
Time bar (total: 15.0s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 0 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 1 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 2 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 3 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 4 |
| 0% | 0% | 19% | 49.4% | 0% | 31.6% | 0% | 5 |
| 0% | 0% | 15.8% | 49.4% | 0% | 34.8% | 0% | 6 |
| 0% | 0% | 11.1% | 49.4% | 0% | 39.5% | 0% | 7 |
| 0% | 0% | 8.7% | 49.4% | 0% | 41.9% | 0% | 8 |
| 0% | 0% | 5.9% | 49.4% | 0% | 44.6% | 0% | 9 |
| 0% | 0% | 4.5% | 49.4% | 0% | 46% | 0% | 10 |
| 0% | 0% | 3.1% | 49.4% | 0% | 47.5% | 0% | 11 |
| 0% | 0% | 2.7% | 49.4% | 0% | 47.9% | 0% | 12 |
Compiled 27 to 19 computations (29.6% saved)
| 3.3s | 26 090× | 0 | invalid |
| 632.0ms | 5 567× | 0 | valid |
| 461.0ms | 2 689× | 1 | valid |
const: 622.0ms (20% of total)ival-sin: 562.0ms (18.1% of total)ival-mult: 537.0ms (17.3% of total)ival-add: 287.0ms (9.2% of total)ival-<=: 261.0ms (8.4% of total)ival-fabs: 254.0ms (8.2% of total)ival-sub: 209.0ms (6.7% of total)ival-<: 164.0ms (5.3% of total)ival-and: 104.0ms (3.3% of total)adjust: 48.0ms (1.5% of total)exact: 48.0ms (1.5% of total)ival-assert: 14.0ms (0.5% of total)| 2× | egg-herbie |
| 114× | sub-neg |
| 80× | accelerator-lowering-fma.f32 |
| 80× | accelerator-lowering-fma.f64 |
| 76× | cancel-sign-sub-inv |
| 62× | associate--r+ |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 46 |
| 1 | 43 | 42 |
| 2 | 92 | 42 |
| 3 | 181 | 42 |
| 4 | 321 | 42 |
| 5 | 398 | 42 |
| 6 | 483 | 42 |
| 7 | 525 | 42 |
| 8 | 534 | 42 |
| 0 | 6 | 7 |
| 1 | 9 | 7 |
| 2 | 14 | 7 |
| 3 | 20 | 7 |
| 4 | 28 | 7 |
| 5 | 43 | 7 |
| 6 | 76 | 7 |
| 7 | 101 | 7 |
| 8 | 144 | 7 |
| 9 | 159 | 7 |
| 10 | 167 | 7 |
| 0 | 167 | 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 |
|---|---|---|---|---|---|
| 222 | 3 | (2.387629466703073e-270 6.323919630425219e-273) | 4 | (4.022650708386591e-65 5.599523165333559e-67) | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3 | 1 | (452.1677815145183 308.6678353255072) | 1 | (66.68374274362472 0.00010012846265434226) | (sin.f64 (+.f64 x eps)) |
| 0 | 0 | - | 0 | - | eps |
| 0 | 0 | - | 0 | - | (+.f64 x eps) |
| 0 | 0 | - | 0 | - | (sin.f64 x) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) | cancellation | 221 | 8 |
sin.f64 | (sin.f64 (+.f64 x eps)) | sensitivity | 3 | 2 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 219 | 4 |
| - | 4 | 29 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 219 | 4 | 0 |
| - | 4 | 4 | 25 |
| number | freq |
|---|---|
| 0 | 33 |
| 1 | 222 |
| 2 | 1 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 17.0ms | 344× | 0 | valid |
| 15.0ms | 160× | 1 | valid |
| 5.0ms | 4× | 3 | valid |
| 2.0ms | 4× | 2 | valid |
Compiled 58 to 28 computations (51.7% saved)
ival-sin: 15.0ms (62.3% of total)adjust: 3.0ms (12.5% of total)ival-add: 3.0ms (12.5% of total)ival-sub: 3.0ms (12.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)Compiled 2 to 2 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 63.0% | (-.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)) |
| 80× | accelerator-lowering-fma.f32 |
| 80× | accelerator-lowering-fma.f64 |
| 48× | *-lowering-*.f32 |
| 48× | *-lowering-*.f64 |
| 36× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 1 | 9 | 18 |
| 2 | 14 | 18 |
| 3 | 20 | 18 |
| 4 | 28 | 18 |
| 5 | 43 | 18 |
| 6 | 76 | 18 |
| 7 | 101 | 18 |
| 8 | 144 | 18 |
| 9 | 159 | 18 |
| 10 | 167 | 18 |
| 0 | 167 | 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 | 99.8% | (sin.f64 (+.f64 x eps)) |
| ✓ | accuracy | 63.2% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 8.0ms | 172× | 0 | valid |
| 7.0ms | 80× | 1 | valid |
| 2.0ms | 2× | 3 | valid |
| 1.0ms | 2× | 2 | valid |
Compiled 20 to 8 computations (60% saved)
ival-sin: 8.0ms (64.3% of total)ival-add: 2.0ms (16.1% of total)adjust: 1.0ms (8% of total)ival-sub: 1.0ms (8% of total)ival-assert: 0.0ms (0% of total)ival-true: 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 | |
|---|---|---|---|---|
| 1.0ms | eps | @ | inf | (- (sin (+ x eps)) (sin x)) |
| 0.0ms | x | @ | 0 | (- (sin (+ x eps)) (sin x)) |
| 0.0ms | eps | @ | 0 | (- (sin (+ x eps)) (sin x)) |
| 0.0ms | x | @ | -inf | (- (sin (+ x eps)) (sin x)) |
| 0.0ms | x | @ | 0 | (sin x) |
| 1× | batch-egg-rewrite |
| 4 986× | accelerator-lowering-fma.f32 |
| 4 986× | accelerator-lowering-fma.f64 |
| 4 676× | *-lowering-*.f32 |
| 4 676× | *-lowering-*.f64 |
| 2 176× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 1 | 49 | 16 |
| 2 | 376 | 16 |
| 3 | 4763 | 16 |
| 0 | 8212 | 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)) (fma.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 (fma.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 (fma.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 binary64) (cos.f64 (+.f64 x x))) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64))))) |
(+.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))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal -1 binary64))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (fma.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 (fma.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 binary64) (cos.f64 (+.f64 x x))) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64)))) |
(-.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 binary64) (cos.f64 (+.f64 x x))) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64))))) |
(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 (fma.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 (fma.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 (sin.f64 x) #s(literal -1 binary64) (sin.f64 (+.f64 x eps))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x))) |
(fma.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.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 (fma.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 binary64) (cos.f64 (+.f64 x x))) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #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 (sin.f64 (+.f64 x eps)) (-.f64 (fma.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 (fma.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 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
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(/.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (-.f64 #s(literal 0 binary64) (fma.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 x eps) (-.f64 eps x))) (neg.f64 (-.f64 eps x))) |
(/.f64 (-.f64 (*.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.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 eps eps) (-.f64 x eps)))) (fma.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps)) (fma.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)) (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))))) |
(/.f64 (-.f64 (*.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)))) (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) |
(/.f64 (*.f64 (fma.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) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x)))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 x x (*.f64 eps eps))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))) #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 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) |
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) |
(*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) |
(*.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.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) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64))) |
(*.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x))) |
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps)) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x)))))) (fma.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x)))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) |
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 x eps) (*.f64 x x))) |
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))))) |
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps eps)))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (fma.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 #s(literal 1 binary64) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps)))) |
(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 1 binary64))) |
(sin.f64 x) |
(pow.f64 (sin.f64 x) #s(literal 1 binary64)) |
| 1× | egg-herbie |
| 16 678× | accelerator-lowering-fma.f32 |
| 16 678× | accelerator-lowering-fma.f64 |
| 4 132× | *-lowering-*.f32 |
| 4 132× | *-lowering-*.f64 |
| 2 614× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 107 | 496 |
| 1 | 314 | 496 |
| 2 | 775 | 489 |
| 3 | 2836 | 489 |
| 4 | 6173 | 489 |
| 0 | 8126 | 458 |
| 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))) |
(fma.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 (fma.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 (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (fma.f64 x (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #s(literal 0 binary64))) 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 (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 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 (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 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))) |
(fma.f64 x (cos.f64 eps) (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (fma.f64 x (cos.f64 eps) #s(literal 0 binary64))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (*.f64 (cos.f64 eps) (*.f64 x (fma.f64 x (*.f64 x #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 (- 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))) |
(fma.f64 eps (cos.f64 x) (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x) (*.f64 eps (cos.f64 x))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x) (*.f64 (*.f64 eps (cos.f64 x)) (fma.f64 eps (*.f64 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 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) #s(literal 1 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 7 832 to 845 computations (89.2% saved)
9 alts after pruning (8 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 290 | 8 | 298 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 290 | 9 | 299 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 63.3% | (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
| ▶ | 61.4% | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
| ✓ | 63.0% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 7.7% | (-.f64 (sin.f64 eps) (sin.f64 x)) | |
| ▶ | 99.8% | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
| 99.2% | (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) | |
| ▶ | 99.1% | (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
| 98.5% | (*.f64 eps (cos.f64 x)) | |
| ▶ | 96.6% | (sin.f64 eps) |
Compiled 211 to 142 computations (32.7% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) |
| ✓ | cost-diff | 0 | (cos.f64 eps) |
| ✓ | cost-diff | 0 | (sin.f64 x) |
| ✓ | cost-diff | 6400 | (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
| ✓ | cost-diff | -64 | (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
| ✓ | cost-diff | 0 | (cos.f64 x) |
| ✓ | cost-diff | 0 | (sin.f64 x) |
| ✓ | cost-diff | 0 | (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) |
| ✓ | cost-diff | 0 | (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
| ✓ | cost-diff | 0 | (+.f64 x eps) |
| ✓ | cost-diff | 0 | (sin.f64 (+.f64 x eps)) |
| ✓ | cost-diff | 192 | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
| ✓ | cost-diff | 0 | (sin.f64 eps) |
| ✓ | cost-diff | 0 | (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 192 | (+.f64 eps #s(literal 0 binary64)) |
| ✓ | cost-diff | 320 | (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
| 10 744× | accelerator-lowering-fma.f32 |
| 10 744× | accelerator-lowering-fma.f64 |
| 7 680× | *-lowering-*.f32 |
| 7 680× | *-lowering-*.f64 |
| 4 974× | associate-*r* |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 36 | 176 |
| 1 | 84 | 176 |
| 2 | 208 | 163 |
| 3 | 446 | 163 |
| 4 | 961 | 163 |
| 5 | 2228 | 163 |
| 6 | 3037 | 163 |
| 7 | 3538 | 163 |
| 8 | 3897 | 163 |
| 9 | 4218 | 163 |
| 10 | 4370 | 163 |
| 11 | 5332 | 163 |
| 12 | 5842 | 163 |
| 13 | 6028 | 163 |
| 14 | 6077 | 163 |
| 15 | 6106 | 163 |
| 16 | 6128 | 163 |
| 17 | 6140 | 163 |
| 18 | 6144 | 163 |
| 19 | 6144 | 163 |
| 20 | 6144 | 163 |
| 21 | 6282 | 163 |
| 22 | 6342 | 163 |
| 23 | 6342 | 163 |
| 24 | 6342 | 163 |
| 0 | 9703 | 152 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) |
(* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) |
(sin (* (+ eps 0) 1/2)) |
(* (+ eps 0) 1/2) |
(+ eps 0) |
eps |
0 |
1/2 |
(cos (* (+ (* x 2) eps) 1/2)) |
(* (+ (* x 2) eps) 1/2) |
(+ (* x 2) eps) |
x |
2 |
(sin eps) |
eps |
(- (sin (+ x eps)) (* x (+ (* x (* x -1/6)) 1))) |
(sin (+ x eps)) |
(+ x eps) |
x |
eps |
(* x (+ (* x (* x -1/6)) 1)) |
(+ (* x (* x -1/6)) 1) |
(* x -1/6) |
-1/6 |
1 |
(* eps (+ (* eps (* -1/2 (sin x))) (cos x))) |
eps |
(+ (* eps (* -1/2 (sin x))) (cos x)) |
(* -1/2 (sin x)) |
-1/2 |
(sin x) |
x |
(cos x) |
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x))) |
(sin x) |
x |
(cos eps) |
eps |
(- (* (cos x) (sin eps)) (sin x)) |
(* (cos x) (sin eps)) |
(cos x) |
(sin eps) |
| Outputs |
|---|
(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) |
(fma.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))) (fma.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 0 binary64)) #s(literal 0 binary64)) |
(* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) |
(fma.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 0 binary64)) |
(sin (* (+ eps 0) 1/2)) |
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))) |
(* (+ eps 0) 1/2) |
(fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64)) |
(+ eps 0) |
eps |
eps |
0 |
#s(literal 0 binary64) |
1/2 |
#s(literal 1/2 binary64) |
(cos (* (+ (* x 2) eps) 1/2)) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(* (+ (* x 2) eps) 1/2) |
(fma.f64 eps #s(literal 1/2 binary64) x) |
(+ (* x 2) eps) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
2 |
#s(literal 2 binary64) |
(sin eps) |
(sin.f64 eps) |
eps |
(- (sin (+ x eps)) (* x (+ (* x (* x -1/6)) 1))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 0 binary64)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x))) |
(sin (+ x eps)) |
(sin.f64 (+.f64 eps x)) |
(+ x eps) |
(+.f64 eps x) |
x |
eps |
(* x (+ (* x (* x -1/6)) 1)) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/6 binary64) #s(literal 0 binary64)) #s(literal 1 binary64)) #s(literal 0 binary64)) |
(+ (* x (* x -1/6)) 1) |
(fma.f64 x (fma.f64 x #s(literal -1/6 binary64) #s(literal 0 binary64)) #s(literal 1 binary64)) |
(* x -1/6) |
(fma.f64 x #s(literal -1/6 binary64) #s(literal 0 binary64)) |
-1/6 |
#s(literal -1/6 binary64) |
1 |
#s(literal 1 binary64) |
(* eps (+ (* eps (* -1/2 (sin x))) (cos x))) |
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) #s(literal 0 binary64)) (cos.f64 x)) #s(literal 0 binary64)) |
eps |
(+ (* eps (* -1/2 (sin x))) (cos x)) |
