward-pass: 0.0ms (0% of total)| Inputs |
|---|
#<alt (* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* -1/2 (* eps (sin x)))))> |
#<alt (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* -1/2 (* eps (sin x))))> |
#<alt (* (+ (* (* eps eps) -1/6) 1) (cos x))> |
#<alt (+ (* (* eps eps) -1/6) 1)> |
#<alt (* eps (+ 1 (* x (* x -1/2))))> |
#<alt (+ 1 (* x (* x -1/2)))> |
#<alt (* x (* x -1/2))> |
#<alt (* x -1/2)> |
#<alt (* eps (+ (+ 1 (* -1/6 (* eps eps))) (* (* -1/6 (* eps (* x (* x x)))) (+ (* 1/24 (* eps eps)) -1/2))))> |
#<alt (+ (+ 1 (* -1/6 (* eps eps))) (* (* -1/6 (* eps (* x (* x x)))) (+ (* 1/24 (* eps eps)) -1/2)))> |
#<alt (* (* -1/6 (* eps (* x (* x x)))) (+ (* 1/24 (* eps eps)) -1/2))> |
#<alt (+ 1 (* -1/6 (* eps eps)))> |
#<alt (* eps (* (- (* x (+ (* x (* x 1/144)) -1/24)) (/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps)) (* -1 (* eps (* eps eps)))))> |
#<alt (* (- (* x (+ (* x (* x 1/144)) -1/24)) (/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps)) (* -1 (* eps (* eps eps))))> |
#<alt (- (* x (+ (* x (* x 1/144)) -1/24)) (/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps))> |
#<alt (* x (+ (* x (* x 1/144)) -1/24))> |
#<alt (* (* eps (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) -1/48)))) 2)> |
#<alt (* eps (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) -1/48))))> |
#<alt (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) -1/48)))> |
#<alt (cos (+ x (* eps 1/2)))> |
#<alt (* (* eps eps) -1/6)> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/6 (* eps eps))> |
#<alt (* 1/24 (* eps eps))> |
#<alt (* x (* x x))> |
#<alt (* -1/6 (* eps (* x (* x x))))> |
#<alt (* x 1/144)> |
#<alt (* (* x x) -1/12)> |
#<alt (* (* eps eps) -1/48)> |
#<alt (* eps 1/2)> |
| Outputs |
|---|
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* -1/6 (* (pow eps 3) (cos x)))> |
#<alt (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2)))))> |
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x)))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))> |
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))> |
#<alt (* -1/6 (* (pow eps 2) (cos x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))> |
#<alt (* -1/6 (* (pow eps 2) (cos x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2)))))))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x))))))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))> |
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))> |
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))> |
#<alt (* -1/6 (* (pow eps 2) (cos x)))> |
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (* -1/6 (* (pow eps 2) (cos x)))> |
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))> |
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2))))))))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))> |
#<alt 1> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt eps> |
#<alt (+ eps (* -1/2 (* eps (pow x 2))))> |
#<alt (+ eps (* -1/2 (* eps (pow x 2))))> |
#<alt (+ eps (* -1/2 (* eps (pow x 2))))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* -1/2 (pow x 2))> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt (* -1/2 x)> |
#<alt eps> |
#<alt (* eps (+ 1 (* 1/12 (* eps (pow x 3)))))> |
#<alt (* eps (+ 1 (* eps (+ (* -1/6 eps) (* 1/12 (pow x 3))))))> |
#<alt (* eps (+ 1 (* eps (+ (* 1/12 (pow x 3)) (* eps (- (* -1/144 (* eps (pow x 3))) 1/6))))))> |
#<alt (* -1/144 (* (pow eps 4) (pow x 3)))> |
#<alt (* (pow eps 4) (- (* -1/144 (pow x 3)) (* 1/6 (/ 1 eps))))> |
#<alt (* (pow eps 4) (- (+ (* -1/144 (pow x 3)) (* 1/12 (/ (pow x 3) (pow eps 2)))) (* 1/6 (/ 1 eps))))> |
#<alt (* (pow eps 4) (- (+ (* -1/144 (pow x 3)) (+ (* 1/12 (/ (pow x 3) (pow eps 2))) (/ 1 (pow eps 3)))) (* 1/6 (/ 1 eps))))> |
#<alt (* -1/144 (* (pow eps 4) (pow x 3)))> |
#<alt (* (pow eps 4) (- (* -1/144 (pow x 3)) (* 1/6 (/ 1 eps))))> |
#<alt (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* -1/12 (/ (pow x 3) eps))) eps)) (* -1/144 (pow x 3))))> |
#<alt (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* -1 (/ (+ (* 1/12 (pow x 3)) (/ 1 eps)) eps))) eps)) (* -1/144 (pow x 3))))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (+ (* -1/6 (* (pow eps 2) (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/6 (* (pow eps 2) (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (+ (* -1/6 (* (pow eps 2) (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (+ 1 (* -1/6 (pow eps 2)))))> |
#<alt (* -1/6 (* (pow eps 2) (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* (pow x 3) (+ (* -1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 3))))> |
#<alt (* (pow x 3) (+ (* -1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 3))))> |
#<alt (* (pow x 3) (+ (* -1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 3))))> |
#<alt (* -1/6 (* (pow eps 2) (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 3))) (* 1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 3))) (* 1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 3))) (* 1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))))> |
#<alt 1> |
#<alt (+ 1 (* 1/12 (* eps (pow x 3))))> |
#<alt (+ 1 (* eps (+ (* -1/6 eps) (* 1/12 (pow x 3)))))> |
#<alt (+ 1 (* eps (+ (* 1/12 (pow x 3)) (* eps (- (* -1/144 (* eps (pow x 3))) 1/6)))))> |
#<alt (* -1/144 (* (pow eps 3) (pow x 3)))> |
#<alt (* (pow eps 3) (- (* -1/144 (pow x 3)) (* 1/6 (/ 1 eps))))> |
#<alt (* (pow eps 3) (- (+ (* -1/144 (pow x 3)) (* 1/12 (/ (pow x 3) (pow eps 2)))) (* 1/6 (/ 1 eps))))> |
#<alt (* (pow eps 3) (- (+ (* -1/144 (pow x 3)) (+ (* 1/12 (/ (pow x 3) (pow eps 2))) (/ 1 (pow eps 3)))) (* 1/6 (/ 1 eps))))> |
#<alt (* -1/144 (* (pow eps 3) (pow x 3)))> |
#<alt (* -1 (* (pow eps 3) (+ (* 1/144 (pow x 3)) (* 1/6 (/ 1 eps)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (/ (pow x 3) eps)) 1/6) eps)) (* 1/144 (pow x 3)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ (- (* -1/12 (pow x 3)) (/ 1 eps)) eps)) 1/6) eps)) (* 1/144 (pow x 3)))))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (+ (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) (* -1/6 (pow eps 2))))> |
#<alt (+ 1 (+ (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) (* -1/6 (pow eps 2))))> |
#<alt (+ 1 (+ (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) (* -1/6 (pow eps 2))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* (pow x 3) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (/ 1 (pow x 3)))))> |
#<alt (* (pow x 3) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (/ 1 (pow x 3)))))> |
#<alt (* (pow x 3) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (/ 1 (pow x 3)))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) (pow x 3))) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) (pow x 3))) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))))))> |
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) (pow x 3))) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))))))> |
#<alt (* 1/12 (* eps (pow x 3)))> |
#<alt (* eps (+ (* -1/144 (* (pow eps 2) (pow x 3))) (* 1/12 (pow x 3))))> |
#<alt (* eps (+ (* -1/144 (* (pow eps 2) (pow x 3))) (* 1/12 (pow x 3))))> |
#<alt (* eps (+ (* -1/144 (* (pow eps 2) (pow x 3))) (* 1/12 (pow x 3))))> |
#<alt (* -1/144 (* (pow eps 3) (pow x 3)))> |
#<alt (* (pow eps 3) (+ (* -1/144 (pow x 3)) (* 1/12 (/ (pow x 3) (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ (* -1/144 (pow x 3)) (* 1/12 (/ (pow x 3) (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ (* -1/144 (pow x 3)) (* 1/12 (/ (pow x 3) (pow eps 2)))))> |
#<alt (* -1/144 (* (pow eps 3) (pow x 3)))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/12 (/ (pow x 3) (pow eps 2))) (* 1/144 (pow x 3)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/12 (/ (pow x 3) (pow eps 2))) (* 1/144 (pow x 3)))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/12 (/ (pow x 3) (pow eps 2))) (* 1/144 (pow x 3)))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2))))> |
#<alt 1> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (+ 1 (* -1/6 (pow eps 2)))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (+ (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))) (* -1/2 (pow x 2)))))> |
