
Time bar (total: 14.1s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 0 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 1 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 2 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 3 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 4 |
| 0% | 0% | 19% | 49.4% | 0% | 31.6% | 0% | 5 |
| 0% | 0% | 15.8% | 49.4% | 0% | 34.8% | 0% | 6 |
| 0% | 0% | 11.1% | 49.4% | 0% | 39.5% | 0% | 7 |
| 0% | 0% | 8.7% | 49.4% | 0% | 41.9% | 0% | 8 |
| 0% | 0% | 5.9% | 49.4% | 0% | 44.6% | 0% | 9 |
| 0% | 0% | 4.5% | 49.4% | 0% | 46% | 0% | 10 |
| 0% | 0% | 3.1% | 49.4% | 0% | 47.5% | 0% | 11 |
| 0% | 0% | 2.7% | 49.4% | 0% | 47.9% | 0% | 12 |
Compiled 27 to 19 computations (29.6% saved)
| 3.1s | 25 541× | 0 | invalid |
| 734.0ms | 5 406× | 0 | valid |
| 474.0ms | 2 850× | 1 | valid |
const: 638.0ms (19.9% of total)ival-sin: 579.0ms (18% of total)ival-sub: 480.0ms (14.9% of total)ival-<=: 386.0ms (12% of total)ival-add: 262.0ms (8.2% of total)ival-mult: 248.0ms (7.7% of total)ival-fabs: 232.0ms (7.2% of total)ival-<: 169.0ms (5.3% of total)ival-and: 96.0ms (3% of total)adjust: 70.0ms (2.2% of total)exact: 43.0ms (1.3% of total)ival-assert: 11.0ms (0.3% of total)| 1× | egg-herbie |
| 102× | sub-neg |
| 80× | lower-fma.f64 |
| 80× | lower-fma.f32 |
| 68× | cancel-sign-sub-inv |
| 64× | associate--r+ |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 39 |
| 1 | 38 | 35 |
| 2 | 86 | 35 |
| 3 | 169 | 35 |
| 4 | 310 | 35 |
| 5 | 367 | 35 |
| 6 | 445 | 35 |
| 7 | 482 | 35 |
| 8 | 491 | 35 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 13 | 7 |
| 2 | 18 | 7 |
| 3 | 24 | 7 |
| 4 | 32 | 7 |
| 5 | 47 | 7 |
| 6 | 80 | 7 |
| 7 | 107 | 7 |
| 8 | 151 | 7 |
| 9 | 166 | 7 |
| 10 | 174 | 7 |
| 0 | 174 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Outputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 221 | 1 | (-5.670654569479482e-178 5.008009389092732e-181) | 2 | (3.225780371294668e-135 3.531463027326352e-137) | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2 | 0 | - | 0 | - | (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 | 220 | 7 |
sin.f64 | (sin.f64 (+.f64 x eps)) | sensitivity | 2 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 221 | 2 |
| - | 1 | 32 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 221 | 2 | 0 |
| - | 1 | 5 | 27 |
| number | freq |
|---|---|
| 0 | 34 |
| 1 | 222 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 19.0ms | 354× | 0 | valid |
| 15.0ms | 154× | 1 | valid |
| 1.0ms | 2× | 3 | valid |
| 0.0ms | 2× | 2 | valid |
Compiled 58 to 28 computations (51.7% saved)
ival-sin: 9.0ms (48.3% of total)adjust: 3.0ms (16.1% of total)ival-add: 3.0ms (16.1% of total)ival-sub: 3.0ms (16.1% 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 |
|---|---|---|
| ▶ | 63.5% | (-.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× | lower-fma.f64 |
| 80× | lower-fma.f32 |
| 48× | lower-*.f64 |
| 48× | lower-*.f32 |
| 36× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 0 | 10 | 18 |
| 1 | 13 | 18 |
| 2 | 18 | 18 |
| 3 | 24 | 18 |
| 4 | 32 | 18 |
| 5 | 47 | 18 |
| 6 | 80 | 18 |
| 7 | 107 | 18 |
| 8 | 151 | 18 |
| 9 | 166 | 18 |
| 10 | 174 | 18 |
| 0 | 174 | 18 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(sin.f64 x) |
| Outputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(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 | 63.7% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 8.0ms | 177× | 0 | valid |
| 7.0ms | 77× | 1 | valid |
| 0.0ms | 1× | 3 | valid |
| 0.0ms | 1× | 2 | valid |
Compiled 20 to 8 computations (60% saved)
ival-sin: 4.0ms (45.8% of total)adjust: 1.0ms (11.5% of total)ival-add: 1.0ms (11.5% of total)ival-sub: 1.0ms (11.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))> |
#<alt (sin.f64 (+.f64 x eps))> |
#<alt (+.f64 x eps)> |
#<alt (sin.f64 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 | eps | @ | -inf | (- (sin (+ x eps)) (sin x)) |
| 0.0ms | eps | @ | 0 | (- (sin (+ x eps)) (sin x)) |
| 0.0ms | x | @ | 0 | (- (sin (+ x eps)) (sin x)) |
| 0.0ms | x | @ | inf | (+ x eps) |
| 1× | batch-egg-rewrite |
| 4 986× | lower-fma.f64 |
| 4 986× | lower-fma.f32 |
| 4 676× | lower-*.f64 |
| 4 676× | lower-*.f32 |
| 2 176× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 53 | 16 |
| 2 | 380 | 16 |
| 3 | 4766 | 16 |
| 0 | 8210 | 16 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(sin.f64 x) |
| Outputs |
|---|
(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 (neg.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) (sin.f64 (neg.f64 x)))) |
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x))) |
(+.f64 (sin.f64 (neg.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 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(+.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps))) |
(+.f64 (+.f64 (sin.f64 (neg.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (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 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(-.f64 #s(literal 0 binary64) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps)))) |
(-.f64 (+.f64 (sin.f64 (+.f64 x eps)) #s(literal 0 binary64)) (sin.f64 x)) |
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (sin.f64 (+.f64 x eps)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (-.f64 (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) (sin.f64 (neg.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) (sin.f64 (neg.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 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 (sin.f64 (+.f64 x eps)) (-.f64 (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))) |
(fma.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 (-.f64 eps x))))) (sin.f64 (neg.f64 x))) |
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (sin.f64 (+.f64 x eps))) |
(fma.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) (sin.f64 (neg.f64 x))) |
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(/.f64 (neg.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)))) (neg.f64 (neg.f64 (-.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 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (fma.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.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 x eps))) (-.f64 x eps))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.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 (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x)))))) |
(*.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.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 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 (-.f64 eps x) (-.f64 eps x)) (-.f64 eps x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps 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 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps))) (fma.f64 x x (*.f64 eps (+.f64 x eps)))) |
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.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 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.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 x x (*.f64 eps (+.f64 x eps))) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x (*.f64 eps (+.f64 x eps))) (-.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× | lower-fma.f64 |
| 16 678× | lower-fma.f32 |
| 4 132× | lower-*.f64 |
| 4 132× | lower-*.f32 |
| 2 614× | lower-+.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))) |
(-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (*.f64 x (cos.f64 eps))) x) |
(+ (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) (*.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))))) 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) (*.f64 x (cos.f64 eps))) |
(+ (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) (fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x))) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (+ eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin (- eps (* -1 x))) |
(sin.f64 (+.f64 eps x)) |