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) #s(literal 0 binary64)) (cos.f64 x)) |
(* -1/2 (sin x)) |
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) #s(literal 0 binary64)) |
-1/2 |
#s(literal -1/2 binary64) |
(sin x) |
(sin.f64 x) |
x |
(cos x) |
(cos.f64 x) |
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x))) |
(fma.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (fma.f64 (sin.f64 eps) (cos.f64 x) #s(literal 0 binary64))) |
(sin x) |
(sin.f64 x) |
x |
(cos eps) |
(cos.f64 eps) |
eps |
(- (* (cos x) (sin eps)) (sin x)) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 x))) |
(* (cos x) (sin eps)) |
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(literal 0 binary64)) |
(cos x) |
(cos.f64 x) |
(sin eps) |
(sin.f64 eps) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (cos.f64 eps) |
| ✓ | accuracy | 100.0% | (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) |
| ✓ | accuracy | 100.0% | (*.f64 (cos.f64 x) (sin.f64 eps)) |
| ✓ | accuracy | 63.3% | (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
| ✓ | accuracy | 100.0% | (sin.f64 x) |
| ✓ | accuracy | 100.0% | (cos.f64 x) |
| ✓ | accuracy | 100.0% | (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) |
| ✓ | accuracy | 100.0% | (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
| ✓ | accuracy | 100.0% | (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
| ✓ | accuracy | 99.8% | (sin.f64 (+.f64 x eps)) |
| ✓ | accuracy | 99.5% | (*.f64 x #s(literal -1/6 binary64)) |
| ✓ | accuracy | 63.8% | (-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
| ✓ | accuracy | 100.0% | (sin.f64 eps) |
| ✓ | accuracy | 100.0% | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 99.8% | (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
| 74.0ms | 169× | 0 | valid |
| 35.0ms | 81× | 1 | valid |
| 8.0ms | 4× | 3 | valid |
| 3.0ms | 2× | 2 | valid |
Compiled 177 to 38 computations (78.5% saved)
ival-cos: 38.0ms (39.6% of total)ival-mult: 23.0ms (23.9% of total)ival-sin: 14.0ms (14.6% of total)ival-add: 8.0ms (8.3% of total)adjust: 5.0ms (5.2% of total)const: 4.0ms (4.2% of total)ival-sub: 3.0ms (3.1% of total)exact: 1.0ms (1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (* (+ (* x 2) eps) 1/2)> |
#<alt (+ eps 0)> |
#<alt (sin (* (+ eps 0) 1/2))> |
#<alt (cos (* (+ (* x 2) eps) 1/2))> |
#<alt (sin eps)> |
#<alt (- (sin (+ x eps)) (* x (+ (* x (* x -1/6)) 1)))> |
#<alt (sin (+ x eps))> |
#<alt (+ x eps)> |
#<alt (+ (* x (* x -1/6)) 1)> |
#<alt (+ (* eps (* -1/2 (sin x))) (cos x))> |
#<alt (sin x)> |
#<alt (cos x)> |
#<alt (* eps (+ (* eps (* -1/2 (sin x))) (cos x)))> |
#<alt (+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))> |
#<alt (cos eps)> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)))> |
#<alt (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)> |
#<alt (* x -1/6)> |
#<alt (* x (+ (* x (* x -1/6)) 1))> |
#<alt (* (cos x) (sin eps))> |
| Outputs |
|---|
#<alt (* 1/2 eps)> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt x> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt x> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* 1/2 eps)> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt 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 (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 (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 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 1> |
#<alt (+ 1 (* -1/6 (pow x 2)))> |
#<alt (+ 1 (* -1/6 (pow x 2)))> |
#<alt (+ 1 (* -1/6 (pow x 2)))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))> |
#<alt (* -1/6 (pow x 2))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))> |
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))> |
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (* eps x)))> |
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))> |
#<alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<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)> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))> |
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt eps> |
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))> |
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))> |
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<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 (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (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 (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (pow eps 2)))> |
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* -1 x))> |
#<alt (+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))> |
#<alt (+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (* -1 (sin x))> |
#<alt (- (* eps (cos x)) (sin x))> |
#<alt (- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))> |
#<alt (- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<alt (- (* (cos x) (sin eps)) (sin x))> |
#<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 (* 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 (* -1/6 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 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) (* -1/2 (* (pow x 2) (sin eps))))> |
#<alt (+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))> |
#<alt (+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))> |
#<alt (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))> |
#<alt (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* (cos x) (sin eps))> |
#<alt (* (cos x) (sin eps))> |
99 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | eps | @ | 0 | (* eps (+ (* eps (* -1/2 (sin x))) (cos x))) |
| 2.0ms | eps | @ | inf | (+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x))) |
| 1.0ms | eps | @ | inf | (- (sin (+ x eps)) (* x (+ (* x (* x -1/6)) 1))) |
| 1.0ms | x | @ | inf | (+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x))) |
| 1.0ms | x | @ | inf | (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) |
| 1× | batch-egg-rewrite |
| 5 448× | accelerator-lowering-fma.f32 |
| 5 448× | accelerator-lowering-fma.f64 |
| 5 000× | *-lowering-*.f32 |
| 5 000× | *-lowering-*.f64 |
| 4 268× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 36 | 136 |
| 1 | 185 | 132 |
| 2 | 1806 | 132 |
| 0 | 9030 | 123 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (+ (* x 2) eps) 1/2) |
(+ eps 0) |
(sin (* (+ eps 0) 1/2)) |
(cos (* (+ (* x 2) eps) 1/2)) |
(sin eps) |
(- (sin (+ x eps)) (* x (+ (* x (* x -1/6)) 1))) |
(sin (+ x eps)) |
(+ x eps) |
(+ (* x (* x -1/6)) 1) |
(+ (* eps (* -1/2 (sin x))) (cos x)) |
(sin x) |
(cos x) |
(* eps (+ (* eps (* -1/2 (sin x))) (cos x))) |
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x))) |
(cos eps) |
(- (* (cos x) (sin eps)) (sin x)) |
(* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) |
(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) |
(* x -1/6) |
(* x (+ (* x (* x -1/6)) 1)) |
(* (cos x) (sin eps)) |
| Outputs |
|---|
(+.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) |
(+.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))) |
(+.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))) |
(fma.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)) (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))) |
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) |
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (/.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) |
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(*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(*.f64 (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64)))) |
(*.f64 (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))) #s(literal 1/2 binary64)) |
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))))) #s(literal 2 binary64)) |
(/.f64 (*.f64 (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))) #s(literal 2 binary64)) #s(literal 2 binary64)) |
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))))) #s(literal -2 binary64)) |
(/.f64 (neg.f64 (*.f64 (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))) #s(literal 2 binary64))) #s(literal -2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))) |
(*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))) |
(*.f64 (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))) #s(literal 2 binary64))) |
(*.f64 (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64)))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(*.f64 x #s(literal -1/6 binary64)) |
(*.f64 #s(literal -1/6 binary64) x) |
(+.f64 x (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) |
(+.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) x) |
(-.f64 (/.f64 (*.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) (-.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) x))) |
(fma.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)) x) |
(fma.f64 x #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) |
(fma.f64 (*.f64 x #s(literal -1/6 binary64)) (*.f64 x x) x) |
(fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 x x)) x x) |
(fma.f64 #s(literal 1 binary64) x (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) |
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal -1/6 binary64) x) |
(fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/6 binary64)) x) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/216 binary64))) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) (-.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) x)))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) (*.f64 x x)) (-.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) x)) |
(/.f64 (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/216 binary64)) #s(literal 1 binary64))) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(/.f64 (*.f64 x (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) #s(literal -1 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/216 binary64)) #s(literal 1 binary64)) x) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) #s(literal -1 binary64)) x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/216 binary64))) (*.f64 x (*.f64 x x)))) (neg.f64 (fma.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) (-.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) x))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) (*.f64 x x))) (neg.f64 (-.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) x))) |
(/.f64 (neg.f64 (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/216 binary64)) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))))) |
(/.f64 (neg.f64 (*.f64 x (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) #s(literal -1 binary64)))) (neg.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1 binary64)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/216 binary64)) #s(literal 1 binary64)) x)) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) #s(literal -1 binary64)) x)) (neg.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1 binary64)))) |
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/216 binary64))))) (fma.f64 x x (-.f64 (*.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) (*.f64 x (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))))) |
(*.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64))) |
(*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x) |
(/.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 2 binary64)) |
(/.f64 (neg.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps)))) #s(literal -2 binary64)) |
(*.f64 (sin.f64 eps) (cos.f64 x)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
| 1× | egg-herbie |
| 14 120× | accelerator-lowering-fma.f32 |
| 14 120× | accelerator-lowering-fma.f64 |
| 5 692× | *-lowering-*.f32 |
| 5 692× | *-lowering-*.f64 |
| 4 362× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 412 | 3565 |
| 1 | 1260 | 3392 |
| 2 | 3428 | 3329 |
| 0 | 8160 | 3043 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
x |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
x |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(* 1/2 eps) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(* 1/2 eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
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)) |
(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)))) |
(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)))) |
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))) |
1 |
(+ 1 (* -1/6 (pow x 2))) |
(+ 1 (* -1/6 (pow x 2))) |
(+ 1 (* -1/6 (pow x 2))) |
(* -1/6 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6)) |
(* -1/6 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6)) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(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))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (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))))))))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
1 |
(+ 1 (* -1/2 (pow eps 2))) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(sin eps) |
(+ (sin eps) (* -1 x)) |
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1))) |
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1))) |
(- (* (cos x) (sin eps)) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(* -1 (sin x)) |
(- (* eps (cos x)) (sin x)) |
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x)) |
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(* 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))) |
(* 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)))) |
(* -1/6 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) |
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) (* -1/2 (* (pow x 2) (sin eps)))) |
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps)))))) |
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps))))))) |
(* (cos x) (sin eps)) |
(* (cos x) (sin eps)) |
(* (cos x) (sin eps)) |
(* (cos x) (sin eps)) |
(* (cos x) (sin eps)) |
(* (cos x) (sin eps)) |
(* (cos x) (sin eps)) |
(* (cos x) (sin eps)) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) |
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) |
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x)))))))) |
(* (cos x) (sin eps)) |
(* (cos x) (sin eps)) |
(* (cos x) (sin eps)) |
(* (cos x) (sin eps)) |
(* (cos x) (sin eps)) |
(* (cos x) (sin eps)) |
(* (cos x) (sin eps)) |
(* (cos x) (sin eps)) |
| Outputs |
|---|
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
x |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 eps x) #s(literal 1 binary64))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 eps x) #s(literal 1 binary64))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 eps x) #s(literal 1 binary64))) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64)))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64)))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64)))) |