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#<alt (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (+ (* -1 (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (+ (* x (+ (* -1 (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* -1/2 (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))) (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (+ (* x (+ (* -1 (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* 1/6 (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))))) (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* 1/2 (cos x))> |
#<alt (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))> |
#<alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))> |
#<alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))> |
#<alt (* -1/48 (* (pow eps 2) (cos (+ x (* 1/2 eps)))))> |
#<alt (* (pow eps 2) (+ (* -1/48 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ (* -1/48 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ (* -1/48 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))> |
#<alt (* -1/48 (* (pow eps 2) (cos (- x (* -1/2 eps)))))> |
#<alt (* (pow eps 2) (+ (* -1/48 (cos (- x (* -1/2 eps)))) (* 1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ (* -1/48 (cos (- x (* -1/2 eps)))) (* 1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ (* -1/48 (cos (- x (* -1/2 eps)))) (* 1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))> |
#<alt (cos (* 1/2 eps))> |
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (- (* 1/2 eps) (* -1 x)))> |
#<alt (cos (- (* 1/2 eps) (* -1 x)))> |
#<alt (cos (- (* 1/2 eps) (* -1 x)))> |
#<alt (cos (- (* 1/2 eps) (* -1 x)))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))> |
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (- x (* -1/2 eps)))> |
#<alt (cos (- x (* -1/2 eps)))> |
#<alt (cos (- x (* -1/2 eps)))> |
#<alt (cos (- x (* -1/2 eps)))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps x))> |
#<alt (* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))> |
#<alt (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))> |
#<alt (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (* 1/24 (pow eps 2))> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* -1/6 (* eps (pow x 3)))> |
#<alt (* 1/144 x)> |
#<alt (* 1/144 x)> |
#<alt (* 1/144 x)> |
#<alt (* 1/144 x)> |
#<alt (* 1/144 x)> |
#<alt (* 1/144 x)> |
#<alt (* 1/144 x)> |
#<alt (* 1/144 x)> |
#<alt (* 1/144 x)> |
#<alt (* 1/144 x)> |
#<alt (* 1/144 x)> |
#<alt (* 1/144 x)> |
#<alt (* -1/12 (pow x 2))> |
#<alt (* -1/12 (pow x 2))> |
#<alt (* -1/12 (pow x 2))> |
#<alt (* -1/12 (pow x 2))> |
#<alt (* -1/12 (pow x 2))> |
#<alt (* -1/12 (pow x 2))> |
#<alt (* -1/12 (pow x 2))> |
#<alt (* -1/12 (pow x 2))> |
#<alt (* -1/12 (pow x 2))> |
#<alt (* -1/12 (pow x 2))> |
#<alt (* -1/12 (pow x 2))> |
#<alt (* -1/12 (pow x 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* -1/48 (pow eps 2))> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
138 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 34.0ms | eps | @ | -inf | (* (* eps (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) -1/48)))) 2) |
| 5.0ms | x | @ | 0 | (* eps (+ (+ 1 (* -1/6 (* eps eps))) (* (* -1/6 (* eps (* x (* x x)))) (+ (* 1/24 (* eps eps)) -1/2)))) |
| 5.0ms | eps | @ | 0 | (* (* -1/6 (* eps (* x (* x x)))) (+ (* 1/24 (* eps eps)) -1/2)) |
| 3.0ms | x | @ | inf | (* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* -1/2 (* eps (sin x))))) |
| 3.0ms | x | @ | inf | (* eps (* (- (* x (+ (* x (* x 1/144)) -1/24)) (/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps)) (* -1 (* eps (* eps eps))))) |
| 1× | batch-egg-rewrite |
| 4116× | *-lowering-*.f32 |
| 4116× | *-lowering-*.f64 |
| 1650× | pow-lowering-pow.f64 |
| 1650× | pow-lowering-pow.f32 |
| 1598× | fma-lowering-fma.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 66 | 367 |
| 1 | 407 | 350 |
| 2 | 3896 | 350 |
| 0 | 8110 | 350 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* -1/2 (* eps (sin x))))) |
(+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* -1/2 (* eps (sin x)))) |
(* (+ (* (* eps eps) -1/6) 1) (cos x)) |
(+ (* (* eps eps) -1/6) 1) |
(* eps (+ 1 (* x (* x -1/2)))) |
(+ 1 (* x (* x -1/2))) |
(* x (* x -1/2)) |
(* x -1/2) |
(* eps (+ (+ 1 (* -1/6 (* eps eps))) (* (* -1/6 (* eps (* x (* x x)))) (+ (* 1/24 (* eps eps)) -1/2)))) |
(+ (+ 1 (* -1/6 (* eps eps))) (* (* -1/6 (* eps (* x (* x x)))) (+ (* 1/24 (* eps eps)) -1/2))) |
(* (* -1/6 (* eps (* x (* x x)))) (+ (* 1/24 (* eps eps)) -1/2)) |
(+ 1 (* -1/6 (* eps eps))) |
(* eps (* (- (* x (+ (* x (* x 1/144)) -1/24)) (/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps)) (* -1 (* eps (* eps eps))))) |
(* (- (* x (+ (* x (* x 1/144)) -1/24)) (/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps)) (* -1 (* eps (* eps eps)))) |
(- (* x (+ (* x (* x 1/144)) -1/24)) (/ (+ (- (* (* x x) 1/12) (/ (- (* x (+ 1/2 (* (* x x) -1/12))) (/ (+ 1 (* x (* x -1/2))) eps)) eps)) -1/6) eps)) |
(* x (+ (* x (* x 1/144)) -1/24)) |
(* (* eps (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) -1/48)))) 2) |
(* eps (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) -1/48)))) |
(* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) -1/48))) |
(cos (+ x (* eps 1/2))) |
(* (* eps eps) -1/6) |
(* -1/2 (* eps (sin x))) |
(* -1/6 (* eps eps)) |
(* 1/24 (* eps eps)) |
(* x (* x x)) |
(* -1/6 (* eps (* x (* x x)))) |
(* x 1/144) |
(* (* x x) -1/12) |
(* (* eps eps) -1/48) |
(* eps 1/2) |
| Outputs |
|---|
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))) |
(+.f64 (*.f64 eps (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))) (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64)))) |
(fma.f64 eps (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64)))) |
(fma.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) eps (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64)))) |
(/.f64 (+.f64 (pow.f64 (*.f64 eps (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 eps (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 eps (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))) (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 eps (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 2 binary64))) (-.f64 (*.f64 eps (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))) (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 eps (+.f64 (pow.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 3 binary64)))) (+.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (-.f64 (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))))) |
(/.f64 (*.f64 eps (-.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (-.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 3 binary64))) eps) (+.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (-.f64 (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) eps) (-.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 (+.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))) eps) |
(+.f64 (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))) |
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(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) |
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) |
(+.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 (*.f64 (neg.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 x)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(+.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(+.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 x x) (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (cos.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (+.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) (*.f64 (sin.f64 (/.f64 (*.f64 x x) (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))) (sin.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))))) |
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) |
(-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(fma.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) |
(*.f64 eps (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(*.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) |
(*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) eps) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 eps #s(literal -1/6 binary64))) eps) |
(*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) |
(*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) |
(*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))) |
(*.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) |
(*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) |