(sin x) |
(sin.f64 x) |
(+ (sin x) (* eps (cos x))) |
(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)))) |
(fma.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 x (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (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)) (*.f64 x (*.f64 x x)) 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) |
(sin x) |
(sin.f64 x) |
Compiled 7 746 to 844 computations (89.1% saved)
11 alts after pruning (10 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 281 | 10 | 291 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 281 | 11 | 292 |
| Status | Accuracy | Program |
|---|---|---|
| 99.6% | (fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))) | |
| ▶ | 7.8% | (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
| ▶ | 63.5% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
| 63.7% | (-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) | |
| ▶ | 61.9% | (-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (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)) (*.f64 x (*.f64 x x)) x)) |
| ✓ | 63.5% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| ▶ | 99.9% | (*.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)) |
| 98.7% | (*.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)))) | |
| 98.7% | (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))) | |
| 98.2% | (*.f64 eps (cos.f64 x)) | |
| ▶ | 96.8% | (sin.f64 eps) |
Compiled 319 to 208 computations (34.8% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
| ✓ | cost-diff | 128 | (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) |
| ✓ | cost-diff | 192 | (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))) |
| ✓ | cost-diff | 256 | (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) |
| ✓ | cost-diff | 0 | (sin.f64 (+.f64 x eps)) |
| ✓ | cost-diff | 0 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
| ✓ | cost-diff | 1408 | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
| ✓ | cost-diff | 0 | (fma.f64 (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)) (*.f64 x (*.f64 x x)) x) |
| ✓ | cost-diff | 0 | (+.f64 x eps) |
| ✓ | cost-diff | 0 | (sin.f64 (+.f64 x eps)) |
| ✓ | cost-diff | 128 | (-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (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)) (*.f64 x (*.f64 x x)) x)) |
| ✓ | cost-diff | 0 | (sin.f64 eps) |
| ✓ | cost-diff | 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)))) |
| ✓ | cost-diff | 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)) |
| ✓ | 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)) |
| 15 492× | lower-fma.f32 |
| 15 482× | lower-fma.f64 |
| 3 322× | lower-*.f32 |
| 3 304× | lower-*.f64 |
| 2 536× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 307 |
| 0 | 79 | 287 |
| 1 | 138 | 287 |
| 2 | 302 | 281 |
| 3 | 749 | 273 |
| 4 | 2327 | 272 |
| 5 | 5626 | 272 |
| 0 | 8336 | 266 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.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 (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)))) |
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)) |
(+.f64 eps #s(literal 0 binary64)) |
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))) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal 2 binary64) |
(sin.f64 eps) |
eps |
(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (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)) (*.f64 x (*.f64 x x)) x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(fma.f64 (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)) (*.f64 x (*.f64 x 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)) |
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) |
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) |
(*.f64 x x) |
#s(literal -1/5040 binary64) |
#s(literal 1/120 binary64) |
#s(literal -1/6 binary64) |
(*.f64 x (*.f64 x x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(sin.f64 x) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) |
#s(literal 1/2 binary64) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))) |
(cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) |
(*.f64 (+.f64 x eps) #s(literal 2 binary64)) |
(+.f64 x eps) |
x |
eps |
#s(literal 2 binary64) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) |
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))) |
#s(literal -1/2 binary64) |
(cos.f64 (+.f64 x x)) |
(+.f64 x x) |
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(sin.f64 x) |
| Outputs |
|---|
(*.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 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(*.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)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)) |
(*.f64 eps #s(literal 1/2 binary64)) |
(+.f64 eps #s(literal 0 binary64)) |
eps |
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))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 eps #s(literal 1/2 binary64) x) |
(fma.f64 x #s(literal 2 binary64) eps) |
(+.f64 eps (+.f64 x x)) |
x |
#s(literal 2 binary64) |
(sin.f64 eps) |
eps |
(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (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)) (*.f64 x (*.f64 x x)) x)) |
(fma.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x 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.f64 (+.f64 eps x))) |
(sin.f64 (+.f64 x eps)) |
(sin.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
(fma.f64 (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)) (*.f64 x (*.f64 x x)) x) |
(fma.f64 x (*.f64 x (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))) 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)) |
(fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) |
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) |
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) |
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) |
(fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) |
(*.f64 x x) |
#s(literal -1/5040 binary64) |
#s(literal 1/120 binary64) |
#s(literal -1/6 binary64) |
(*.f64 x (*.f64 x x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
#s(literal 1 binary64) |
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(sin.f64 (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
(sin.f64 x) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) (-.f64 (cos.f64 (+.f64 x x)) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) |
(-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) |
(*.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (+.f64 x x)) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) |
#s(literal 1/2 binary64) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))) |
(fma.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (cos.f64 (+.f64 x x))) #s(literal 1/2 binary64)) |
(cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) |
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) |
(*.f64 (+.f64 x eps) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (+.f64 eps x)) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
#s(literal 2 binary64) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) |
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))) |
#s(literal -1/2 binary64) |
(cos.f64 (+.f64 x x)) |
(+.f64 x x) |
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 x) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.6% | (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| ✓ | accuracy | 55.7% | (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) |
| ✓ | accuracy | 55.1% | (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) |
| ✓ | accuracy | 53.9% | (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
| ✓ | accuracy | 99.8% | (sin.f64 (+.f64 x eps)) |
| ✓ | accuracy | 99.7% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
| ✓ | accuracy | 63.7% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| ✓ | accuracy | 99.9% | (*.f64 x (*.f64 x x)) |
| ✓ | accuracy | 99.8% | (sin.f64 (+.f64 x eps)) |
| ✓ | accuracy | 99.8% | (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) |