x |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ x (* 1/2 eps)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* eps (+ 1/2 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(cos (* 1/2 eps)) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(fma.f64 x (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) #s(literal 1 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))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 x (cos.f64 eps) (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (-.f64 #s(literal 0 binary64) x))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 x (+.f64 (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps)))) (sin.f64 eps)) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* (pow x 3) (- 1/6 (/ 1 (pow x 2)))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2)))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/6 binary64))))) |
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2)))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/6 binary64))))) |
(* 1/6 (pow x 3)) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/6 binary64))))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/6 binary64))))) |
(- (sin x) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 x) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (fma.f64 eps (cos.f64 x) (sin.f64 x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(fma.f64 eps (cos.f64 x) (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x) (-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))))) |
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (sin.f64 x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2))))) |
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (cos eps))) |
(fma.f64 x (cos.f64 eps) (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(fma.f64 x (cos.f64 eps) (*.f64 (fma.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)))))))) |
(fma.f64 x (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))) (sin.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))) |
(fma.f64 eps (cos.f64 x) (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(fma.f64 eps (cos.f64 x) (*.f64 (fma.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)))))))) |
(fma.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (sin.f64 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 (- 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))) |
(fma.f64 x (/.f64 eps x) x) |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
(* x (+ 1 (/ eps x))) |
(fma.f64 x (/.f64 eps x) x) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 x (/.f64 eps x) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 x (/.f64 eps x) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 x (/.f64 eps x) x) |
x |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
(+ eps x) |
(+.f64 eps x) |
eps |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* eps (+ 1 (/ x eps))) |
(fma.f64 eps (/.f64 x eps) eps) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 eps (/.f64 x eps) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 eps (/.f64 x eps) eps) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/6 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(+ 1 (* -1/6 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(+ 1 (* -1/6 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(* -1/6 (pow x 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 x x)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6)) |
(fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6)) |
(fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6)) |
(fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(* -1/6 (pow x 2)) |
(*.f64 #s(literal -1/6 binary64) (*.f64 x x)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6)) |
(fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6)) |
(fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6)) |
(fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(* -1/2 (* eps (sin x))) |
(*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* -1/2 (* eps (sin x))) |
(*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (* eps x))) |
(fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) #s(literal 1 binary64))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 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) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(fma.f64 x (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (*.f64 x (*.f64 x (*.f64 (*.f64 eps eps) #s(literal 1/12 binary64))))) eps) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 x (cos.f64 eps) (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (-.f64 #s(literal 0 binary64) x))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 x (+.f64 (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps)))) (sin.f64 eps)) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 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 (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x)) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow eps 2))) |
(fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* -1 x)) |
(-.f64 (sin.f64 eps) x) |
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (-.f64 #s(literal 0 binary64) x)) |
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) #s(literal -1 binary64)) (sin.f64 eps)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(* -1 (sin x)) |
(-.f64 #s(literal 0 binary64) (sin.f64 x)) |
(- (* eps (cos x)) (sin x)) |
(fma.f64 eps (cos.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 x))) |
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x)) |
(-.f64 (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 eps (cos.f64 x))) (sin.f64 x)) |
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x)) |
(fma.f64 eps (*.f64 (cos.f64 x) (+.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(- (* (cos x) (sin eps)) (sin x)) |
(-.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)) (sin.f64 x)) |
(* 1/2 (* eps (cos x))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.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 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.f64 eps (fma.f64 (sin.f64 x) #s(literal -1/4 binary64) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/12 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)))))))))) |
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(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) 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)))) |
(fma.f64 x (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) 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)))) |
(fma.f64 x (fma.f64 x (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 x #s(literal -2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))) |
(fma.f64 #s(literal -2 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (fma.f64 x (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64)))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2)))))))) |
(fma.f64 x (fma.f64 x (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/3 binary64)) #s(literal -2 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
(* -1/6 x) |
(*.f64 x #s(literal -1/6 binary64)) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* -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 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6)) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* -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 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* -1/2 (* (pow x 2) (sin eps)))) |
(*.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps)) |
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps)))))) |
(*.f64 (sin.f64 eps) (+.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))))) |
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps))))))) |
(fma.f64 (*.f64 x x) (*.f64 (sin.f64 eps) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps))) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) |
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 eps (cos.f64 x))) |
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) |
(*.f64 eps (*.f64 (cos.f64 x) (+.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64)))))) |
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x)))))))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (*.f64 (cos.f64 x) (*.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))))) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
(* (cos x) (sin eps)) |
(*.f64 (cos.f64 x) (sin.f64 eps)) |
Compiled 30 383 to 2 616 computations (91.4% saved)
21 alts after pruning (17 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 066 | 14 | 1 080 |
| Fresh | 0 | 3 | 3 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 068 | 21 | 1 089 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 97.6% | (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
| 99.2% | (fma.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x) (*.f64 eps (cos.f64 x))) | |
| ✓ | 63.3% | (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
| 99.4% | (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) | |
| ▶ | 99.2% | (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps eps #s(literal 0 binary64)))) |
| 96.5% | (fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps) | |
| ✓ | 63.0% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 7.7% | (-.f64 (sin.f64 eps) (sin.f64 x)) | |
| 99.2% | (*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) | |
| ▶ | 99.0% | (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
| ▶ | 99.8% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
| 5.9% | (*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) | |
| 99.2% | (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) | |
| 97.7% | (*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) | |
| 97.6% | (*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64))) | |
| 99.2% | (*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))) | |
| ✓ | 99.1% | (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
| 98.6% | (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) x) (cos.f64 x))) | |
| 98.5% | (*.f64 eps (cos.f64 x)) | |
| ✓ | 96.6% | (sin.f64 eps) |
| ▶ | 96.6% | eps |
Compiled 494 to 322 computations (34.8% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sin.f64 x) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
| ✓ | cost-diff | 0 | (cos.f64 x) |
| ✓ | cost-diff | 448 | (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps eps #s(literal 0 binary64)))) |
| ✓ | cost-diff | 0 | (fma.f64 x #s(literal 2 binary64) eps) |
| ✓ | cost-diff | 0 | (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 320 | (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 704 | (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
| ✓ | cost-diff | -64 | (*.f64 eps (+.f64 eps x)) |
| ✓ | cost-diff | -64 | (*.f64 x #s(literal -1/2 binary64)) |
| ✓ | cost-diff | 0 | (+.f64 eps x) |
| ✓ | cost-diff | 0 | (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
| ✓ | cost-diff | 0 | (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
| ✓ | cost-diff | 0 | (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
| ✓ | cost-diff | 0 | (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
| 9 062× | accelerator-lowering-fma.f32 |
| 9 062× | accelerator-lowering-fma.f64 |
| 5 808× | *-lowering-*.f32 |
| 5 808× | *-lowering-*.f64 |
| 1 876× | --lowering--.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 31 | 157 |
| 1 | 73 | 155 |
| 2 | 192 | 151 |
| 3 | 403 | 147 |
| 4 | 600 | 147 |
| 5 | 1541 | 147 |
| 6 | 2424 | 147 |
| 7 | 3229 | 147 |
| 8 | 4272 | 147 |
| 9 | 7791 | 147 |
| 0 | 8011 | 136 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x))) 2) |
(* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x))) |
(sin (* 1/2 eps)) |
(* 1/2 eps) |
1/2 |
eps |
(cos (+ (* 1/2 eps) x)) |
(+ (* 1/2 eps) x) |
x |
2 |
eps |
(+ (* (* x -1/2) (* eps (+ eps x))) eps) |
(* x -1/2) |
x |
-1/2 |
(* eps (+ eps x)) |
eps |
(+ eps x) |
(* (* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) 2) |
(* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) |
(* 1/2 eps) |
1/2 |
eps |
(cos (* (+ (* x 2) eps) 1/2)) |
(* (+ (* x 2) eps) 1/2) |
(+ (* x 2) eps) |
x |
2 |
(+ (* (cos x) eps) (* (* -1/2 (sin x)) (+ (* eps eps) 0))) |
(cos x) |
x |
eps |
(* (* -1/2 (sin x)) (+ (* eps eps) 0)) |
(* -1/2 (sin x)) |
-1/2 |
(sin x) |
(+ (* eps eps) 0) |
0 |
| Outputs |
|---|
(* (* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x))) 2) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x))) |
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(sin (* 1/2 eps)) |
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))) |
(* 1/2 eps) |
(fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
eps |
(cos (+ (* 1/2 eps) x)) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(+ (* 1/2 eps) x) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
x |
2 |
#s(literal 2 binary64) |
eps |
(+ (* (* x -1/2) (* eps (+ eps x))) eps) |
(fma.f64 eps (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (+.f64 eps x) #s(literal 0 binary64)) #s(literal 1 binary64)) #s(literal 0 binary64)) |
(* x -1/2) |
(fma.f64 x #s(literal -1/2 binary64) #s(literal 0 binary64)) |
x |
-1/2 |
#s(literal -1/2 binary64) |
(* eps (+ eps x)) |
(fma.f64 eps (+.f64 eps x) #s(literal 0 binary64)) |
eps |
(+ eps x) |
(+.f64 eps x) |
(* (* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) 2) |
(fma.f64 eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 0 binary64)) |
(* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) |
(fma.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 0 binary64)) |
(* 1/2 eps) |
(fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
eps |
(cos (* (+ (* x 2) eps) 1/2)) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(* (+ (* x 2) eps) 1/2) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(+ (* x 2) eps) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
2 |
#s(literal 2 binary64) |
(+ (* (cos x) eps) (* (* -1/2 (sin x)) (+ (* eps eps) 0))) |
(fma.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) #s(literal 0 binary64)) |
(cos x) |
(cos.f64 x) |
x |
eps |
(* (* -1/2 (sin x)) (+ (* eps eps) 0)) |
(fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (fma.f64 eps (sin.f64 x) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
-1/2 |
#s(literal -1/2 binary64) |
(sin x) |
(sin.f64 x) |
(+ (* eps eps) 0) |
(fma.f64 eps eps #s(literal 0 binary64)) |
0 |
#s(literal 0 binary64) |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (sin.f64 x) |
| ✓ | accuracy | 100.0% | (cos.f64 x) |
| ✓ | accuracy | 100.0% | (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps eps #s(literal 0 binary64)))) |
| ✓ | accuracy | 99.9% | (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps eps #s(literal 0 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/2 binary64) eps) |
| ✓ | accuracy | 100.0% | (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 99.8% | (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 100.0% | (+.f64 eps x) |
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal -1/2 binary64)) |
| ✓ | accuracy | 100.0% | (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
| ✓ | accuracy | 99.8% | (*.f64 eps (+.f64 eps x)) |
| ✓ | accuracy | 100.0% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
| ✓ | accuracy | 100.0% | (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
| ✓ | accuracy | 99.8% | (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
| 53.0ms | 255× | 0 | valid |
| 1.0ms | 1× | 3 | valid |
Compiled 155 to 33 computations (78.7% saved)