(*.f64 eps (*.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(*.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))) |
(*.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) eps) |
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 eps #s(literal -1/6 binary64))) eps) |
(*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 eps #s(literal 1/24 binary64)) eps) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64))) |
(pow.f64 x #s(literal 3 binary64)) |
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64)) |
(*.f64 x (*.f64 x x)) |
(*.f64 (*.f64 x x) x) |
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) |
(*.f64 eps (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64))) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) |
(*.f64 (*.f64 x (*.f64 x x)) (*.f64 eps #s(literal -1/6 binary64))) |
(*.f64 (*.f64 eps (*.f64 x (*.f64 x x))) #s(literal -1/6 binary64)) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(*.f64 (*.f64 eps x) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) |
(*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x))) eps) |
(*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) (*.f64 x x)) |
(*.f64 (*.f64 (*.f64 eps #s(literal -1/6 binary64)) x) (*.f64 x x)) |
(*.f64 (*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x x)) x) |
(*.f64 x #s(literal 1/144 binary64)) |
(*.f64 #s(literal 1/144 binary64) x) |
(*.f64 x (*.f64 x #s(literal -1/12 binary64))) |
(*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
(*.f64 #s(literal -1/12 binary64) (*.f64 x x)) |
(*.f64 (*.f64 x #s(literal -1/12 binary64)) x) |
(*.f64 eps (*.f64 eps #s(literal -1/48 binary64))) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64))) |
(*.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) |
(*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 eps #s(literal 1/24 binary64)) (*.f64 eps #s(literal -1/2 binary64))) |
(*.f64 (*.f64 eps #s(literal -1/48 binary64)) eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) eps) |
| 1× | egg-herbie |
| 5976× | *-lowering-*.f32 |
| 5976× | *-lowering-*.f64 |
| 5588× | +-lowering-+.f64 |
| 5588× | +-lowering-+.f32 |
| 1404× | distribute-lft-in |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 814 | 7901 |
| 1 | 3075 | 7537 |
| 0 | 8262 | 7537 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* -1/6 (* (pow eps 3) (cos x))) |
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x))))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x)))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x)))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))))))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/12 (* eps x)))))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) |
(cos x) |
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))) |
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))) |
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2)))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))))))) |
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2)))))))))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
(* (cos x) (+ 1 (* -1/6 (pow eps 2)))) |
1 |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (* -1/6 (pow eps 2))) |
(* -1/6 (pow eps 2)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* -1/6 (pow eps 2)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(* -1/2 (* eps (pow x 2))) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
(* -1/2 (* eps (pow x 2))) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* -1/2 (pow x 2))) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* -1/2 (pow x 2)) |
(* -1/2 (pow x 2)) |
(* -1/2 (pow x 2)) |
(* -1/2 (pow x 2)) |
(* -1/2 (pow x 2)) |
(* -1/2 (pow x 2)) |
(* -1/2 (pow x 2)) |
(* -1/2 (pow x 2)) |
(* -1/2 (pow x 2)) |
(* -1/2 (pow x 2)) |
(* -1/2 (pow x 2)) |
(* -1/2 (pow x 2)) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
eps |
(* eps (+ 1 (* 1/12 (* eps (pow x 3))))) |
(* eps (+ 1 (* eps (+ (* -1/6 eps) (* 1/12 (pow x 3)))))) |
(* eps (+ 1 (* eps (+ (* 1/12 (pow x 3)) (* eps (- (* -1/144 (* eps (pow x 3))) 1/6)))))) |
(* -1/144 (* (pow eps 4) (pow x 3))) |
(* (pow eps 4) (- (* -1/144 (pow x 3)) (* 1/6 (/ 1 eps)))) |
(* (pow eps 4) (- (+ (* -1/144 (pow x 3)) (* 1/12 (/ (pow x 3) (pow eps 2)))) (* 1/6 (/ 1 eps)))) |
(* (pow eps 4) (- (+ (* -1/144 (pow x 3)) (+ (* 1/12 (/ (pow x 3) (pow eps 2))) (/ 1 (pow eps 3)))) (* 1/6 (/ 1 eps)))) |
(* -1/144 (* (pow eps 4) (pow x 3))) |
(* (pow eps 4) (- (* -1/144 (pow x 3)) (* 1/6 (/ 1 eps)))) |
(* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* -1/12 (/ (pow x 3) eps))) eps)) (* -1/144 (pow x 3)))) |
(* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* -1 (/ (+ (* 1/12 (pow x 3)) (/ 1 eps)) eps))) eps)) (* -1/144 (pow x 3)))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(+ (* -1/6 (* (pow eps 2) (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/6 (* (pow eps 2) (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(+ (* -1/6 (* (pow eps 2) (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(* -1/6 (* (pow eps 2) (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* (pow x 3) (+ (* -1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 3)))) |
(* (pow x 3) (+ (* -1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 3)))) |
(* (pow x 3) (+ (* -1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 3)))) |
(* -1/6 (* (pow eps 2) (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 3))) (* 1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 3))) (* 1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 3))) (* 1/6 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))) |
1 |
(+ 1 (* 1/12 (* eps (pow x 3)))) |
(+ 1 (* eps (+ (* -1/6 eps) (* 1/12 (pow x 3))))) |
(+ 1 (* eps (+ (* 1/12 (pow x 3)) (* eps (- (* -1/144 (* eps (pow x 3))) 1/6))))) |
(* -1/144 (* (pow eps 3) (pow x 3))) |
(* (pow eps 3) (- (* -1/144 (pow x 3)) (* 1/6 (/ 1 eps)))) |
(* (pow eps 3) (- (+ (* -1/144 (pow x 3)) (* 1/12 (/ (pow x 3) (pow eps 2)))) (* 1/6 (/ 1 eps)))) |
(* (pow eps 3) (- (+ (* -1/144 (pow x 3)) (+ (* 1/12 (/ (pow x 3) (pow eps 2))) (/ 1 (pow eps 3)))) (* 1/6 (/ 1 eps)))) |
(* -1/144 (* (pow eps 3) (pow x 3))) |
(* -1 (* (pow eps 3) (+ (* 1/144 (pow x 3)) (* 1/6 (/ 1 eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (/ (pow x 3) eps)) 1/6) eps)) (* 1/144 (pow x 3))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ (- (* -1/12 (pow x 3)) (/ 1 eps)) eps)) 1/6) eps)) (* 1/144 (pow x 3))))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (+ (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) (* -1/6 (pow eps 2)))) |
(+ 1 (+ (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) (* -1/6 (pow eps 2)))) |
(+ 1 (+ (* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) (* -1/6 (pow eps 2)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (/ 1 (pow x 3))))) |
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (/ 1 (pow x 3))))) |
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (+ (* -1/6 (/ (pow eps 2) (pow x 3))) (/ 1 (pow x 3))))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) (pow x 3))) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) (pow x 3))) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))) |
(* -1 (* (pow x 3) (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) (pow x 3))) (* 1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))) |
(* 1/12 (* eps (pow x 3))) |
(* eps (+ (* -1/144 (* (pow eps 2) (pow x 3))) (* 1/12 (pow x 3)))) |
(* eps (+ (* -1/144 (* (pow eps 2) (pow x 3))) (* 1/12 (pow x 3)))) |
(* eps (+ (* -1/144 (* (pow eps 2) (pow x 3))) (* 1/12 (pow x 3)))) |
(* -1/144 (* (pow eps 3) (pow x 3))) |
(* (pow eps 3) (+ (* -1/144 (pow x 3)) (* 1/12 (/ (pow x 3) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/144 (pow x 3)) (* 1/12 (/ (pow x 3) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/144 (pow x 3)) (* 1/12 (/ (pow x 3) (pow eps 2))))) |
(* -1/144 (* (pow eps 3) (pow x 3))) |
(* -1 (* (pow eps 3) (+ (* -1/12 (/ (pow x 3) (pow eps 2))) (* 1/144 (pow x 3))))) |
(* -1 (* (pow eps 3) (+ (* -1/12 (/ (pow x 3) (pow eps 2))) (* 1/144 (pow x 3))))) |
(* -1 (* (pow eps 3) (+ (* -1/12 (/ (pow x 3) (pow eps 2))) (* 1/144 (pow x 3))))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
(* -1/6 (* eps (* (pow x 3) (- (* 1/24 (pow eps 2)) 1/2)))) |