| ✓ | accuracy | 63.8% | (-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (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)) (*.f64 x (*.f64 x x)) x)) |
| ✓ | 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 | 99.9% | (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
| 184.0ms | 141× | 2 | valid |
| 158.0ms | 37× | 3 | valid |
| 45.0ms | 71× | 1 | valid |
| 3.0ms | 7× | 0 | valid |
Compiled 327 to 49 computations (85% saved)
ival-cos: 177.0ms (56.6% of total)adjust: 45.0ms (14.4% of total)ival-mult: 29.0ms (9.3% of total)ival-add: 18.0ms (5.8% of total)const: 15.0ms (4.8% of total)ival-sin: 11.0ms (3.5% of total)ival-div: 10.0ms (3.2% of total)ival-sub: 7.0ms (2.2% of total)exact: 1.0ms (0.3% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))> |
#<alt (+.f64 eps #s(literal 0 binary64))> |
#<alt (*.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))> |
#<alt (*.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))))> |
#<alt (sin.f64 eps)> |
#<alt (-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (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)) (*.f64 x (*.f64 x x)) x))> |
#<alt (sin.f64 (+.f64 x eps))> |
#<alt (+.f64 x eps)> |
#<alt (fma.f64 (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)) (*.f64 x (*.f64 x x)) x)> |
#<alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))> |
#<alt (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))> |
#<alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))> |
#<alt (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))))> |
#<alt (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))> |
#<alt (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))> |
#<alt (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))> |
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))> |
#<alt (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))> |
#<alt (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))> |
#<alt (*.f64 x (*.f64 x x))> |
#<alt (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))> |
| 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 (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))> |
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))> |
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 1/2 (* eps (cos x)))> |
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))> |
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt 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 (* 1/5040 (pow x 7))> |
#<alt (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))> |
#<alt (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))> |
#<alt (* 1/5040 (pow x 7))> |
#<alt (* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))> |
#<alt (* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))> |
#<alt (* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))> |
#<alt (- (sin x) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (- (+ (sin x) (* eps (cos x))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))> |
#<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 (* -1/5040 (pow x 7))> |
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))> |
#<alt (* -1/5040 (pow x 7))> |
#<alt (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))> |
#<alt (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 (/ 1 (sin eps))> |
#<alt (+ (* x (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))> |
#<alt (+ (* x (- (+ (* x (- (* 1/2 (/ 1 (sin eps))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (/ 1 (pow (sin eps) 2))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))> |
#<alt (+ (* x (- (+ (* x (- (+ (* -1 (* x (+ (* -1/2 (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/6 (/ 1 (pow (sin eps) 2))) (/ (* (- (cos eps) 1) (- (* 1/2 (/ 1 (sin eps))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (sin eps))))))) (* 1/2 (/ 1 (sin eps)))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (/ 1 (pow (sin eps) 2))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))> |
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))> |
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))> |
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))> |
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))> |
#<alt (/ 1 (- (sin (- eps (* -1 x))) (sin x)))> |
#<alt (/ 1 (- (sin (- eps (* -1 x))) (sin x)))> |
#<alt (/ 1 (- (sin (- eps (* -1 x))) (sin x)))> |
#<alt (/ 1 (- (sin (- eps (* -1 x))) (sin x)))> |
#<alt (/ 1 (* eps (cos x)))> |
#<alt (/ (+ (* 1/2 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x))) eps)> |
#<alt (/ (+ (* eps (- (* eps (- (* 1/6 (/ 1 (cos x))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/2 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) eps)> |
#<alt (/ (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- (* 1/6 (/ 1 (cos x))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/12 (/ (sin x) (pow (cos x) 2))) (* 1/24 (/ (sin x) (pow (cos x) 2))))))) (* 1/6 (/ 1 (cos x)))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/2 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) eps)> |
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))> |
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))> |
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))> |
#<alt (/ 1 (- (sin (+ eps x)) (sin x)))> |
#<alt (/ 1 (- (sin (- x (* -1 eps))) (sin x)))> |
#<alt (/ 1 (- (sin (- x (* -1 eps))) (sin x)))> |
#<alt (/ 1 (- (sin (- x (* -1 eps))) (sin x)))> |
#<alt (/ 1 (- (sin (- x (* -1 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 (- (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 (- 1/2 (* 1/2 (cos (* 2 eps))))> |
#<alt (- (+ 1/2 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps))))> |
#<alt (- (+ 1/2 (* x (- (* -1 (* x (+ 1 (* -1 (cos (* 2 eps)))))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps))))> |
#<alt (- (+ 1/2 (* x (- (* x (- (* -2/3 (* x (sin (* 2 eps)))) (+ 1 (* -1 (cos (* 2 eps)))))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps))))> |
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))> |
#<alt (* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))> |
#<alt (* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))> |
#<alt (* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))> |
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))> |
#<alt (- (* eps (sin (* 2 x))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))> |
#<alt (- (* eps (- (* eps (cos (* 2 x))) (* -1 (sin (* 2 x))))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))> |
#<alt (- (* eps (- (* eps (- (* -2/3 (* eps (sin (* 2 x)))) (* -1 (cos (* 2 x))))) (* -1 (sin (* 2 x))))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))> |
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))> |
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))> |
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))> |
#<alt (* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))> |
#<alt (* 1/2 (cos (* 2 eps)))> |
#<alt (+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps))))> |
#<alt (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (* -1 (cos (* 2 eps))))))))> |
#<alt (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 2 eps))))))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))> |
#<alt (+ 1/2 (+ (* -1 (* eps (sin (* 2 x)))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x)))))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x)))))))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))> |
#<alt (+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))> |
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))> |
#<alt (+ 1/2 (* -1/2 (cos (* 2 x))))> |
#<alt (+ 1/2 (* -1/2 (cos (* 2 x))))> |
#<alt (+ 1/2 (* -1/2 (cos (* 2 x))))> |
#<alt (+ 1/2 (* -1/2 (cos (* 2 x))))> |
#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))> |
#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))> |
#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))> |
#<alt (+ 1/2 (* -1/2 (cos (neg (* -2 x)))))> |