ival-mult: 22.0ms (57.2% of total)ival-add: 6.0ms (15.6% of total)ival-cos: 5.0ms (13% of total)ival-sin: 4.0ms (10.4% of total)adjust: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt (* (* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x))) 2)> |
#<alt (* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x)))> |
#<alt (sin (* 1/2 eps))> |
#<alt (cos (+ (* 1/2 eps) x))> |
#<alt (+ (* (* x -1/2) (* eps (+ eps x))) eps)> |
#<alt (+ eps x)> |
#<alt (* x -1/2)> |
#<alt (* eps (+ eps x))> |
#<alt (* (* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) 2)> |
#<alt (* (+ (* x 2) eps) 1/2)> |
#<alt (cos (* (+ (* x 2) eps) 1/2))> |
#<alt (+ (* x 2) eps)> |
#<alt (+ (* (cos x) eps) (* (* -1/2 (sin x)) (+ (* eps eps) 0)))> |
#<alt (cos x)> |
#<alt (* -1/2 (sin x))> |
#<alt (sin x)> |
#<alt (* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2)))> |
#<alt (* 1/2 eps)> |
#<alt (* (* -1/2 (sin x)) (+ (* eps eps) 0))> |
| Outputs |
|---|
#<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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))> |
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))> |
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))> |
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))> |
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))> |
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))> |
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))> |
#<alt (* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))> |
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))> |
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))> |
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))> |
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))> |
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))> |
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))> |
#<alt (* (cos (- (* 1/2 eps) (* -1 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 (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 (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 eps> |
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))> |
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))> |
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))> |
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))> |
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))> |
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))> |
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))> |
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))> |
#<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 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 (* -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 x)> |
#<alt (* eps (+ eps x))> |
#<alt (* eps (+ eps x))> |
#<alt (* eps (+ eps x))> |
#<alt (pow eps 2)> |
#<alt (* (pow eps 2) (+ 1 (/ x eps)))> |
#<alt (* (pow eps 2) (+ 1 (/ x eps)))> |
#<alt (* (pow eps 2) (+ 1 (/ x eps)))> |
#<alt (pow eps 2)> |
#<alt (* (pow eps 2) (+ 1 (/ x eps)))> |
#<alt (* (pow eps 2) (+ 1 (/ x eps)))> |
#<alt (* (pow eps 2) (+ 1 (/ x eps)))> |
#<alt (pow eps 2)> |
#<alt (+ (* eps x) (pow eps 2))> |
#<alt (+ (* eps x) (pow eps 2))> |
#<alt (+ (* eps x) (pow eps 2))> |
#<alt (* eps x)> |
#<alt (* x (+ eps (/ (pow eps 2) x)))> |
#<alt (* x (+ eps (/ (pow eps 2) x)))> |
#<alt (* x (+ eps (/ (pow eps 2) x)))> |
#<alt (* eps x)> |
#<alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))> |
#<alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))> |
#<alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))> |
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))> |
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))> |
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))> |
#<alt (* eps (cos (* 1/2 eps)))> |
#<alt (+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))> |
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))> |
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))> |
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))> |
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))> |
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))> |
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))> |
#<alt (* 1/2 eps)> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt x> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt (* x (+ 1 (* 1/2 (/ eps x))))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))> |
#<alt x> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (+ x (* 1/2 eps))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* eps (+ 1/2 (/ x eps)))> |
#<alt (* 1/2 eps)> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))> |
#<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 (* 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 (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 eps> |
#<alt (+ eps (* 2 x))> |
#<alt (+ eps (* 2 x))> |
#<alt (+ eps (* 2 x))> |
#<alt (* 2 x)> |
#<alt (* x (+ 2 (/ eps x)))> |
#<alt (* x (+ 2 (/ eps x)))> |
#<alt (* x (+ 2 (/ eps x)))> |
#<alt (* 2 x)> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))> |
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))> |
#<alt (* 2 x)> |
#<alt (+ eps (* 2 x))> |
#<alt (+ eps (* 2 x))> |
#<alt (+ eps (* 2 x))> |
#<alt eps> |
#<alt (* eps (+ 1 (* 2 (/ x eps))))> |
#<alt (* eps (+ 1 (* 2 (/ x eps))))> |
#<alt (* eps (+ 1 (* 2 (/ x eps))))> |
#<alt eps> |
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))> |
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))> |
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))> |
#<alt eps> |
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))> |
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))> |
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))> |
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (* -1/2 x)> |
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))> |
#<alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))> |
#<alt (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<alt (* -1/2 (sin x))> |
#<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)> |
#<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)) (* -1/16 (* eps (cos x)))))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 eps))))> |
#<alt (+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))> |
#<alt (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))> |
#<alt (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))> |
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))> |
#<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 (* -1/2 (* (pow eps 2) x))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2)))))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (pow eps 2)) (* 1/10080 (* (pow eps 2) (pow x 2)))))))))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
96 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | x | @ | inf | (sin x) |
| 5.0ms | x | @ | 0 | (* (* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) 2) |
| 1.0ms | x | @ | inf | (+ (* (cos x) eps) (* (* -1/2 (sin x)) (+ (* eps eps) 0))) |
| 1.0ms | x | @ | -inf | (+ (* (cos x) eps) (* (* -1/2 (sin x)) (+ (* eps eps) 0))) |
| 1.0ms | eps | @ | 0 | (* (* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) 2) |
| 1× | batch-egg-rewrite |
| 13 252× | accelerator-lowering-fma.f32 |
| 13 252× | accelerator-lowering-fma.f64 |
| 4 580× | *-lowering-*.f32 |
| 4 580× | *-lowering-*.f64 |
| 3 264× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 31 | 134 |
| 1 | 150 | 132 |
| 2 | 1250 | 130 |
| 0 | 8591 | 120 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x))) 2) |
(* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x))) |
(sin (* 1/2 eps)) |
(cos (+ (* 1/2 eps) x)) |
(+ (* (* x -1/2) (* eps (+ eps x))) eps) |
(+ eps x) |
(* x -1/2) |
(* eps (+ eps x)) |
(* (* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) 2) |
(* (+ (* x 2) eps) 1/2) |
(cos (* (+ (* x 2) eps) 1/2)) |
(+ (* x 2) eps) |
(+ (* (cos x) eps) (* (* -1/2 (sin x)) (+ (* eps eps) 0))) |
(cos x) |
(* -1/2 (sin x)) |
(sin x) |
(* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) |
(* 1/2 eps) |
(* (* -1/2 (sin x)) (+ (* eps eps) 0)) |
| Outputs |
|---|
(+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) |
(+.f64 (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(fma.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) |
(fma.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) |
(/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)))) |
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 2 binary64)) |
(/.f64 (*.f64 (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #s(literal 2 binary64)) |
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))))) #s(literal -2 binary64)) |
(/.f64 (neg.f64 (*.f64 (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))) #s(literal -2 binary64)) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(*.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) |
(+.f64 (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) |
(fma.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) |
(neg.f64 (/.f64 (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))) |
(/.f64 (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal -2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 1 binary64))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))))) #s(literal 2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -1 binary64)) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(*.f64 (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 1/2 binary64)) |
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal -1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(+.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) |
(+.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 1/4 binary64) #s(literal 0 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))) (cos.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))) (*.f64 (sin.f64 (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 1/4 binary64) #s(literal 0 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))) (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))) |
(fma.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) |
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) |
(fma.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))) #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) |
(fma.f64 (cos.f64 (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 1/4 binary64) #s(literal 0 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))) (cos.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))) (*.f64 (sin.f64 (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 1/4 binary64) #s(literal 0 binary64)) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))))) |
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(/.f64 (neg.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) (fma.f64 eps eps #s(literal 0 binary64)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) (-.f64 #s(literal 0 binary64) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) (-.f64 #s(literal 0 binary64) (fma.f64 eps eps #s(literal 0 binary64)))) |
(/.f64 (+.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (fma.f64 (sin.f64 x) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 3 binary64)) #s(literal 0 binary64))) (pow.f64 (fma.f64 (sin.f64 x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 2 binary64))) |
(/.f64 (-.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (fma.f64 (sin.f64 x) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 3 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (pow.f64 (fma.f64 (sin.f64 x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 2 binary64))) |
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (fma.f64 (sin.f64 x) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 3 binary64)) #s(literal 0 binary64))) (fma.f64 #s(literal -1/4 binary64) (pow.f64 (fma.f64 (sin.f64 x) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))) |
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(*.f64 #s(literal -1/2 binary64) (fma.f64 (sin.f64 x) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64))) |
(*.f64 (sin.f64 x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64))) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps eps #s(literal 0 binary64))) |
(*.f64 (fma.f64 eps eps #s(literal 0 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps eps #s(literal 0 binary64)))) |
(*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (fma.f64 (sin.f64 x) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 3 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (sin.f64 x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 2 binary64)))) |
(*.f64 (pow.f64 (fma.f64 (sin.f64 x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) |
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal -1/2 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 eps eps #s(literal 0 binary64))) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))))) |
(*.f64 (*.f64 (fma.f64 eps eps #s(literal 0 binary64)) #s(literal -1/2 binary64)) (sin.f64 x)) |
(*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps #s(literal 0 binary64)))) |
(*.f64 (*.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) |
(*.f64 (*.f64 (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps #s(literal 0 binary64)))) |
(*.f64 (/.f64 (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) eps) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) |
(*.f64 (/.f64 (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 (sin.f64 x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) |
(*.f64 (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)) |
(*.f64 (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) eps) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)))) |
(*.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) (/.f64 (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) eps)) |
(*.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)))) |
(*.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps eps #s(literal 0 binary64))) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) |
(*.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) eps)) |
(*.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))))) |
(*.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) |
| 1× | egg-herbie |
| 14 110× | accelerator-lowering-fma.f32 |
| 14 110× | accelerator-lowering-fma.f64 |
| 6 608× | *-lowering-*.f32 |
| 6 608× | *-lowering-*.f64 |
| 3 672× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 396 | 3534 |
| 1 | 1254 | 3441 |
| 2 | 3471 | 3376 |
| 0 | 8332 | 3093 |
| 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)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2)))))))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))) |
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))) |
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))) |
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))) |
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))) |
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))) |
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))) |
(* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))) |
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))) |
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))) |
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))) |
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))) |
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))) |
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))) |
(* (cos (- (* 1/2 eps) (* -1 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)) |
(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))) |
(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))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(* -1/2 (* eps (pow x 2))) |
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x)))) |
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2))))) |
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2))))) |
(* -1/2 (* eps (pow x 2))) |
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))) |
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))) |
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))) |
(* -1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* -1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))) |
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))) |
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))) |
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))) |
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))) |
(* -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 x) |
(* eps (+ eps x)) |
(* eps (+ eps x)) |
(* eps (+ eps x)) |
(pow eps 2) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(pow eps 2) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(pow eps 2) |
(+ (* eps x) (pow eps 2)) |
(+ (* eps x) (pow eps 2)) |
(+ (* eps x) (pow eps 2)) |
(* eps x) |
(* x (+ eps (/ (pow eps 2) x))) |
(* x (+ eps (/ (pow eps 2) x))) |
(* x (+ eps (/ (pow eps 2) x))) |
(* eps x) |
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x))))) |
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x))))) |
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))) |
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))) |
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))) |
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))) |
(* eps (cos (* 1/2 eps))) |
(+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps)))) |
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps)))))))) |
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps)))))))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(* eps (cos (* 1/2 (- eps (* -2 x))))) |
(* eps (cos (* 1/2 (- eps (* -2 x))))) |
(* eps (cos (* 1/2 (- eps (* -2 x))))) |
(* eps (cos (* 1/2 (- eps (* -2 x))))) |
(* 1/2 eps) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
x |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
x |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(+ x (* 1/2 eps)) |
(* 1/2 eps) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(* eps (+ 1/2 (/ x eps))) |
(* 1/2 eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(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 (* 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)))) |
(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)))) |
eps |
(+ eps (* 2 x)) |
(+ eps (* 2 x)) |
(+ eps (* 2 x)) |
(* 2 x) |
(* x (+ 2 (/ eps x))) |
(* x (+ 2 (/ eps x))) |
(* x (+ 2 (/ eps x))) |
(* 2 x) |
(* -1 (* x (- (* -1 (/ eps x)) 2))) |
(* -1 (* x (- (* -1 (/ eps x)) 2))) |
(* -1 (* x (- (* -1 (/ eps x)) 2))) |
(* 2 x) |
(+ eps (* 2 x)) |
(+ eps (* 2 x)) |
(+ eps (* 2 x)) |
eps |
(* eps (+ 1 (* 2 (/ x eps)))) |
(* eps (+ 1 (* 2 (/ x eps)))) |
(* eps (+ 1 (* 2 (/ x eps)))) |
eps |
(* -1 (* eps (- (* -2 (/ x eps)) 1))) |
(* -1 (* eps (- (* -2 (/ x eps)) 1))) |
(* -1 (* eps (- (* -2 (/ x eps)) 1))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(* -1/2 x) |
(* x (- (* 1/12 (pow x 2)) 1/2)) |
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) |
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(* 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)) (* -1/16 (* eps (cos x))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x))))))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* 1/2 (* eps (cos (* 1/2 eps)))) |
(+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps))))) |
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps)))))))) |
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps)))))))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(* 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 (* (pow eps 2) x)) |
(* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))) |
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))) |
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (pow eps 2)) (* 1/10080 (* (pow eps 2) (pow x 2))))))))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
| Outputs |
|---|
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))) (cos.f64 x))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (fma.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 x #s(literal -2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))) |
(fma.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x #s(literal -2 binary64)) (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (fma.f64 x (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64)))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2)))))))) |
(fma.f64 x (fma.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) x)) (*.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/3 binary64)) #s(literal -2 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(* 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 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (*.f64 eps (*.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)))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 (cos.f64 x) #s(literal 1/2 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 (fma.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64)) (*.f64 (cos.f64 x) #s(literal -1/12 binary64))) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 (cos.f64 x) #s(literal 1/2 binary64)))) |
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
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(cos x) |
(cos.f64 x) |
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(cos (* 1/2 eps)) |
(cos.f64 (*.f64 eps #s(literal 1/2 binary64))) |
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x |
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eps |
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(fma.f64 eps (/.f64 x eps) eps) |
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eps |
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eps |
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(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))))))) |
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(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
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(* eps (cos (* 1/2 eps))) |
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(*.f64 eps (fma.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps)))))))) |
(fma.f64 x (*.f64 eps (-.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))))) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
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(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
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(* eps (cos (* 1/2 (+ eps (* 2 x))))) |
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(* eps (cos (* 1/2 (- eps (* -2 x))))) |
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(* eps (cos (* 1/2 (- eps (* -2 x))))) |
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
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(fma.f64 eps #s(literal 1/2 binary64) x) |
(+ x (* 1/2 eps)) |
(fma.f64 eps #s(literal 1/2 binary64) x) |
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(fma.f64 eps #s(literal 1/2 binary64) x) |
x |
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x |
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(fma.f64 eps #s(literal 1/2 binary64) x) |
(+ x (* 1/2 eps)) |
(fma.f64 eps #s(literal 1/2 binary64) x) |
(+ x (* 1/2 eps)) |
(fma.f64 eps #s(literal 1/2 binary64) x) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
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(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
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(* eps (+ 1/2 (/ x eps))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
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(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
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(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(cos (* 1/2 eps)) |
(cos.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(fma.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
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(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
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(cos (* 1/2 (+ eps (* 2 x)))) |
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(cos (* 1/2 (+ eps (* 2 x)))) |
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(cos (* 1/2 (- eps (* -2 x)))) |
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(cos (* 1/2 (- eps (* -2 x)))) |
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(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos x) |
(cos.f64 x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
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(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
eps |
(+ eps (* 2 x)) |
(fma.f64 x #s(literal 2 binary64) eps) |
(+ eps (* 2 x)) |
(fma.f64 x #s(literal 2 binary64) eps) |
(+ eps (* 2 x)) |
(fma.f64 x #s(literal 2 binary64) eps) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* x (+ 2 (/ eps x))) |
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x))) |
(* x (+ 2 (/ eps x))) |
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(* x (+ 2 (/ eps x))) |
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x))) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* -1 (* x (- (* -1 (/ eps x)) 2))) |
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x))) |
(* -1 (* x (- (* -1 (/ eps x)) 2))) |
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(* -1 (* x (- (* -1 (/ eps x)) 2))) |
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x))) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(+ eps (* 2 x)) |
(fma.f64 x #s(literal 2 binary64) eps) |
(+ eps (* 2 x)) |
(fma.f64 x #s(literal 2 binary64) eps) |
(+ eps (* 2 x)) |
(fma.f64 x #s(literal 2 binary64) eps) |
eps |
(* eps (+ 1 (* 2 (/ x eps)))) |
(*.f64 eps (fma.f64 #s(literal 2 binary64) (/.f64 x eps) #s(literal 1 binary64))) |
(* eps (+ 1 (* 2 (/ x eps)))) |
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(* eps (+ 1 (* 2 (/ x eps)))) |
(*.f64 eps (fma.f64 #s(literal 2 binary64) (/.f64 x eps) #s(literal 1 binary64))) |
eps |
(* -1 (* eps (- (* -2 (/ x eps)) 1))) |
(*.f64 eps (fma.f64 #s(literal 2 binary64) (/.f64 x eps) #s(literal 1 binary64))) |
(* -1 (* eps (- (* -2 (/ x eps)) 1))) |
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(* -1 (* eps (- (* -2 (/ x eps)) 1))) |
(*.f64 eps (fma.f64 #s(literal 2 binary64) (/.f64 x eps) #s(literal 1 binary64))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(*.f64 eps (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)) #s(literal 1 binary64))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(fma.f64 x (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) (*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) eps) |
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(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
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(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
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(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
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(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
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(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
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(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
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(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
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(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* x (- (* 1/12 (pow x 2)) 1/2)) |
(*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))) |
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) |
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) |
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/10080 binary64) #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(* -1/2 (sin x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* 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)))) |
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(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) |
(* 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 (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/16 (* eps (cos x))))))) |
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(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/16 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/96 binary64)) #s(literal -1/4 binary64)))) (*.f64 (cos.f64 x) #s(literal 1/2 binary64)))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 eps)))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps))))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps)))))))) |
(fma.f64 x (*.f64 eps (fma.f64 (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -1/4 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps)))))))))) |
(fma.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (*.f64 (*.f64 x x) (*.f64 eps (fma.f64 (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/12 binary64) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal -1/4 binary64)))))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x)))))) |
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* 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)) |
(* -1/2 (* (pow eps 2) x)) |
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))) |
(* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))) |
(*.f64 x (*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) |
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))) |
(*.f64 x (fma.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))) |
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (pow eps 2)) (* 1/10080 (* (pow eps 2) (pow x 2))))))))) |
(*.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) (*.f64 (*.f64 eps (*.f64 eps (*.f64 x x))) (fma.f64 (*.f64 x x) #s(literal 1/10080 binary64) #s(literal -1/240 binary64))))))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* -1/2 (* (pow eps 2) (sin x))) |
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
Compiled 19 775 to 1 912 computations (90.3% saved)
25 alts after pruning (18 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 852 | 13 | 865 |