1 |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (* -1/6 (pow eps 2))) |
(+ 1 (* -1/6 (pow eps 2))) |
(* -1/6 (pow eps 2)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* -1/6 (pow eps 2)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6)) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (+ (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))) (* -1/2 (pow x 2))))) |
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1 (* eps (- 1/6 (* 1/12 (pow x 2))))) (* -1 (* x (+ 1/2 (* -1/12 (pow x 2)))))))))) |
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (* eps (+ (* -1 (* eps (* x (- (* 1/144 (pow x 2)) 1/24)))) (* -1 (- 1/6 (* 1/12 (pow x 2))))))))))) |
(* -1 (* (pow eps 4) (* x (- (* 1/144 (pow x 2)) 1/24)))) |
(* (pow eps 4) (+ (* -1 (* x (- (* 1/144 (pow x 2)) 1/24))) (* -1 (/ (- 1/6 (* 1/12 (pow x 2))) eps)))) |
(* (pow eps 4) (+ (* -1 (* x (- (* 1/144 (pow x 2)) 1/24))) (+ (* -1 (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) (pow eps 2))) (* -1 (/ (- 1/6 (* 1/12 (pow x 2))) eps))))) |
(* (pow eps 4) (+ (* -1 (* x (- (* 1/144 (pow x 2)) 1/24))) (+ (* -1 (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) (pow eps 2))) (+ (* -1 (/ (- 1/6 (* 1/12 (pow x 2))) eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (/ 1 (pow eps 3))))))) |
(* -1 (* (pow eps 4) (* x (- (* 1/144 (pow x 2)) 1/24)))) |
(* (pow eps 4) (- (+ (* -1 (* x (- (* 1/144 (pow x 2)) 1/24))) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps)))) |
(* (pow eps 4) (+ (* -1 (* x (- (* 1/144 (pow x 2)) 1/24))) (* -1 (/ (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) eps)) eps)))) |
(* (pow eps 4) (+ (* -1 (* x (- (* 1/144 (pow x 2)) 1/24))) (* -1 (/ (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))) eps))) eps)))) |
(* -1 (* (pow eps 4) (- (* 1/6 (/ 1 eps)) (/ 1 (pow eps 3))))) |
(+ (* -1 (* (pow eps 4) (* x (- (* 1/2 (/ 1 (pow eps 2))) 1/24)))) (* -1 (* (pow eps 4) (- (* 1/6 (/ 1 eps)) (/ 1 (pow eps 3)))))) |
(+ (* -1 (* (pow eps 4) (- (* 1/6 (/ 1 eps)) (/ 1 (pow eps 3))))) (* x (+ (* -1 (* (pow eps 4) (* x (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps)))))) (* -1 (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)))))) |
(+ (* -1 (* (pow eps 4) (- (* 1/6 (/ 1 eps)) (/ 1 (pow eps 3))))) (* x (+ (* -1 (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 2))) 1/24))) (* x (+ (* -1 (* (pow eps 4) (* x (- 1/144 (* 1/12 (/ 1 (pow eps 2))))))) (* -1 (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps)))))))))) |
(* -1 (* (pow eps 4) (* (pow x 3) (- 1/144 (* 1/12 (/ 1 (pow eps 2))))))) |
(* (pow x 3) (+ (* -1 (* (pow eps 4) (- 1/144 (* 1/12 (/ 1 (pow eps 2)))))) (* -1 (/ (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps)))) x)))) |
(* (pow x 3) (+ (* -1 (* (pow eps 4) (- 1/144 (* 1/12 (/ 1 (pow eps 2)))))) (+ (* -1 (/ (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)) (pow x 2))) (* -1 (/ (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps)))) x))))) |
(* (pow x 3) (+ (* -1 (* (pow eps 4) (- 1/144 (* 1/12 (/ 1 (pow eps 2)))))) (+ (* -1 (/ (* (pow eps 4) (- (* 1/6 (/ 1 eps)) (/ 1 (pow eps 3)))) (pow x 3))) (+ (* -1 (/ (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)) (pow x 2))) (* -1 (/ (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps)))) x)))))) |
(* (pow eps 4) (* (pow x 3) (- (* 1/12 (/ 1 (pow eps 2))) 1/144))) |
(* -1 (* (pow x 3) (+ (* -1 (* (pow eps 4) (- (* 1/12 (/ 1 (pow eps 2))) 1/144))) (/ (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps)))) x)))) |
(* -1 (* (pow x 3) (+ (* -1 (* (pow eps 4) (- (* 1/12 (/ 1 (pow eps 2))) 1/144))) (* -1 (/ (+ (* -1 (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps))))) (/ (* (pow eps 4) (- 1/24 (* 1/2 (/ 1 (pow eps 2))))) x)) x))))) |
(* -1 (* (pow x 3) (+ (* -1 (* (pow eps 4) (- (* 1/12 (/ 1 (pow eps 2))) 1/144))) (* -1 (/ (+ (* -1 (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps))))) (* -1 (/ (+ (* -1 (* (pow eps 4) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))) (/ (* (pow eps 4) (- (* 1/6 (/ 1 eps)) (/ 1 (pow eps 3)))) x)) x))) x))))) |
(* -1 (* (pow eps 3) (- (* 1/6 (/ 1 eps)) (/ 1 (pow eps 3))))) |
(+ (* -1 (* (pow eps 3) (* x (- (* 1/2 (/ 1 (pow eps 2))) 1/24)))) (* -1 (* (pow eps 3) (- (* 1/6 (/ 1 eps)) (/ 1 (pow eps 3)))))) |
(+ (* -1 (* (pow eps 3) (- (* 1/6 (/ 1 eps)) (/ 1 (pow eps 3))))) (* x (+ (* -1 (* (pow eps 3) (* x (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps)))))) (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)))))) |
(+ (* -1 (* (pow eps 3) (- (* 1/6 (/ 1 eps)) (/ 1 (pow eps 3))))) (* x (+ (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/24))) (* x (+ (* -1 (* (pow eps 3) (* x (- 1/144 (* 1/12 (/ 1 (pow eps 2))))))) (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps)))))))))) |
(* -1 (* (pow eps 3) (* (pow x 3) (- 1/144 (* 1/12 (/ 1 (pow eps 2))))))) |
(* (pow x 3) (+ (* -1 (* (pow eps 3) (- 1/144 (* 1/12 (/ 1 (pow eps 2)))))) (* -1 (/ (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps)))) x)))) |
(* (pow x 3) (+ (* -1 (* (pow eps 3) (- 1/144 (* 1/12 (/ 1 (pow eps 2)))))) (+ (* -1 (/ (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)) (pow x 2))) (* -1 (/ (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps)))) x))))) |
(* (pow x 3) (+ (* -1 (* (pow eps 3) (- 1/144 (* 1/12 (/ 1 (pow eps 2)))))) (+ (* -1 (/ (* (pow eps 3) (- (* 1/6 (/ 1 eps)) (/ 1 (pow eps 3)))) (pow x 3))) (+ (* -1 (/ (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)) (pow x 2))) (* -1 (/ (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps)))) x)))))) |
(* (pow eps 3) (* (pow x 3) (- (* 1/12 (/ 1 (pow eps 2))) 1/144))) |
(* -1 (* (pow x 3) (+ (* -1 (* (pow eps 3) (- (* 1/12 (/ 1 (pow eps 2))) 1/144))) (/ (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps)))) x)))) |
(* -1 (* (pow x 3) (+ (* -1 (* (pow eps 3) (- (* 1/12 (/ 1 (pow eps 2))) 1/144))) (* -1 (/ (+ (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps))))) (/ (* (pow eps 3) (- 1/24 (* 1/2 (/ 1 (pow eps 2))))) x)) x))))) |
(* -1 (* (pow x 3) (+ (* -1 (* (pow eps 3) (- (* 1/12 (/ 1 (pow eps 2))) 1/144))) (* -1 (/ (+ (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps))))) (* -1 (/ (+ (* -1 (* (pow eps 3) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))) (/ (* (pow eps 3) (- (* 1/6 (/ 1 eps)) (/ 1 (pow eps 3)))) x)) x))) x))))) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (+ (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2)))))) (* -1/2 (pow x 2)))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1 (* eps (- 1/6 (* 1/12 (pow x 2))))) (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))))))) |
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1 (* x (+ 1/2 (* -1/12 (pow x 2))))) (* eps (+ (* -1 (* eps (* x (- (* 1/144 (pow x 2)) 1/24)))) (* -1 (- 1/6 (* 1/12 (pow x 2)))))))))) |
(* -1 (* (pow eps 3) (* x (- (* 1/144 (pow x 2)) 1/24)))) |
(* (pow eps 3) (+ (* -1 (* x (- (* 1/144 (pow x 2)) 1/24))) (* -1 (/ (- 1/6 (* 1/12 (pow x 2))) eps)))) |
(* (pow eps 3) (+ (* -1 (* x (- (* 1/144 (pow x 2)) 1/24))) (+ (* -1 (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) (pow eps 2))) (* -1 (/ (- 1/6 (* 1/12 (pow x 2))) eps))))) |
(* (pow eps 3) (+ (* -1 (* x (- (* 1/144 (pow x 2)) 1/24))) (+ (* -1 (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) (pow eps 2))) (+ (* -1 (/ (- 1/6 (* 1/12 (pow x 2))) eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (/ 1 (pow eps 3))))))) |
(* -1 (* (pow eps 3) (* x (- (* 1/144 (pow x 2)) 1/24)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* x (- (* 1/144 (pow x 2)) 1/24))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* x (- (* 1/144 (pow x 2)) 1/24))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2))))) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* x (- (* 1/144 (pow x 2)) 1/24))))) |
(- (* 1/6 (/ 1 eps)) (/ 1 (pow eps 3))) |
(- (+ (* 1/6 (/ 1 eps)) (* x (- (* 1/2 (/ 1 (pow eps 2))) 1/24))) (/ 1 (pow eps 3))) |
(- (+ (* 1/6 (/ 1 eps)) (* x (- (+ (* 1/2 (/ 1 (pow eps 2))) (* x (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps))))) 1/24))) (/ 1 (pow eps 3))) |
(- (+ (* 1/6 (/ 1 eps)) (* x (- (+ (* 1/2 (/ 1 (pow eps 2))) (* x (- (+ (* 1/2 (/ 1 (pow eps 3))) (* x (- 1/144 (* 1/12 (/ 1 (pow eps 2)))))) (* 1/12 (/ 1 eps))))) 1/24))) (/ 1 (pow eps 3))) |
(* (pow x 3) (- 1/144 (* 1/12 (/ 1 (pow eps 2))))) |
(* (pow x 3) (- (+ 1/144 (/ 1/2 (* (pow eps 3) x))) (+ (* 1/12 (/ 1 (pow eps 2))) (/ 1/12 (* eps x))))) |