#<alt (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps)))> |
#<alt (+ (* -1 (* x (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2))))) (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))))> |
#<alt (+ (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (* x (+ (* -1 (* x (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps)))))) (* -1 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))))))> |
#<alt (+ (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (* x (+ (* -1 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (* x (+ (* -1 (* x (- (* 2/3 (/ (sin (* 2 eps)) (sin eps))) (+ (* -1/2 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (+ (/ (* (+ 1 (cos eps)) (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps))))) (sin eps)) (/ (* (- (* -1/6 (cos eps)) 1/6) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2))))))) (* -1 (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps))))))))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x))))))> |
#<alt (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x)))> |
#<alt (+ (* -1 (* eps (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2)))))) (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))))> |
#<alt (+ (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* eps (+ (* -1 (* eps (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x))))))) (* -1 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))))))> |
#<alt (+ (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* eps (+ (* -1 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (* eps (+ (* -1 (* eps (- (* 1/3 (/ (sin (* 2 x)) (sin x))) (+ (* -1/4 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (+ (* -1/24 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x)))))) (sin x)))))))) (* -1 (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x)))))))))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x)))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))> |
#<alt (* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps))))))> |
#<alt (cos (* 1/2 eps))> |
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (+ eps (* 2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (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 (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (* 1/120 x)> |
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))> |
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))> |
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))> |
#<alt (* -1/5040 (pow x 3))> |
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))> |
#<alt (* -1/5040 (pow x 3))> |
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))> |
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (sin eps)> |
#<alt (+ (sin eps) (* x (+ 1 (cos eps))))> |
#<alt (+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))> |
#<alt (+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6))))))))> |
#<alt (+ (sin x) (sin (+ eps x)))> |
#<alt (+ (sin x) (sin (+ eps x)))> |
#<alt (+ (sin x) (sin (+ eps x)))> |
#<alt (+ (sin x) (sin (+ eps x)))> |
#<alt (+ (sin x) (sin (- eps (* -1 x))))> |
#<alt (+ (sin x) (sin (- eps (* -1 x))))> |
#<alt (+ (sin x) (sin (- eps (* -1 x))))> |
#<alt (+ (sin x) (sin (- eps (* -1 x))))> |
#<alt (* 2 (sin x))> |
#<alt (+ (* 2 (sin x)) (* eps (cos x)))> |
#<alt (+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))> |
#<alt (+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))> |
#<alt (+ (sin x) (sin (+ eps x)))> |
#<alt (+ (sin x) (sin (+ eps x)))> |
#<alt (+ (sin x) (sin (+ eps x)))> |
#<alt (+ (sin x) (sin (+ eps x)))> |
#<alt (+ (sin x) (sin (- x (* -1 eps))))> |
#<alt (+ (sin x) (sin (- x (* -1 eps))))> |
#<alt (+ (sin x) (sin (- x (* -1 eps))))> |
#<alt (+ (sin x) (sin (- x (* -1 eps))))> |
105 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 60.0ms | x | @ | 0 | (+ 1/2 (* -1/2 (cos (+ x x)))) |
| 3.0ms | x | @ | 0 | (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) |
| 2.0ms | x | @ | 0 | (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x))) |
| 2.0ms | eps | @ | -inf | (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x))) |
| 2.0ms | eps | @ | inf | (/ (- 1/2 (+ (* 1/2 (cos (* (+ x eps) 2))) (+ 1/2 (* -1/2 (cos (+ x x)))))) (+ (sin (+ x eps)) (sin x))) |
| 1× | batch-egg-rewrite |
| 1 270× | lower-*.f32 |
| 1 254× | lower-*.f64 |
| 1 244× | lower-fma.f32 |
| 1 236× | lower-fma.f64 |
| 994× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 217 |
| 0 | 79 | 220 |
| 1 | 321 | 169 |
| 0 | 2837 | 164 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(+.f64 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 (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)))) |
(sin.f64 eps) |
(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (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)) (*.f64 x (*.f64 x x)) x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(fma.f64 (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)) (*.f64 x (*.f64 x x)) x) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) |
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x))))) |
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) |
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) |
(*.f64 x (*.f64 x x)) |
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Outputs |
|---|
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/2 binary64))) |
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) #s(literal 0 binary64)) |
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(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))))) |
(-.f64 (/.f64 (sin.f64 (+.f64 x eps)) #s(literal 1 binary64)) (/.f64 (sin.f64 x) #s(literal 1 binary64))) |
(fma.f64 (sin.f64 (+.f64 x eps)) #s(literal 1 binary64) (*.f64 (neg.f64 (sin.f64 x)) #s(literal 1 binary64))) |
(fma.f64 #s(literal 1 binary64) (sin.f64 (+.f64 x eps)) (*.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x)))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))) |
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (sin.f64 (+.f64 x eps))) |
(neg.f64 (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))) (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))))) |
(/.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(/.f64 (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal -1 binary64)) |
(/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))))) |
(/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) |
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))))) |
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (*.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))))) |
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))))) |
(/.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))))) (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))))) |
(/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x))) (*.f64 (sin.f64 (+.f64 x eps)) (neg.f64 (sin.f64 x)))))) |
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps)))) |
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 x)))) (-.f64 (sin.f64 (+.f64 x eps)) (neg.f64 (sin.f64 x)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps eps))))) #s(literal 2 binary64)) |
(/.f64 (*.f64 (+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 eps eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps eps)))) #s(literal 2 binary64)) #s(literal 2 binary64)) |
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) #s(literal 1 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal -1 binary64)) |
(pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1 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))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(*.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 1 binary64)) |
(*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(literal -1 binary64) (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(*.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))))) |
(*.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64)))))))) |