| Fresh | 7 | 5 | 12 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 4 | 4 |
| Total | 861 | 25 | 886 |
| Status | Accuracy | Program |
|---|---|---|
| 99.2% | (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps (*.f64 eps (cos.f64 x))) | |
| 97.6% | (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps) | |
| ✓ | 97.6% | (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
| ▶ | 97.4% | (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
| 96.5% | (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps) | |
| ✓ | 63.3% | (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
| ▶ | 99.4% | (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
| ▶ | 98.3% | (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
| 98.5% | (fma.f64 (cos.f64 x) eps (*.f64 x (*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) | |
| ✓ | 63.0% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 7.7% | (-.f64 (sin.f64 eps) (sin.f64 x)) | |
| 99.2% | (*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) | |
| ✓ | 99.8% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
| 53.4% | (*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps))) | |
| 99.2% | (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) | |
| 97.4% | (*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) | |
| 99.2% | (*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))) | |
| ✓ | 99.1% | (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
| 5.5% | (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))) | |
| ▶ | 4.9% | (*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
| 99.0% | (*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) | |
| ▶ | 96.6% | (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
| 98.5% | (*.f64 eps (cos.f64 x)) | |
| ✓ | 96.6% | (sin.f64 eps) |
| ✓ | 96.6% | eps |
Compiled 571 to 367 computations (35.7% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) |
| ✓ | cost-diff | 0 | (cos.f64 x) |
| ✓ | cost-diff | 384 | (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 eps #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 eps x) |
| ✓ | cost-diff | 0 | (*.f64 x #s(literal -1/2 binary64)) |
| ✓ | cost-diff | 0 | (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
| ✓ | cost-diff | -64 | (*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) |
| ✓ | cost-diff | 0 | (sin.f64 x) |
| ✓ | cost-diff | 0 | (sin.f64 eps) |
| ✓ | cost-diff | 0 | (cos.f64 x) |
| ✓ | cost-diff | 0 | (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
| 10 026× | accelerator-lowering-fma.f32 |
| 10 026× | accelerator-lowering-fma.f64 |
| 3 214× | *-lowering-*.f32 |
| 3 214× | *-lowering-*.f64 |
| 2 450× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 38 | 187 |
| 1 | 97 | 187 |
| 2 | 221 | 185 |
| 3 | 452 | 185 |
| 4 | 1007 | 185 |
| 5 | 2417 | 185 |
| 6 | 3020 | 185 |
| 7 | 3634 | 185 |
| 8 | 5000 | 185 |
| 9 | 5693 | 185 |
| 10 | 6508 | 185 |
| 0 | 8013 | 172 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ (* (cos x) (sin eps)) (* (sin x) (+ -1 (cos eps)))) |
(cos x) |
x |
(sin eps) |
eps |
(* (sin x) (+ -1 (cos eps))) |
(sin x) |
(+ -1 (cos eps)) |
-1 |
(cos eps) |
(* eps (* -1/2 (* x x))) |
eps |
(* -1/2 (* x x)) |
-1/2 |
(* x x) |
x |
(+ (* (* x -1/2) (* eps x)) eps) |
(* x -1/2) |
x |
-1/2 |
(* eps x) |
eps |
(* eps (cos (* eps 1/2))) |
eps |
(cos (* eps 1/2)) |
(* eps 1/2) |
1/2 |
(+ (* (cos x) eps) (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0))) |
(cos x) |
x |
eps |
(* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0)) |
(* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) |
(+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2) |
(* x (+ (* x (* x -1/240)) 1/12)) |
(+ (* x (* x -1/240)) 1/12) |
(* x -1/240) |
-1/240 |
1/12 |
-1/2 |
(+ (* eps eps) 0) |
0 |
| Outputs |
|---|
(+ (* (cos x) (sin eps)) (* (sin x) (+ -1 (cos eps)))) |
(fma.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64))) |
(cos x) |
(cos.f64 x) |
x |
(sin eps) |
(sin.f64 eps) |
eps |
(* (sin x) (+ -1 (cos eps))) |
(fma.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)) #s(literal 0 binary64)) |
(sin x) |
(sin.f64 x) |
(+ -1 (cos eps)) |
(+.f64 #s(literal -1 binary64) (cos.f64 eps)) |
-1 |
#s(literal -1 binary64) |
(cos eps) |
(cos.f64 eps) |
(* eps (* -1/2 (* x x))) |
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x eps) #s(literal 0 binary64))) |
eps |
(* -1/2 (* x x)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
-1/2 |
#s(literal -1/2 binary64) |
(* x x) |
(*.f64 x x) |
x |
(+ (* (* x -1/2) (* eps x)) eps) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* x -1/2) |
(*.f64 x #s(literal -1/2 binary64)) |
x |
-1/2 |
#s(literal -1/2 binary64) |
(* eps x) |
(*.f64 x eps) |
eps |
(* eps (cos (* eps 1/2))) |
(*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
eps |
(cos (* eps 1/2)) |
(cos.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(* eps 1/2) |
(*.f64 eps #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(+ (* (cos x) eps) (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0))) |
(fma.f64 eps (fma.f64 (*.f64 x eps) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (cos.f64 x)) #s(literal 0 binary64)) |
(cos x) |
(cos.f64 x) |
x |
eps |
(* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0)) |
(fma.f64 eps (fma.f64 (*.f64 x eps) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) |
(* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) |
(* x (+ (* x (* x -1/240)) 1/12)) |
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64))) |
(+ (* x (* x -1/240)) 1/12) |
(fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) |
(* x -1/240) |
(*.f64 x #s(literal -1/240 binary64)) |
-1/240 |
#s(literal -1/240 binary64) |
1/12 |
#s(literal 1/12 binary64) |
-1/2 |
#s(literal -1/2 binary64) |
(+ (* eps eps) 0) |
(fma.f64 eps eps #s(literal 0 binary64)) |
0 |
#s(literal 0 binary64) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
| ✓ | accuracy | 99.9% | (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))) |
| ✓ | accuracy | 99.8% | (*.f64 x #s(literal -1/240 binary64)) |
| ✓ | accuracy | 99.6% | (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 eps #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal -1/2 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 eps x) |
| ✓ | accuracy | 100.0% | (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
| ✓ | accuracy | 100.0% | (*.f64 x x) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal -1/2 binary64) (*.f64 x x)) |
| ✓ | accuracy | 99.8% | (*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
| ✓ | accuracy | 100.0% | (cos.f64 eps) |
| ✓ | accuracy | 100.0% | (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
| ✓ | accuracy | 99.9% | (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) |
| ✓ | accuracy | 51.6% | (+.f64 #s(literal -1 binary64) (cos.f64 eps)) |
| 162.0ms | 163× | 2 | valid |
| 44.0ms | 90× | 1 | valid |
| 1.0ms | 3× | 0 | valid |
Compiled 179 to 40 computations (77.7% saved)
ival-mult: 54.0ms (37.6% of total)ival-cos: 32.0ms (22.3% of total)adjust: 26.0ms (18.1% of total)ival-add: 15.0ms (10.4% of total)const: 10.0ms (7% of total)ival-sin: 5.0ms (3.5% of total)exact: 1.0ms (0.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (+ -1 (cos eps))))> |
#<alt (cos x)> |
#<alt (sin eps)> |
#<alt (sin x)> |
#<alt (* -1/2 (* x x))> |
#<alt (* x x)> |
#<alt (* eps (* -1/2 (* x x)))> |
#<alt (+ (* (* x -1/2) (* eps x)) eps)> |
#<alt (* x -1/2)> |
#<alt (* eps x)> |
#<alt (* eps (cos (* eps 1/2)))> |
#<alt (cos (* eps 1/2))> |
#<alt (* eps 1/2)> |
#<alt (+ (* (cos x) eps) (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0)))> |
#<alt (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2))> |
#<alt (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)> |
#<alt (+ -1 (cos eps))> |
#<alt (* (sin x) (+ -1 (cos eps)))> |
#<alt (cos eps)> |
#<alt (* x (+ (* x (* x -1/240)) 1/12))> |
#<alt (* x -1/240)> |
#<alt (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0))> |
| 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)) (* -1/6 (* x (- (cos eps) 1)))))) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<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 (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (pow x 2)))> |
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))> |
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<alt (cos x)> |
#<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 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)> |
#<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 (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (pow x 2)))> |
#<alt (* -1/2 (* eps (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 (* 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 (* -1 (* eps (- (* 1/2 (pow x 2)) 1)))> |
#<alt (* -1 (* eps (- (* 1/2 (pow x 2)) 1)))> |
#<alt (* -1 (* eps (- (* 1/2 (pow x 2)) 1)))> |
#<alt (* -1 (* eps (- (* 1/2 (pow x 2)) 1)))> |
#<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 x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt (* eps x)> |
#<alt eps> |
#<alt (* eps (+ 1 (* -1/8 (pow eps 2))))> |
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8))))> |
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8))))> |
#<alt (* eps (cos (* 1/2 eps)))> |
#<alt (* eps (cos (* 1/2 eps)))> |
#<alt (* eps (cos (* 1/2 eps)))> |
#<alt (* eps (cos (* 1/2 eps)))> |
#<alt (* eps (cos (* 1/2 eps)))> |
#<alt (* eps (cos (* 1/2 eps)))> |
#<alt (* eps (cos (* 1/2 eps)))> |
#<alt (* eps (cos (* 1/2 eps)))> |
#<alt 1> |
#<alt (+ 1 (* -1/8 (pow eps 2)))> |
#<alt (+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8)))> |
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8)))> |
#<alt (cos (* 1/2 eps))> |
#<alt (cos (* 1/2 eps))> |
#<alt (cos (* 1/2 eps))> |
#<alt (cos (* 1/2 eps))> |
#<alt (cos (* 1/2 eps))> |
#<alt (cos (* 1/2 eps))> |
#<alt (cos (* 1/2 eps))> |
#<alt (cos (* 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 eps> |
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))> |
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))> |
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))> |
#<alt (* -1/240 (* (pow eps 2) (pow x 5)))> |
#<alt (* (pow x 5) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2)))))> |
#<alt (* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2))))))> |
#<alt (* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (+ (* 1/12 (/ (pow eps 2) (pow x 2))) (/ (* eps (cos x)) (pow x 5))))))> |
#<alt (* -1/240 (* (pow eps 2) (pow x 5)))> |
#<alt (* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (* 1/240 (pow eps 2)))))> |
#<alt (* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4)))))))> |
#<alt (* -1 (* (pow x 5) (+ (* -1 (/ (* eps (cos x)) (pow x 5))) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4))))))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* eps (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))))> |
#<alt (* eps (+ (cos x) (* eps (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))))> |
#<alt (* eps (+ (cos x) (* eps (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))))> |
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))> |
#<alt (* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))> |
#<alt (* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))> |
#<alt (* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))> |
#<alt (* -1/2 x)> |
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))> |
#<alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))> |
#<alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))> |
#<alt (* -1/240 (pow x 5))> |
#<alt (* (pow x 5) (- (* 1/12 (/ 1 (pow x 2))) 1/240))> |
#<alt (* (pow x 5) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))> |
#<alt (* (pow x 5) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))> |
#<alt (* -1/240 (pow x 5))> |
#<alt (* -1 (* (pow x 5) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 5) (- (+ 1/240 (/ 1/2 (pow x 4))) (* 1/12 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 5) (- (+ 1/240 (/ 1/2 (pow x 4))) (* 1/12 (/ 1 (pow x 2))))))> |
#<alt -1/2> |
#<alt (- (* 1/12 (pow x 2)) 1/2)> |
#<alt (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)> |
#<alt (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)> |
#<alt (* -1/240 (pow x 4))> |
#<alt (* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) 1/240))> |
#<alt (* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))> |
#<alt (* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))> |
#<alt (* -1/240 (pow x 4))> |
#<alt (* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) 1/240))> |
#<alt (* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))> |
#<alt (* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))> |
#<alt (* -1/2 (pow eps 2))> |
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))> |
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))> |
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))> |
#<alt (- (cos eps) 1)> |
#<alt (- (cos eps) 1)> |
#<alt (- (cos eps) 1)> |
#<alt (- (cos eps) 1)> |
#<alt (- (cos eps) 1)> |
#<alt (- (cos eps) 1)> |
#<alt (- (cos eps) 1)> |
#<alt (- (cos eps) 1)> |
#<alt (* x (- (cos eps) 1))> |
#<alt (* x (- (+ (cos eps) (* -1/6 (* (pow x 2) (- (cos eps) 1)))) 1))> |
#<alt (* x (- (+ (cos eps) (* (pow x 2) (+ (* -1/6 (- (cos eps) 1)) (* 1/120 (* (pow x 2) (- (cos eps) 1)))))) 1))> |
#<alt (* x (- (+ (cos eps) (* (pow x 2) (+ (* -1/6 (- (cos eps) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (cos eps) 1))) (* 1/120 (- (cos eps) 1))))))) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* -1/2 (* (pow eps 2) (sin x)))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))> |
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt (* (sin x) (- (cos eps) 1))> |
#<alt 1> |
#<alt (+ 1 (* -1/2 (pow eps 2)))> |
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))> |
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (cos eps)> |
#<alt (* 1/12 x)> |
#<alt (* x (+ 1/12 (* -1/240 (pow x 2))))> |
#<alt (* x (+ 1/12 (* -1/240 (pow x 2))))> |
#<alt (* x (+ 1/12 (* -1/240 (pow x 2))))> |
#<alt (* -1/240 (pow x 3))> |
#<alt (* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240))> |
#<alt (* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240))> |
#<alt (* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240))> |
#<alt (* -1/240 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))> |
#<alt (* -1/240 x)> |
#<alt (* -1/240 x)> |
#<alt (* -1/240 x)> |
#<alt (* -1/240 x)> |
#<alt (* -1/240 x)> |
#<alt (* -1/240 x)> |
#<alt (* -1/240 x)> |
#<alt (* -1/240 x)> |
#<alt (* -1/240 x)> |
#<alt (* -1/240 x)> |
#<alt (* -1/240 x)> |
#<alt (* -1/240 x)> |
#<alt (* -1/2 (* (pow eps 2) x))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2)))))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))> |
#<alt (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))> |
#<alt (* -1/240 (* (pow eps 2) (pow x 5)))> |
#<alt (* (pow x 5) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2)))))> |
#<alt (* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2))))))> |
#<alt (* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2))))))> |
#<alt (* -1/240 (* (pow eps 2) (pow x 5)))> |