(* (pow x 3) (- (+ 1/144 (+ (/ 1/2 (* (pow eps 3) x)) (* 1/2 (/ 1 (* (pow eps 2) (pow x 2)))))) (+ (* 1/12 (/ 1 (pow eps 2))) (+ (/ 1/24 (pow x 2)) (/ 1/12 (* eps x)))))) |
(* (pow x 3) (- (+ 1/144 (+ (/ 1/6 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 3) x)) (* 1/2 (/ 1 (* (pow eps 2) (pow x 2))))))) (+ (* 1/12 (/ 1 (pow eps 2))) (+ (/ 1/24 (pow x 2)) (+ (/ 1/12 (* eps x)) (/ 1 (* (pow eps 3) (pow x 3)))))))) |
(* -1 (* (pow x 3) (- (* 1/12 (/ 1 (pow eps 2))) 1/144))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (- (* 1/2 (/ 1 (pow eps 3))) (* 1/12 (/ 1 eps))) x)) (* 1/12 (/ 1 (pow eps 2)))) 1/144))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (- (+ (* -1 (/ (- 1/24 (* 1/2 (/ 1 (pow eps 2)))) x)) (* 1/2 (/ 1 (pow eps 3)))) (* 1/12 (/ 1 eps))) x)) (* 1/12 (/ 1 (pow eps 2)))) 1/144))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (- (+ (* -1 (/ (- (+ 1/24 (* -1 (/ (- (* 1/6 (/ 1 eps)) (/ 1 (pow eps 3))) x))) (* 1/2 (/ 1 (pow eps 2)))) x)) (* 1/2 (/ 1 (pow eps 3)))) (* 1/12 (/ 1 eps))) x)) (* 1/12 (/ 1 (pow eps 2)))) 1/144))) |
(* -1 (/ (+ 1 (* -1/2 (pow x 2))) (pow eps 3))) |
(/ (- (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))) (+ 1 (* -1/2 (pow x 2)))) (pow eps 3)) |
(/ (- (* eps (+ (* eps (- 1/6 (* 1/12 (pow x 2)))) (* x (+ 1/2 (* -1/12 (pow x 2)))))) (+ 1 (* -1/2 (pow x 2)))) (pow eps 3)) |
(/ (- (* eps (+ (* eps (- (+ 1/6 (* eps (* x (- (* 1/144 (pow x 2)) 1/24)))) (* 1/12 (pow x 2)))) (* x (+ 1/2 (* -1/12 (pow x 2)))))) (+ 1 (* -1/2 (pow x 2)))) (pow eps 3)) |
(* x (- (* 1/144 (pow x 2)) 1/24)) |
(- (+ (* x (- (* 1/144 (pow x 2)) 1/24)) (* 1/6 (/ 1 eps))) (* 1/12 (/ (pow x 2) eps))) |
(- (+ (* x (- (* 1/144 (pow x 2)) 1/24)) (+ (* 1/6 (/ 1 eps)) (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) (pow eps 2)))) (* 1/12 (/ (pow x 2) eps))) |
(- (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) (pow eps 3))) (+ (* x (- (* 1/144 (pow x 2)) 1/24)) (* 1/6 (/ 1 eps)))) (+ (* -1 (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) (pow eps 2))) (* 1/12 (/ (pow x 2) eps)))) |
(* x (- (* 1/144 (pow x 2)) 1/24)) |
(+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* x (- (* 1/144 (pow x 2)) 1/24))) |
(+ (* -1 (/ (- (* -1 (/ (* x (+ 1/2 (* -1/12 (pow x 2)))) eps)) (* -1 (- (* 1/12 (pow x 2)) 1/6))) eps)) (* x (- (* 1/144 (pow x 2)) 1/24))) |
(+ (* -1 (/ (- (* -1 (/ (- (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* -1 (* x (+ 1/2 (* -1/12 (pow x 2)))))) eps)) (* -1 (- (* 1/12 (pow x 2)) 1/6))) eps)) (* x (- (* 1/144 (pow x 2)) 1/24))) |
(* -1/24 x) |
(* x (- (* 1/144 (pow x 2)) 1/24)) |
(* x (- (* 1/144 (pow x 2)) 1/24)) |
(* x (- (* 1/144 (pow x 2)) 1/24)) |
(* 1/144 (pow x 3)) |
(* (pow x 3) (- 1/144 (* 1/24 (/ 1 (pow x 2))))) |
(* (pow x 3) (- 1/144 (* 1/24 (/ 1 (pow x 2))))) |
(* (pow x 3) (- 1/144 (* 1/24 (/ 1 (pow x 2))))) |
(* 1/144 (pow x 3)) |
(* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/144))) |
(* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/144))) |
(* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/144))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(* -1/24 (* (pow eps 3) (cos (+ x (* 1/2 eps))))) |
(* (pow eps 3) (+ (* -1/24 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))) |
(* (pow eps 3) (+ (* -1/24 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))) |
(* (pow eps 3) (+ (* -1/24 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))) |
(* -1/24 (* (pow eps 3) (cos (- x (* -1/2 eps))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/24 (cos (- x (* -1/2 eps))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/24 (cos (- x (* -1/2 eps))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/24 (cos (- x (* -1/2 eps))))))) |
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(* -1/48 (* (pow eps 3) (cos (+ x (* 1/2 eps))))) |
(* (pow eps 3) (+ (* -1/48 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/48 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/48 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))) |
(* -1/48 (* (pow eps 3) (cos (- x (* -1/2 eps))))) |
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/48 (cos (- x (* -1/2 eps))))))) |
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/48 (cos (- x (* -1/2 eps))))))) |
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/48 (cos (- x (* -1/2 eps))))))) |
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) |
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))))) |
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))))))) |
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))) |
(+ (* -1 (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) |
(+ (* x (+ (* -1 (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* -1/2 (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))) (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) |
(+ (* x (+ (* -1 (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* 1/6 (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))))) (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2)))) |
(* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2)))) |
(* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2)))) |
(* (cos (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 2)))) |
(* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2)))) |
(* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2)))) |
(* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2)))) |
(* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 2)))) |
(* 1/2 (cos x)) |
(+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))) |
(+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))) |
(+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))) |
(* -1/48 (* (pow eps 2) (cos (+ x (* 1/2 eps))))) |
(* (pow eps 2) (+ (* -1/48 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/48 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/48 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))) |
(* -1/48 (* (pow eps 2) (cos (- x (* -1/2 eps))))) |
(* (pow eps 2) (+ (* -1/48 (cos (- x (* -1/2 eps)))) (* 1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/48 (cos (- x (* -1/2 eps)))) (* 1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))) |
(* (pow eps 2) (+ (* -1/48 (cos (- x (* -1/2 eps)))) (* 1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))) |
(cos (* 1/2 eps)) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (- x (* -1/2 eps))) |
(cos (- x (* -1/2 eps))) |
(cos (- x (* -1/2 eps))) |
(cos (- x (* -1/2 eps))) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps x)) |
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2))))) |
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps))))) |
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2))))))))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/2 (* eps (sin x))) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(* 1/24 (pow eps 2)) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* -1/6 (* eps (pow x 3))) |
(* 1/144 x) |
(* 1/144 x) |
(* 1/144 x) |
(* 1/144 x) |
(* 1/144 x) |
(* 1/144 x) |
(* 1/144 x) |
(* 1/144 x) |
(* 1/144 x) |
(* 1/144 x) |
(* 1/144 x) |
(* 1/144 x) |
(* -1/12 (pow x 2)) |
(* -1/12 (pow x 2)) |
(* -1/12 (pow x 2)) |
(* -1/12 (pow x 2)) |
(* -1/12 (pow x 2)) |
(* -1/12 (pow x 2)) |
(* -1/12 (pow x 2)) |
(* -1/12 (pow x 2)) |
(* -1/12 (pow x 2)) |
(* -1/12 (pow x 2)) |
(* -1/12 (pow x 2)) |
(* -1/12 (pow x 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* -1/48 (pow eps 2)) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
| Outputs |
|---|
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64)))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64)))))) |
(* -1/6 (* (pow eps 3) (cos x))) |
(*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) (cos.f64 x)) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps)) (+.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (/.f64 (cos.f64 x) (*.f64 eps eps))))) |
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps)) (+.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (/.f64 (cos.f64 x) (*.f64 eps eps))))) |
(* -1/6 (* (pow eps 3) (cos x))) |
(*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) (cos.f64 x)) |
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))) |