(*.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))))) |
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (fma.f64 #s(literal 2 binary64) eps #s(literal 0 binary64))))))) |
| 1× | egg-herbie |
| 8 230× | lower-fma.f64 |
| 8 230× | lower-fma.f32 |
| 5 272× | lower-*.f64 |
| 5 272× | lower-*.f32 |
| 3 282× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 626 | 5677 |
| 1 | 1924 | 5339 |
| 2 | 5669 | 5205 |
| 0 | 8103 | 4828 |
| 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 |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2)))))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
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))) |
(* 1/5040 (pow x 7)) |
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))) |
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))) |
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))) |
(* 1/5040 (pow x 7)) |
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))) |
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))) |
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))) |
(- (sin x) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(- (+ (sin x) (* eps (cos x))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(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)))) |
(* -1/5040 (pow x 7)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(* -1/5040 (pow x 7)) |
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(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)) |
(/ 1 (sin eps)) |
(+ (* x (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps))) |
(+ (* x (- (+ (* x (- (* 1/2 (/ 1 (sin eps))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (/ 1 (pow (sin eps) 2))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps))) |
(+ (* x (- (+ (* x (- (+ (* -1 (* x (+ (* -1/2 (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/6 (/ 1 (pow (sin eps) 2))) (/ (* (- (cos eps) 1) (- (* 1/2 (/ 1 (sin eps))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (sin eps))))))) (* 1/2 (/ 1 (sin eps)))) (/ (* (- (cos eps) 1) (- (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps)))) (/ 1 (pow (sin eps) 2))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps))) |
(/ 1 (- (sin (+ eps x)) (sin x))) |
(/ 1 (- (sin (+ eps x)) (sin x))) |
(/ 1 (- (sin (+ eps x)) (sin x))) |
(/ 1 (- (sin (+ eps x)) (sin x))) |
(/ 1 (- (sin (- eps (* -1 x))) (sin x))) |
(/ 1 (- (sin (- eps (* -1 x))) (sin x))) |
(/ 1 (- (sin (- eps (* -1 x))) (sin x))) |
(/ 1 (- (sin (- eps (* -1 x))) (sin x))) |
(/ 1 (* eps (cos x))) |
(/ (+ (* 1/2 (/ (* eps (sin x)) (pow (cos x) 2))) (/ 1 (cos x))) eps) |
(/ (+ (* eps (- (* eps (- (* 1/6 (/ 1 (cos x))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/2 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) eps) |
(/ (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- (* 1/6 (/ 1 (cos x))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (cos x))) (+ (* -1/12 (/ (sin x) (pow (cos x) 2))) (* 1/24 (/ (sin x) (pow (cos x) 2))))))) (* 1/6 (/ 1 (cos x)))) (* -1/4 (/ (pow (sin x) 2) (pow (cos x) 3))))) (* -1/2 (/ (sin x) (pow (cos x) 2))))) (/ 1 (cos x))) eps) |
(/ 1 (- (sin (+ eps x)) (sin x))) |
(/ 1 (- (sin (+ eps x)) (sin x))) |
(/ 1 (- (sin (+ eps x)) (sin x))) |
(/ 1 (- (sin (+ eps x)) (sin x))) |
(/ 1 (- (sin (- x (* -1 eps))) (sin x))) |
(/ 1 (- (sin (- x (* -1 eps))) (sin x))) |
(/ 1 (- (sin (- x (* -1 eps))) (sin x))) |
(/ 1 (- (sin (- x (* -1 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))) |
(- (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)) |
(- 1/2 (* 1/2 (cos (* 2 eps)))) |
(- (+ 1/2 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps)))) |
(- (+ 1/2 (* x (- (* -1 (* x (+ 1 (* -1 (cos (* 2 eps)))))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps)))) |
(- (+ 1/2 (* x (- (* x (- (* -2/3 (* x (sin (* 2 eps)))) (+ 1 (* -1 (cos (* 2 eps)))))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps)))) |
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x))))))) |
(* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x))))))) |
(* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x))))))) |
(* -1 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x))))))) |
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) |
(- (* eps (sin (* 2 x))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) |
(- (* eps (- (* eps (cos (* 2 x))) (* -1 (sin (* 2 x))))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) |
(- (* eps (- (* eps (- (* -2/3 (* eps (sin (* 2 x)))) (* -1 (cos (* 2 x))))) (* -1 (sin (* 2 x))))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) |
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps))))))) |
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps))))))) |
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps))))))) |
(* -1 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps))))))) |
(* 1/2 (cos (* 2 eps))) |
(+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps)))) |
(+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (* -1 (cos (* 2 eps)))))))) |
(+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 2 eps)))))))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x))))))) |
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x))))))) |
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x))))))) |
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x))))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) |
(+ 1/2 (+ (* -1 (* eps (sin (* 2 x)))) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x))))))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x))))))))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps))))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps))))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps))))))) |
(+ 1/2 (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps))))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) |
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3)))) |
(+ 1/2 (* -1/2 (cos (* 2 x)))) |
(+ 1/2 (* -1/2 (cos (* 2 x)))) |
(+ 1/2 (* -1/2 (cos (* 2 x)))) |
(+ 1/2 (* -1/2 (cos (* 2 x)))) |
(+ 1/2 (* -1/2 (cos (neg (* -2 x))))) |
(+ 1/2 (* -1/2 (cos (neg (* -2 x))))) |
(+ 1/2 (* -1/2 (cos (neg (* -2 x))))) |
(+ 1/2 (* -1/2 (cos (neg (* -2 x))))) |
(* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) |
(+ (* -1 (* x (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2))))) (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps)))) |
(+ (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (* x (+ (* -1 (* x (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps)))))) (* -1 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2))))))) |
(+ (* -1 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (* x (+ (* -1 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (* x (+ (* -1 (* x (- (* 2/3 (/ (sin (* 2 eps)) (sin eps))) (+ (* -1/2 (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (+ (/ (* (+ 1 (cos eps)) (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps))))) (sin eps)) (/ (* (- (* -1/6 (cos eps)) 1/6) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2))))))) (* -1 (- (+ (* -1 (/ (cos (* 2 eps)) (sin eps))) (/ 1 (sin eps))) (+ (* -1/2 (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* -1 (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (sin eps) 2)))) (sin eps)))))))))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x))))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x))))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x))))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x))))) |
(* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x)))))) |
(* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x)))))) |
(* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x)))))) |
(* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x)))))) |
(* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) |
(+ (* -1 (* eps (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2)))))) (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x)))) |