#<alt (* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (* 1/240 (pow eps 2)))))> |
#<alt (* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4)))))))> |
#<alt (* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4)))))))> |
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))> |
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))> |
87 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | inf | (+ (* (cos x) eps) (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0))) |
| 1.0ms | eps | @ | 0 | (+ (* (cos x) eps) (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0))) |
| 1.0ms | eps | @ | 0 | (* eps (* -1/2 (* x x))) |
| 1.0ms | eps | @ | -inf | (* eps (cos (* eps 1/2))) |
| 0.0ms | eps | @ | 0 | (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0)) |
| 1× | batch-egg-rewrite |
| 12 470× | accelerator-lowering-fma.f32 |
| 12 470× | accelerator-lowering-fma.f64 |
| 4 378× | *-lowering-*.f32 |
| 4 378× | *-lowering-*.f64 |
| 3 280× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 38 | 158 |
| 1 | 190 | 158 |
| 2 | 1541 | 153 |
| 0 | 8350 | 142 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(+ (* (cos x) (sin eps)) (* (sin x) (+ -1 (cos eps)))) |
(cos x) |
(sin eps) |
(sin x) |
(* -1/2 (* x x)) |
(* x x) |
(* eps (* -1/2 (* x x))) |
(+ (* (* x -1/2) (* eps x)) eps) |
(* x -1/2) |
(* eps x) |
(* eps (cos (* eps 1/2))) |
(cos (* eps 1/2)) |
(* eps 1/2) |
(+ (* (cos x) eps) (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0))) |
(* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) |
(+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2) |
(+ -1 (cos eps)) |
(* (sin x) (+ -1 (cos eps))) |
(cos eps) |
(* x (+ (* x (* x -1/240)) 1/12)) |
(* x -1/240) |
(* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0)) |
| Outputs |
|---|
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(+.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (+.f64 x eps))) |
(+.f64 (/.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.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) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))) (neg.f64 (/.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))))) |
(+.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps))) |
(-.f64 (/.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.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) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))) (/.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (-.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps)))) (/.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.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 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(fma.f64 (sin.f64 x) #s(literal -1 binary64) (sin.f64 (+.f64 x eps))) |
(fma.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (sin.f64 (+.f64 x eps))) |
(fma.f64 (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))) (neg.f64 (/.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))))) |
(fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(fma.f64 (+.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps)))) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 eps) (+.f64 (cos.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 (*.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 eps) (+.f64 (cos.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (+.f64 x eps)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (+.f64 x eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (+.f64 x eps)))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) (*.f64 (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))))) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.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 #s(literal -1 binary64) (cos.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) (*.f64 (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))))))) |
(/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.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 #s(literal -1 binary64) (cos.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) (*.f64 (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))) |
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(*.f64 (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 x (fma.f64 eps eps #s(literal 0 binary64))) #s(literal 0 binary64))) |
(*.f64 (/.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) eps)) |
(*.f64 (/.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) eps) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 eps (fma.f64 eps eps #s(literal 0 binary64))))) |
(*.f64 (/.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64))) |
(*.f64 (/.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps (fma.f64 eps eps #s(literal 0 binary64)))) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) eps)) |
(*.f64 (/.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64))))) |
(*.f64 (/.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) |
| 1× | egg-herbie |
| 13 948× | accelerator-lowering-fma.f32 |
| 13 948× | accelerator-lowering-fma.f64 |
| 5 052× | *-lowering-*.f32 |
| 5 052× | *-lowering-*.f64 |
| 4 216× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 300 | 3092 |
| 1 | 893 | 3062 |
| 2 | 2613 | 2976 |
| 3 | 5393 | 2936 |
| 0 | 8264 | 2753 |
| 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)) (* -1/6 (* x (- (cos eps) 1)))))) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
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) |
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) |
(* -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)) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (pow x 2))) |
(* -1/2 (* eps (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)))) |
(* 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)))) |
(* -1 (* eps (- (* 1/2 (pow x 2)) 1))) |
(* -1 (* eps (- (* 1/2 (pow x 2)) 1))) |
(* -1 (* eps (- (* 1/2 (pow x 2)) 1))) |
(* -1 (* eps (- (* 1/2 (pow x 2)) 1))) |
(* -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 x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
(* eps x) |
eps |
(* eps (+ 1 (* -1/8 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8)))) |
(* eps (cos (* 1/2 eps))) |
(* eps (cos (* 1/2 eps))) |
(* eps (cos (* 1/2 eps))) |
(* eps (cos (* 1/2 eps))) |
(* eps (cos (* 1/2 eps))) |
(* eps (cos (* 1/2 eps))) |
(* eps (cos (* 1/2 eps))) |
(* eps (cos (* 1/2 eps))) |
1 |
(+ 1 (* -1/8 (pow eps 2))) |
(+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8))) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8))) |
(cos (* 1/2 eps)) |
(cos (* 1/2 eps)) |
(cos (* 1/2 eps)) |
(cos (* 1/2 eps)) |
(cos (* 1/2 eps)) |
(cos (* 1/2 eps)) |
(cos (* 1/2 eps)) |
(cos (* 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) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
(* -1/240 (* (pow eps 2) (pow x 5))) |
(* (pow x 5) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2))))) |
(* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2)))))) |
(* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (+ (* 1/12 (/ (pow eps 2) (pow x 2))) (/ (* eps (cos x)) (pow x 5)))))) |
(* -1/240 (* (pow eps 2) (pow x 5))) |
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (* 1/240 (pow eps 2))))) |
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4))))))) |
(* -1 (* (pow x 5) (+ (* -1 (/ (* eps (cos x)) (pow x 5))) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4)))))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* eps (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))) |
(* eps (+ (cos x) (* eps (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))) |
(* eps (+ (cos x) (* eps (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps))) |
(* -1/2 x) |
(* x (- (* 1/12 (pow x 2)) 1/2)) |
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) |
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) |
(* -1/240 (pow x 5)) |
(* (pow x 5) (- (* 1/12 (/ 1 (pow x 2))) 1/240)) |
(* (pow x 5) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4))))) |
(* (pow x 5) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4))))) |
(* -1/240 (pow x 5)) |
(* -1 (* (pow x 5) (- 1/240 (* 1/12 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 5) (- (+ 1/240 (/ 1/2 (pow x 4))) (* 1/12 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 5) (- (+ 1/240 (/ 1/2 (pow x 4))) (* 1/12 (/ 1 (pow x 2)))))) |
-1/2 |
(- (* 1/12 (pow x 2)) 1/2) |
(- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2) |
(- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2) |
(* -1/240 (pow x 4)) |
(* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) 1/240)) |
(* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4))))) |
(* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4))))) |
(* -1/240 (pow x 4)) |
(* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) 1/240)) |
(* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4))))) |
(* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4))))) |
(* -1/2 (pow eps 2)) |
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2)) |
(- (cos eps) 1) |
(- (cos eps) 1) |
(- (cos eps) 1) |
(- (cos eps) 1) |
(- (cos eps) 1) |
(- (cos eps) 1) |
(- (cos eps) 1) |
(- (cos eps) 1) |
(* x (- (cos eps) 1)) |
(* x (- (+ (cos eps) (* -1/6 (* (pow x 2) (- (cos eps) 1)))) 1)) |
(* x (- (+ (cos eps) (* (pow x 2) (+ (* -1/6 (- (cos eps) 1)) (* 1/120 (* (pow x 2) (- (cos eps) 1)))))) 1)) |
(* x (- (+ (cos eps) (* (pow x 2) (+ (* -1/6 (- (cos eps) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (cos eps) 1))) (* 1/120 (- (cos eps) 1))))))) 1)) |
(* (sin x) (- (cos eps) 1)) |
(* (sin x) (- (cos eps) 1)) |
(* (sin x) (- (cos eps) 1)) |
(* (sin x) (- (cos eps) 1)) |
(* (sin x) (- (cos eps) 1)) |
(* (sin x) (- (cos eps) 1)) |
(* (sin x) (- (cos eps) 1)) |
(* (sin x) (- (cos eps) 1)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x))))))))) |
(* (sin x) (- (cos eps) 1)) |
(* (sin x) (- (cos eps) 1)) |
(* (sin x) (- (cos eps) 1)) |
(* (sin x) (- (cos eps) 1)) |
(* (sin x) (- (cos eps) 1)) |
(* (sin x) (- (cos eps) 1)) |
(* (sin x) (- (cos eps) 1)) |
(* (sin x) (- (cos eps) 1)) |
1 |
(+ 1 (* -1/2 (pow eps 2))) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(cos eps) |
(* 1/12 x) |
(* x (+ 1/12 (* -1/240 (pow x 2)))) |
(* x (+ 1/12 (* -1/240 (pow x 2)))) |
(* x (+ 1/12 (* -1/240 (pow x 2)))) |
(* -1/240 (pow x 3)) |
(* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240)) |
(* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240)) |
(* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240)) |
(* -1/240 (pow x 3)) |
(* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2)))))) |
(* -1/240 x) |
(* -1/240 x) |
(* -1/240 x) |
(* -1/240 x) |
(* -1/240 x) |
(* -1/240 x) |
(* -1/240 x) |
(* -1/240 x) |
(* -1/240 x) |
(* -1/240 x) |
(* -1/240 x) |
(* -1/240 x) |
(* -1/2 (* (pow eps 2) x)) |
(* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))) |
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))) |
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))) |
(* -1/240 (* (pow eps 2) (pow x 5))) |
(* (pow x 5) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2))))) |
(* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2)))))) |
(* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2)))))) |
(* -1/240 (* (pow eps 2) (pow x 5))) |
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (* 1/240 (pow eps 2))))) |
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4))))))) |
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4))))))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
| Outputs |
|---|
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(fma.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(fma.f64 x (+.f64 (fma.f64 x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64)) (cos.f64 eps)) #s(literal -1 binary64)) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (- (cos eps) 1)))))) 1))) |
(fma.f64 x (fma.f64 (sin.f64 eps) (*.f64 x #s(literal -1/2 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) (sin.f64 eps)) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 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 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow x 2))) |
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
(cos x) |
(cos.f64 x) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) #s(literal 1 binary64))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 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) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) #s(literal 1 binary64))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) #s(literal 1 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) |
(* -1/2 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
(* -1/2 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
(* -1/2 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
(* -1/2 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
(* -1/2 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
(* -1/2 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
(* -1/2 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
(* -1/2 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
(* -1/2 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
(* -1/2 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
(* -1/2 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
(* -1/2 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/2 binary64))) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* -1/2 (* eps (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal -1/2 binary64)))) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* -1 (* eps (- (* 1/2 (pow x 2)) 1))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* -1 (* eps (- (* 1/2 (pow x 2)) 1))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* -1 (* eps (- (* 1/2 (pow x 2)) 1))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* -1 (* eps (- (* 1/2 (pow x 2)) 1))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
(* eps x) |
(*.f64 eps x) |
eps |
(* eps (+ 1 (* -1/8 (pow eps 2)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/384 binary64) #s(literal -1/8 binary64))) #s(literal 1 binary64))) |
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1 |
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(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))) |
(*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))) |
(*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x))))))))) |
(*.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
(* (sin x) (- (cos eps) 1)) |
(*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x)) |
(* (sin x) (- (cos eps) 1)) |
(*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x)) |
(* (sin x) (- (cos eps) 1)) |
(*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x)) |
(* (sin x) (- (cos eps) 1)) |
(*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x)) |
(* (sin x) (- (cos eps) 1)) |
(*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x)) |
(* (sin x) (- (cos eps) 1)) |
(*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x)) |
(* (sin x) (- (cos eps) 1)) |
(*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x)) |
(* (sin x) (- (cos eps) 1)) |