(*.f64 (+.f64 (*.f64 (cos.f64 x) #s(literal 1/6 binary64)) (/.f64 (*.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(*.f64 (-.f64 (*.f64 (cos.f64 x) #s(literal 1/6 binary64)) (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps)) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps)))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))) |
(*.f64 (-.f64 (*.f64 (cos.f64 x) #s(literal 1/6 binary64)) (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) eps)) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps)))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) x)) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* -1/2 (pow eps 2))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps))))) |
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* 1/12 (* (pow eps 2) x))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (*.f64 x (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x (*.f64 eps eps)) #s(literal 1/12 binary64))))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
(* eps (+ (* -1/2 (* eps (sin x))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))) |
(*.f64 eps (+.f64 (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+.f64 (cos.f64 x) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
(+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))))) |
(* -1/6 (* (pow eps 2) (cos x))) |
(*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (cos.f64 x)) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))) |
(*.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 x) eps)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 eps eps)) |
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))) |
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(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps x)) |
(*.f64 #s(literal -1/2 binary64) (*.f64 eps x)) |
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2))))) |
(*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 #s(literal 1/12 binary64) (*.f64 eps (*.f64 x x))))) |
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps))))) |
(*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 eps (*.f64 x x)) #s(literal -1/240 binary64)) (*.f64 eps #s(literal 1/12 binary64)))))) |
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2))))))))) |
(*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal 1/12 binary64)) (*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/240 binary64)) (*.f64 (*.f64 eps (*.f64 x x)) #s(literal 1/10080 binary64)))))))) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* -1/6 (pow eps 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(* 1/24 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(* 1/24 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(* 1/24 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(* 1/24 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(* 1/24 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(* 1/24 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(* 1/24 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(* 1/24 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(* 1/24 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(* 1/24 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(* 1/24 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(* 1/24 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* -1/6 (* eps (pow x 3))) |
(*.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x))) |
(* 1/144 x) |
(*.f64 x #s(literal 1/144 binary64)) |
(* 1/144 x) |
(*.f64 x #s(literal 1/144 binary64)) |
(* 1/144 x) |
(*.f64 x #s(literal 1/144 binary64)) |
(* 1/144 x) |
(*.f64 x #s(literal 1/144 binary64)) |
(* 1/144 x) |
(*.f64 x #s(literal 1/144 binary64)) |
(* 1/144 x) |
(*.f64 x #s(literal 1/144 binary64)) |
(* 1/144 x) |
(*.f64 x #s(literal 1/144 binary64)) |
(* 1/144 x) |
(*.f64 x #s(literal 1/144 binary64)) |
(* 1/144 x) |
(*.f64 x #s(literal 1/144 binary64)) |
(* 1/144 x) |
(*.f64 x #s(literal 1/144 binary64)) |
(* 1/144 x) |
(*.f64 x #s(literal 1/144 binary64)) |
(* 1/144 x) |
(*.f64 x #s(literal 1/144 binary64)) |
(* -1/12 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
(* -1/12 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
(* -1/12 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
(* -1/12 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
(* -1/12 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
(* -1/12 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
(* -1/12 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
(* -1/12 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
(* -1/12 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
(* -1/12 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
(* -1/12 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
(* -1/12 (pow x 2)) |
(*.f64 (*.f64 x x) #s(literal -1/12 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* -1/48 (pow eps 2)) |
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
Compiled 34993 to 2517 computations (92.8% saved)
23 alts after pruning (19 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 973 | 11 | 984 |
| Fresh | 3 | 8 | 11 |
| Picked | 2 | 3 | 5 |
| Done | 1 | 1 | 2 |
| Total | 979 | 23 | 1002 |
| Status | Accuracy | Program |
|---|---|---|
| 98.7% | (+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) | |
| 100.0% | (+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))) | |
| 98.9% | (+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps))))) | |
| 99.8% | (+.f64 (*.f64 eps (cos.f64 x)) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) | |
| 99.8% | (*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) | |
| 29.8% | (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 x x))))) | |
| 52.9% | (*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (*.f64 x x)))) | |
| ✓ | 99.9% | (*.f64 (*.f64 eps (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))) #s(literal 2 binary64)) |
| 98.8% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) | |
| 98.7% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/6 binary64))) (/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) x))))) | |
| 98.8% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))))) | |
| 98.8% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 eps x))) #s(literal -1/2 binary64))))))) | |
| 98.8% | (*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 #s(literal 1/12 binary64) (*.f64 eps x)))))))) | |
| ✓ | 100.0% | (*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
| 99.8% | (*.f64 eps (+.f64 (cos.f64 x) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))) | |
| 98.2% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (*.f64 x (*.f64 x x))))) | |
| ✓ | 98.7% | (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
| 27.3% | (*.f64 eps (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) | |
| 29.7% | (*.f64 eps (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 #s(literal -1/6 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x x))))) (+.f64 (+.f64 (/.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) x))) (/.f64 #s(literal -1/2 binary64) x))))) | |
| 50.3% | (*.f64 eps (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))) | |
| 5.2% | (*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) | |
| 99.4% | (*.f64 eps (cos.f64 x)) | |
| ✓ | 98.2% | eps |
Compiled 1599 to 593 computations (62.9% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) |
(*.f64 eps (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (*.f64 x (*.f64 x x))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (*.f64 x x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 eps x))) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 eps (+.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 #s(literal 1/12 binary64) (*.f64 eps x)))))))) |
(*.f64 eps (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 x x))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 (*.f64 eps x) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/6 binary64))) (/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) x))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))))) |
(*.f64 eps (*.f64 (-.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/144 binary64))) #s(literal -1/24 binary64))) (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) (/.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps)) #s(literal -1/6 binary64)) eps)) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