(+ (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* eps (+ (* -1 (* eps (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x))))))) (* -1 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2)))))))) |
(+ (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* eps (+ (* -1 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (* eps (+ (* -1 (* eps (- (* 1/3 (/ (sin (* 2 x)) (sin x))) (+ (* -1/4 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (+ (* -1/24 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x)))))) (sin x)))))))) (* -1 (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x))))))))))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x))))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x))))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x))))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x))))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps)))))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps)))))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps)))))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps)))))) |
(cos (* 1/2 eps)) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(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)))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(* 1/120 x) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
(* -1/5040 (pow x 3)) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(* -1/5040 (pow x 3)) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(sin eps) |
(+ (sin eps) (* x (+ 1 (cos eps)))) |
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps))))))) |
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6)))))))) |
(+ (sin x) (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)))) |
(* 2 (sin x)) |
(+ (* 2 (sin x)) (* eps (cos x))) |
(+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(+ (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)))) |
| 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)))) |
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) |
(* x (+ 1 (* 1/2 (/ eps x)))) |
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x) |
x |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
(* -1 (* x (- (* -1/2 (/ eps x)) 1))) |
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x) |
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 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (neg.f64 eps)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (neg.f64 eps)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) (neg.f64 eps)) |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
(* 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)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 (*.f64 eps (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 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (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))))) |
(fma.f64 x (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.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 x (-.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) 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 (* (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 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 x #s(literal 1/3 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (*.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)))) |
(* 1/2 (* 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 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 (*.f64 eps (cos.f64 x)) #s(literal -1/12 binary64) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 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)))))))))) |
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (*.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)))))) |
(* (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 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) |
(+ (* 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 (*.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))) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (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 (fma.f64 x (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))) (neg.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (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 |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 eps (*.f64 eps eps)) eps) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(fma.f64 (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)) (*.f64 eps (*.f64 eps eps)) 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) |
(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 (+.f64 #s(literal -1 binary64) (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 x (+.f64 (cos.f64 eps) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) #s(literal -1 binary64))) (sin.f64 eps)) |
(* 1/5040 (pow x 7)) |
(*.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64))) |
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x)))) |
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/5040 binary64) (+.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))))) |
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/5040 binary64) (-.f64 (/.f64 #s(literal -1/120 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))))))) |
(* 1/5040 (pow x 7)) |
(*.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64))) |
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x)))) |
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))) |
(*.f64 (-.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (neg.f64 (pow.f64 x #s(literal 7 binary64)))) |
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (neg.f64 (pow.f64 x #s(literal 7 binary64)))) |
(- (sin x) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(-.f64 (sin.f64 x) (fma.f64 (*.f64 x x) (*.f64 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))) x)) |
(- (+ (sin x) (* eps (cos x))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(-.f64 (fma.f64 eps (cos.f64 x) (sin.f64 x)) (fma.f64 (*.f64 x x) (*.f64 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))) x)) |
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (-.f64 (sin.f64 x) (fma.f64 (*.f64 x x) (*.f64 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))) x))) |
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(-.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)) (sin.f64 x)) (fma.f64 (*.f64 x x) (*.f64 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))) x)) |
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (neg.f64 x) (fma.f64 x (*.f64 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.f64 (+.f64 eps x))) |
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (neg.f64 x) (fma.f64 x (*.f64 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.f64 (+.f64 eps x))) |
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (neg.f64 x) (fma.f64 x (*.f64 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.f64 (+.f64 eps x))) |
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (neg.f64 x) (fma.f64 x (*.f64 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.f64 (+.f64 eps x))) |
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (neg.f64 x) (fma.f64 x (*.f64 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.f64 (+.f64 eps x))) |
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (neg.f64 x) (fma.f64 x (*.f64 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.f64 (+.f64 eps x))) |
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (neg.f64 x) (fma.f64 x (*.f64 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.f64 (+.f64 eps x))) |