(*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1/2 (pow eps 2))) |
(fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) |
(fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)) |
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))) |
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(cos eps) |
(cos.f64 eps) |
(* 1/12 x) |
(*.f64 x #s(literal 1/12 binary64)) |
(* x (+ 1/12 (* -1/240 (pow x 2)))) |
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64))) |
(* x (+ 1/12 (* -1/240 (pow x 2)))) |
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64))) |
(* x (+ 1/12 (* -1/240 (pow x 2)))) |
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64))) |
(* -1/240 (pow x 3)) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal -1/240 binary64))) |
(* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240)) |
(*.f64 (+.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/12 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x))) |
(* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240)) |
(*.f64 (+.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/12 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x))) |
(* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240)) |
(*.f64 (+.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/12 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x))) |
(* -1/240 (pow x 3)) |
(*.f64 x (*.f64 (*.f64 x x) #s(literal -1/240 binary64))) |
(* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2)))))) |
(*.f64 (+.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/12 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x))) |
(* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2)))))) |
(*.f64 (+.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/12 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x))) |
(* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2)))))) |
(*.f64 (+.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/12 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x))) |
(* -1/240 x) |
(*.f64 x #s(literal -1/240 binary64)) |
(* -1/240 x) |
(*.f64 x #s(literal -1/240 binary64)) |
(* -1/240 x) |
(*.f64 x #s(literal -1/240 binary64)) |
(* -1/240 x) |
(*.f64 x #s(literal -1/240 binary64)) |
(* -1/240 x) |
(*.f64 x #s(literal -1/240 binary64)) |
(* -1/240 x) |
(*.f64 x #s(literal -1/240 binary64)) |
(* -1/240 x) |
(*.f64 x #s(literal -1/240 binary64)) |
(* -1/240 x) |
(*.f64 x #s(literal -1/240 binary64)) |
(* -1/240 x) |
(*.f64 x #s(literal -1/240 binary64)) |
(* -1/240 x) |
(*.f64 x #s(literal -1/240 binary64)) |
(* -1/240 x) |
(*.f64 x #s(literal -1/240 binary64)) |
(* -1/240 x) |
(*.f64 x #s(literal -1/240 binary64)) |
(* -1/2 (* (pow eps 2) x)) |
(*.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) |
(* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))) |
(*.f64 x (*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))) |
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))) |
(*.f64 x (fma.f64 (*.f64 eps (*.f64 eps (*.f64 x x))) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))) |
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))) |
(*.f64 x (fma.f64 (*.f64 eps (*.f64 eps (*.f64 x x))) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))) |
(* -1/240 (* (pow eps 2) (pow x 5))) |
(*.f64 #s(literal -1/240 binary64) (*.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) eps) eps)) |
(* (pow x 5) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/12 binary64) (*.f64 x x))))) |
(* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2)))))) |
(*.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/240 binary64) (+.f64 (/.f64 #s(literal 1/12 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))) |
(* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2)))))) |
(*.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/240 binary64) (+.f64 (/.f64 #s(literal 1/12 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))) |
(* -1/240 (* (pow eps 2) (pow x 5))) |
(*.f64 #s(literal -1/240 binary64) (*.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) eps) eps)) |
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (* 1/240 (pow eps 2))))) |
(*.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/12 binary64) (*.f64 x x))))) |
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4))))))) |
(*.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/240 binary64) (+.f64 (/.f64 #s(literal 1/12 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))) |
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4))))))) |
(*.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/240 binary64) (+.f64 (/.f64 #s(literal 1/12 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))) |
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) |
Compiled 26 953 to 1 906 computations (92.9% saved)
26 alts after pruning (18 fresh and 8 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 847 | 8 | 855 |
| Fresh | 3 | 10 | 13 |
| Picked | 3 | 2 | 5 |
| Done | 1 | 6 | 7 |
| Total | 854 | 26 | 880 |
| Status | Accuracy | Program |
|---|---|---|
| 98.0% | (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) | |
| 97.8% | (fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) | |
| 97.6% | (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) | |
| 99.4% | (fma.f64 (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps))) | |
| 98.3% | (fma.f64 (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) eps) eps (*.f64 (cos.f64 x) eps)) | |
| 99.2% | (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps (*.f64 eps (cos.f64 x))) | |
| 97.4% | (fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps) | |
| 97.6% | (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps) | |
| ✓ | 97.6% | (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
| 96.5% | (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps) | |
| 99.2% | (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) | |
| 96.6% | (fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) | |
| ✓ | 63.0% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 7.7% | (-.f64 (sin.f64 eps) (sin.f64 x)) | |
| 99.2% | (*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) | |
| ✓ | 99.8% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
| 53.4% | (*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps))) | |
| 99.2% | (*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) | |
| ✓ | 99.1% | (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
| 5.5% | (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))) | |
| ✓ | 4.9% | (*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
| 99.0% | (*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) | |
| ✓ | 96.6% | (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
| 98.5% | (*.f64 eps (cos.f64 x)) | |
| ✓ | 96.6% | (sin.f64 eps) |
| ✓ | 96.6% | eps |
Compiled 975 to 407 computations (58.3% saved)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps) |
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps) |
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) x) (cos.f64 x))) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(fma.f64 (cos.f64 x) eps (*.f64 x (*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(fma.f64 (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) eps) eps (*.f64 (cos.f64 x) eps)) |
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(-.f64 (sin.f64 eps) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(fma.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x) (*.f64 eps (cos.f64 x))) |
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps (*.f64 eps (cos.f64 x))) |
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps eps #s(literal 0 binary64)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))) |
(fma.f64 (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
3 calls:
| 13.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 13.0ms | eps |
| 13.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
| 99.8% | 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 x (*.f64 eps #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps) |
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps) |
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) x) (cos.f64 x))) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(fma.f64 (cos.f64 x) eps (*.f64 x (*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(fma.f64 (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) eps) eps (*.f64 (cos.f64 x) eps)) |
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(-.f64 (sin.f64 eps) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) |
| Outputs |
|---|
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
3 calls:
| 16.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 10.0ms | x |
| 9.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.2% | 1 | x |
| 99.2% | 1 | eps |
| 99.2% | 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 x (*.f64 eps #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps) |
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps) |
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) x) (cos.f64 x))) |
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))) |
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
| Outputs |
|---|
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
3 calls:
| 8.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 7.0ms | eps |
| 7.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.0% | 1 | x |
| 99.0% | 1 | eps |
| 99.0% | 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 x (*.f64 eps #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps) |
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps) |
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
| Outputs |
|---|
(*.f64 eps (cos.f64 x)) |
3 calls:
| 8.0ms | x |
| 7.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.5% | 1 | x |
| 98.5% | 1 | eps |
| 98.5% | 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 x (*.f64 eps #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps) |
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps) |
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(sin.f64 eps) |
| Outputs |
|---|
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
3 calls:
| 6.0ms | x |
| 6.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.0% | 1 | x |
| 98.0% | 1 | eps |
| 98.0% | 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 x (*.f64 eps #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps) |
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps) |
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
| Outputs |
|---|
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
3 calls:
| 6.0ms | x |
| 5.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 5.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.8% | 1 | x |
| 97.8% | 1 | eps |
| 97.8% | 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 x (*.f64 eps #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps) |
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps) |
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
| Outputs |
|---|
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) |
3 calls:
| 5.0ms | x |
| 5.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 5.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.7% | 1 | x |
| 97.7% | 1 | eps |
| 97.7% | 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 x (*.f64 eps #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps) |
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
| Outputs |
|---|
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
3 calls:
| 4.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 4.0ms | x |
| 4.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.6% | 1 | eps |
| 97.6% | 1 | x |
| 97.6% | 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 x (*.f64 eps #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps) |
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64))) |
| Outputs |
|---|
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64))) |
3 calls:
| 5.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 4.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.6% | 1 | x |
| 97.6% | 1 | eps |
| 97.6% | 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 x (*.f64 eps #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps) |
| Outputs |
|---|
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
3 calls:
| 3.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | eps |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.4% | 1 | x |
| 97.4% | 1 | eps |
| 97.4% | 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 x (*.f64 eps #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps) |
| Outputs |
|---|
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
3 calls:
| 22.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.4% | 1 | x |
| 97.4% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 97.4% | 1 | eps |
Compiled 15 to 10 computations (33.3% saved)
Total -58.7b remaining (-2705.7%)
Threshold costs -58.7b (-2705.7%)
| Inputs |
|---|
eps |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) |
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))) |
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) |
| Outputs |
|---|
eps |
3 calls:
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2.0ms | eps |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 96.6% | 1 | x |
| 96.6% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 96.6% | 1 | eps |
Compiled 15 to 10 computations (33.3% saved)
| 1× | egg-herbie |
| 46× | *-commutative_binary64 |
| 2× | +-commutative_binary64 |
| 2× | 1-exp_binary64 |
| 2× | 1-exp_binary32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 61 | 159 |
| 1 | 87 | 159 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(*.f64 eps (cos.f64 x)) |
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
eps |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))) |
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(*.f64 eps (cos.f64 x)) |
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))) |
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps) |
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps) |
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) |
eps |
| 16 678× | accelerator-lowering-fma.f32 |
| 16 678× | accelerator-lowering-fma.f64 |
| 14 120× | accelerator-lowering-fma.f32 |
| 14 120× | accelerator-lowering-fma.f64 |
| 14 110× | accelerator-lowering-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 300 | 3092 |
| 1 | 893 | 3062 |
| 2 | 2613 | 2976 |
| 3 | 5393 | 2936 |
| 0 | 8264 | 2753 |
| 0 | 6 | 16 |
| 1 | 49 | 16 |
| 2 | 376 | 16 |
| 3 | 4763 | 16 |
| 0 | 8212 | 16 |
| 0 | 107 | 496 |
| 1 | 314 | 496 |
| 2 | 775 | 489 |
| 3 | 2836 | 489 |
| 4 | 6173 | 489 |
| 0 | 8126 | 458 |
| 0 | 396 | 3534 |
| 1 | 1254 | 3441 |
| 2 | 3471 | 3376 |
| 0 | 8332 | 3093 |
| 0 | 412 | 3565 |
| 1 | 1260 | 3392 |
| 2 | 3428 | 3329 |
| 0 | 8160 | 3043 |
| 0 | 36 | 136 |
| 1 | 185 | 132 |
| 2 | 1806 | 132 |
| 0 | 9030 | 123 |
| 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 569 to 324 computations (43.1% saved)
Compiled 434 to 200 computations (53.9% saved)
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