(*.f64 eps (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 #s(literal -1/6 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x x))))) (+.f64 (+.f64 (/.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) x))) (/.f64 #s(literal -1/2 binary64) x))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(*.f64 (*.f64 eps (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x #s(literal 1/120 binary64)))))))) |
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))) |
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps #s(literal -1/6 binary64))) (*.f64 x (*.f64 x (+.f64 (*.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 eps (*.f64 x x))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps #s(literal 1/120 binary64)))))))))))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(+.f64 (*.f64 eps (cos.f64 x)) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) |
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))) |
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64)) (*.f64 (cos.f64 x) eps)) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) |
| Outputs |
|---|
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))) |
3 calls:
| 19.0ms | eps |
| 18.0ms | x |
| 18.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | eps |
| 100.0% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) |
(*.f64 eps (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (*.f64 x (*.f64 x x))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (*.f64 x x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 eps x))) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 eps (+.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 #s(literal 1/12 binary64) (*.f64 eps x)))))))) |
(*.f64 eps (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 x x))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 (*.f64 eps x) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/6 binary64))) (/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) x))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))))) |
(*.f64 eps (*.f64 (-.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/144 binary64))) #s(literal -1/24 binary64))) (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) (/.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps)) #s(literal -1/6 binary64)) eps)) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
(*.f64 eps (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 #s(literal -1/6 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x x))))) (+.f64 (+.f64 (/.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) x))) (/.f64 #s(literal -1/2 binary64) x))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(*.f64 (*.f64 eps (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x #s(literal 1/120 binary64)))))))) |
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))) |
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps #s(literal -1/6 binary64))) (*.f64 x (*.f64 x (+.f64 (*.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 eps (*.f64 x x))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps #s(literal 1/120 binary64)))))))))))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(+.f64 (*.f64 eps (cos.f64 x)) (*.f64 eps (*.f64 (sin.f64 x) (*.f64 eps (+.f64 (*.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))) |
| Outputs |
|---|
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
3 calls:
| 18.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 17.0ms | x |
| 16.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | eps |
| 100.0% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) |
(*.f64 eps (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (*.f64 x (*.f64 x x))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (*.f64 x x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 eps x))) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 eps (+.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 #s(literal 1/12 binary64) (*.f64 eps x)))))))) |
(*.f64 eps (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 x x))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 (*.f64 eps x) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/6 binary64))) (/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) x))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))))) |
(*.f64 eps (*.f64 (-.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/144 binary64))) #s(literal -1/24 binary64))) (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) (/.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps)) #s(literal -1/6 binary64)) eps)) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
(*.f64 eps (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 #s(literal -1/6 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x x))))) (+.f64 (+.f64 (/.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) x))) (/.f64 #s(literal -1/2 binary64) x))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
(*.f64 (*.f64 eps (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x #s(literal 1/120 binary64)))))))) |
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))) |
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps #s(literal -1/6 binary64))) (*.f64 x (*.f64 x (+.f64 (*.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 eps (*.f64 x x))) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps #s(literal 1/120 binary64)))))))))))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
| Outputs |
|---|
(*.f64 (*.f64 eps (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))) #s(literal 2 binary64)) |
3 calls:
| 20.0ms | x |
| 16.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 16.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
| 99.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) |
(*.f64 eps (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (*.f64 x (*.f64 x x))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (*.f64 x x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 eps x))) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 eps (+.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 #s(literal 1/12 binary64) (*.f64 eps x)))))))) |
(*.f64 eps (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 x x))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 (*.f64 eps x) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/6 binary64))) (/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) x))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))))) |
(*.f64 eps (*.f64 (-.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/144 binary64))) #s(literal -1/24 binary64))) (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) (/.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps)) #s(literal -1/6 binary64)) eps)) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
(*.f64 eps (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 #s(literal -1/6 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x x))))) (+.f64 (+.f64 (/.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) x))) (/.f64 #s(literal -1/2 binary64) x))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) |
| Outputs |
|---|
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
2 calls:
| 14.0ms | x |
| 12.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) |
(*.f64 eps (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (*.f64 x (*.f64 x x))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (*.f64 x x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 eps x))) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 eps (+.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 #s(literal 1/12 binary64) (*.f64 eps x)))))))) |
(*.f64 eps (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 x x))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 (*.f64 eps x) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/6 binary64))) (/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) x))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))))) |
(*.f64 eps (*.f64 (-.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/144 binary64))) #s(literal -1/24 binary64))) (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) (/.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps)) #s(literal -1/6 binary64)) eps)) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