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (neg.f64 x) (fma.f64 x (*.f64 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.f64 (+.f64 eps 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 x (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (cos.f64 eps)) (sin.f64 eps)) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 #s(literal -1/6 binary64) (cos.f64 eps)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) (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 (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (sin.f64 x)) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (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 (neg.f64 x) (/.f64 eps (neg.f64 x)) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 x)) x) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(fma.f64 (neg.f64 x) (/.f64 eps (neg.f64 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 (/.f64 x (neg.f64 eps)) (neg.f64 eps) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (/.f64 x (neg.f64 eps)) (neg.f64 eps) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(fma.f64 (/.f64 x (neg.f64 eps)) (neg.f64 eps) eps) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(fma.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)) x) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(fma.f64 (*.f64 x x) (*.f64 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))) x) |
(* -1/5040 (pow x 7)) |
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 7 binary64))) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x)))) |
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) |
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(* -1/5040 (pow x 7)) |
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 7 binary64))) |
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(*.f64 (pow.f64 x #s(literal 7 binary64)) (neg.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))) |
(neg.f64 (*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/5040 binary64) (+.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal -1/120 binary64) (*.f64 x x)))))) |
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/5040 binary64) (-.f64 (/.f64 #s(literal -1/120 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))))) (neg.f64 (pow.f64 x #s(literal 7 binary64)))) |
(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 (+.f64 #s(literal -1 binary64) (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (cos.f64 eps))) (sin.f64 eps)) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(fma.f64 x (+.f64 (cos.f64 eps) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) #s(literal -1 binary64))) (sin.f64 eps)) |
(- (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)) |
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(pow x 2) |
(*.f64 x x) |
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(* -1 (/ (+ (* -1/2 (cos (neg (* -2 x)))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x)))))) |
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(* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) |
#s(literal 0 binary64) |
(+ (* -1 (* eps (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2)))))) (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x)))) |
(*.f64 eps (fma.f64 #s(literal 1/2 binary64) (/.f64 (sin.f64 (*.f64 x #s(literal 2 binary64))) (sin.f64 x)) #s(literal 0 binary64))) |
(+ (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* eps (+ (* -1 (* eps (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x))))))) (* -1 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2)))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 x #s(literal 2 binary64))) (sin.f64 x)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 (*.f64 x #s(literal 2 binary64))) (sin.f64 x)) #s(literal 0 binary64)) (/.f64 (cos.f64 x) (sin.f64 x))) #s(literal 0 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sin.f64 (*.f64 x #s(literal 2 binary64))) (sin.f64 x)) #s(literal 0 binary64)))) |
(+ (* -1/2 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* eps (+ (* -1 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (* eps (+ (* -1 (* eps (- (* 1/3 (/ (sin (* 2 x)) (sin x))) (+ (* -1/4 (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (+ (* -1/24 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x)))))) (sin x)))))))) (* -1 (- (* -1/2 (/ (cos (* 2 x)) (sin x))) (+ (* -1/8 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x)))) (sin x))) (* 1/2 (/ (* (cos x) (- (* -1/2 (/ (sin (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 x))))) (pow (sin x) 2))))) (sin x))))))))))) |
(*.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 eps (fma.f64 #s(literal 1/3 binary64) (/.f64 (sin.f64 (*.f64 x #s(literal 2 binary64))) (sin.f64 x)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (sin.f64 (*.f64 x #s(literal 2 binary64))) (sin.f64 x)) #s(literal 0 binary64)) (/.f64 (cos.f64 x) (sin.f64 x))) (*.f64 (cos.f64 (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (sin.f64 x)))) (/.f64 (cos.f64 x) (sin.f64 x))) (fma.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sin.f64 (*.f64 x #s(literal 2 binary64))) (sin.f64 x)) #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (sin.f64 (*.f64 x #s(literal 2 binary64))) (sin.f64 x)) #s(literal 0 binary64)) (/.f64 (cos.f64 x) (sin.f64 x))) (*.f64 (cos.f64 (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (sin.f64 x))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sin.f64 (*.f64 x #s(literal 2 binary64))) (sin.f64 x)) #s(literal 0 binary64)))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x))))) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x))))) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x))))) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x))))) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps)))))) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps)))))) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps)))))) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(* -1 (/ (+ (* -1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps)))))) |
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(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)) (neg.f64 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 (-.f64 (*.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (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 eps (*.f64 #s(literal -1/2 binary64) (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 (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64)) (*.f64 (cos.f64 x) #s(literal -1/8 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (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)) |
(* 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 (*.f64 eps 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 (*.f64 eps 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)) |
(* 1/120 x) |
(*.f64 x #s(literal 1/120 binary64)) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
(*.f64 x (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
(*.f64 x (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))) |
(* x (+ 1/120 (* -1/5040 (pow x 2)))) |
(*.f64 x (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))) |
(* -1/5040 (pow x 3)) |
(*.f64 #s(literal -1/5040 binary64) (*.f64 x (*.f64 x x))) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x))) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x))) |
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)) |
(*.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x))) |
(* -1/5040 (pow x 3)) |
(*.f64 #s(literal -1/5040 binary64) (*.f64 x (*.f64 x x))) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(*.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))) (neg.f64 (*.f64 x (*.f64 x x)))) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(*.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))) (neg.f64 (*.f64 x (*.f64 x x)))) |
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))) |
(*.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))) (neg.f64 (*.f64 x (*.f64 x x)))) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(sin eps) |
(sin.f64 eps) |
(+ (sin eps) (* x (+ 1 (cos eps)))) |
(+.f64 x (fma.f64 x (cos.f64 eps) (sin.f64 eps))) |
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps))))))) |
(+.f64 x (fma.f64 x (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (cos.f64 eps)) (sin.f64 eps))) |
(+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6)))))))) |
(fma.f64 x (+.f64 (cos.f64 eps) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) #s(literal 1 binary64))) (sin.f64 eps)) |