(*.f64 eps (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 #s(literal -1/6 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x x))))) (+.f64 (+.f64 (/.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) x))) (/.f64 #s(literal -1/2 binary64) x))))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
| Outputs |
|---|
(*.f64 eps (cos.f64 x)) |
2 calls:
| 11.0ms | x |
| 11.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.4% | 1 | x |
| 99.4% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) |
(*.f64 eps (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (*.f64 x (*.f64 x x))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (*.f64 x x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 eps x))) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 eps (+.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 #s(literal 1/12 binary64) (*.f64 eps x)))))))) |
(*.f64 eps (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 x x))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))) (*.f64 x (+.f64 (*.f64 (*.f64 eps eps) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 (*.f64 eps x) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/6 binary64))) (/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) x))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps x)) (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))))) |
(*.f64 eps (*.f64 (-.f64 (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/144 binary64))) #s(literal -1/24 binary64))) (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) (/.f64 (-.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) eps)) eps)) #s(literal -1/6 binary64)) eps)) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
(*.f64 eps (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 #s(literal -1/6 binary64) (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x x))))) (+.f64 (+.f64 (/.f64 (*.f64 eps (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) x))) (/.f64 #s(literal -1/2 binary64) x))))) |
(sin.f64 eps) |
| Outputs |
|---|
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
2 calls:
| 11.0ms | x |
| 11.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 1 | x |
| 98.9% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) |
(*.f64 eps (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (*.f64 x (*.f64 x x))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (*.f64 x x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 eps x))) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 eps (+.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))) (*.f64 #s(literal 1/12 binary64) (*.f64 eps x)))))))) |
(*.f64 eps (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/12 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (*.f64 eps (*.f64 eps eps))) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 eps eps))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 x x))))) |
| Outputs |
|---|
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps))))) |
2 calls:
| 11.0ms | eps |
| 9.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 1 | eps |
| 98.9% | 1 | x |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) |
(*.f64 eps (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (*.f64 x (*.f64 x x))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (*.f64 x x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 eps x))) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))))) |
| Outputs |
|---|
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 eps x))) #s(literal -1/2 binary64))))))) |
2 calls:
| 7.0ms | eps |
| 7.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.8% | 1 | x |
| 98.8% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) |
(*.f64 eps (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (*.f64 x (*.f64 x x))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (*.f64 x x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))))) |
| Outputs |
|---|
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))))) |
2 calls:
| 6.0ms | eps |
| 6.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.8% | 1 | x |
| 98.8% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) |
(*.f64 eps (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (*.f64 x (*.f64 x x))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (*.f64 x x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 eps x)))) |
| Outputs |
|---|
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
2 calls:
| 13.0ms | x |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.8% | 1 | x |
| 98.8% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) |
(*.f64 eps (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal 1/12 binary64)) (*.f64 x (*.f64 x x))))) |
(*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 eps (*.f64 x x)))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))) |
| Outputs |
|---|
(+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) |
2 calls:
| 5.0ms | x |
| 5.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.7% | 1 | x |
| 98.7% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
| Outputs |
|---|
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
2 calls:
| 3.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.7% | 1 | x |
| 98.7% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
| Outputs |
|---|
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
2 calls:
| 3.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.2% | 1 | eps |
| 98.2% | 1 | x |
Compiled 6 to 4 computations (33.3% saved)
Total -59.6b remaining (-5208.3%)
Threshold costs -59.6b (-5208.3%)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
| Outputs |
|---|
eps |
2 calls:
| 6.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.2% | 1 | x |
| 98.2% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| 1× | egg-herbie |
| 96× | *-commutative_binary64 |
| 48× | +-commutative_binary64 |
| 2× | 1-exp_binary64 |
| 2× | 1-exp_binary32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 90 | 239 |
| 1 | 166 | 239 |
| 1× | saturated |
| Inputs |
|---|
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
(*.f64 (*.f64 eps (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 eps (cos.f64 x)) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 eps x))) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
eps |
| Outputs |
|---|
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))))))) |
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
(*.f64 eps (+.f64 (*.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))))) |
(*.f64 (*.f64 eps (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) |
(*.f64 eps (cos.f64 x)) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 (*.f64 eps x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)))))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) eps))))) |
(+.f64 (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) (*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 eps (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 eps x))) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/12 binary64) (*.f64 x (+.f64 eps x))))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/12 binary64) (*.f64 x x)))))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))))) |
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) (*.f64 x (*.f64 eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/12 binary64) (*.f64 x x))))))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 x #s(literal -1/2 binary64))) x) eps) |
(+.f64 eps (*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64))))) |
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
eps |
| 7938× | *-lowering-*.f32 |
| 7938× | *-lowering-*.f64 |
| 5976× | *-lowering-*.f32 |
| 5976× | *-lowering-*.f64 |
| 5588× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 814 | 7901 |
| 1 | 3075 | 7537 |
| 0 | 8262 | 7537 |
| 0 | 66 | 367 |
| 1 | 407 | 350 |
| 2 | 3896 | 350 |
| 0 | 8110 | 350 |
| 0 | 488 | 4908 |
| 1 | 1674 | 4492 |
| 2 | 6169 | 4490 |
| 0 | 8122 | 4490 |
| 0 | 694 | 6691 |
| 1 | 2480 | 6360 |
| 0 | 8717 | 6360 |
| 0 | 6 | 16 |
| 1 | 49 | 16 |
| 2 | 402 | 16 |
| 3 | 5232 | 16 |
| 0 | 8309 | 16 |
| 0 | 107 | 488 |
| 1 | 327 | 465 |
| 2 | 963 | 459 |
| 3 | 3572 | 459 |
| 0 | 8267 | 459 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 489 to 262 computations (46.4% saved)
Compiled 530 to 206 computations (61.1% saved)
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