(+ (sin x) (sin (+ eps x))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+ (sin x) (sin (+ eps x))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+ (sin x) (sin (+ eps x))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+ (sin x) (sin (+ eps x))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+ (sin x) (sin (- eps (* -1 x)))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+ (sin x) (sin (- eps (* -1 x)))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+ (sin x) (sin (- eps (* -1 x)))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+ (sin x) (sin (- eps (* -1 x)))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(* 2 (sin x)) |
(*.f64 (sin.f64 x) #s(literal 2 binary64)) |
(+ (* 2 (sin x)) (* eps (cos x))) |
(fma.f64 eps (cos.f64 x) (*.f64 (sin.f64 x) #s(literal 2 binary64))) |
(+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(fma.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 2 binary64))) |
(+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)) (*.f64 (sin.f64 x) #s(literal 2 binary64))) |
(+ (sin x) (sin (+ eps x))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+ (sin x) (sin (+ eps x))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+ (sin x) (sin (+ eps x))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+ (sin x) (sin (+ eps x))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+ (sin x) (sin (- x (* -1 eps)))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+ (sin x) (sin (- x (* -1 eps)))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+ (sin x) (sin (- x (* -1 eps)))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
(+ (sin x) (sin (- x (* -1 eps)))) |
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) |
Compiled 30 648 to 2 421 computations (92.1% saved)
18 alts after pruning (16 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 154 | 13 | 1 167 |
| Fresh | 2 | 3 | 5 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 160 | 18 | 1 178 |
| Status | Accuracy | Program |
|---|---|---|
| 99.6% | (fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))) | |
| 96.8% | (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) | |
| 7.8% | (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) | |
| 98.4% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))) | |
| ✓ | 63.5% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.1% | (*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps 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))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) | |
| 98.9% | (*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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)) | |
| ▶ | 98.9% | (*.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)) |
| 98.6% | (*.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)) | |
| 25.4% | (*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 0 binary64)) eps (*.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 eps eps))) (*.f64 (fma.f64 x x #s(literal 0 binary64)) eps)) #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)) | |
| ▶ | 21.1% | (*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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)) |
| ▶ | 63.6% | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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)) |
| 53.0% | (*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #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)) | |
| ▶ | 99.9% | (*.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)) |
| 98.7% | (*.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)))) | |
| 98.2% | (*.f64 eps (cos.f64 x)) | |
| ✓ | 96.8% | (sin.f64 eps) |
| ▶ | 5.5% | #s(literal 0 binary64) |
Compiled 649 to 407 computations (37.3% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 192 | (fma.f64 x x (*.f64 (+.f64 x eps) x)) |
| ✓ | cost-diff | 256 | (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))) |
| ✓ | cost-diff | 320 | (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 5440 | (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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)) |
| ✓ | cost-diff | 320 | (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 384 | (+.f64 x (-.f64 eps x)) |
| ✓ | cost-diff | 0 | (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (*.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)))) |
| ✓ | cost-diff | 320 | (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 320 | (*.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)) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) eps) |
| ✓ | 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)) |
| 19 884× | lower-fma.f32 |
| 19 874× | lower-fma.f64 |
| 4 868× | lower-*.f32 |
| 4 838× | lower-*.f64 |
| 3 210× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 40 | 435 |
| 0 | 76 | 378 |
| 1 | 140 | 378 |
| 2 | 299 | 365 |
| 3 | 706 | 356 |
| 4 | 1983 | 348 |
| 5 | 6507 | 348 |
| 0 | 8369 | 341 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 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 (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 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
eps |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
x |
#s(literal 2 binary64) |
#s(literal 0 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)) |
(*.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)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
eps |
(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) |
(*.f64 eps #s(literal -1/48 binary64)) |
#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))) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal 2 binary64) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) |
(*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64)) |
(+.f64 x (-.f64 eps x)) |
x |
(-.f64 eps x) |
eps |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 2 binary64) eps) |
#s(literal 2 binary64) |
(*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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 (sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #s(literal 1/2 binary64)) |
(/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) |
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) |
(pow.f64 (+.f64 x eps) #s(literal 3 binary64)) |
(+.f64 x eps) |
x |
eps |
#s(literal 3 binary64) |
(*.f64 x (*.f64 x x)) |
(*.f64 x x) |
(fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))) |
(fma.f64 x x (*.f64 (+.f64 x eps) x)) |
(*.f64 (+.f64 x eps) x) |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 2 binary64) eps) |
#s(literal 2 binary64) |
| 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 (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)))) |
(*.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 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
eps |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
x |
#s(literal 2 binary64) |
#s(literal 0 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)) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/24 binary64)) eps)) |
(*.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)))) |
(*.f64 (*.f64 eps (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))) (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 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))) |
eps |
(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) |
(*.f64 eps #s(literal -1/48 binary64)) |
#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))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(fma.f64 x #s(literal 2 binary64) eps) |
(+.f64 eps (+.f64 x x)) |
x |
#s(literal 2 binary64) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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 (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)))) |
(*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 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 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) eps) |
(+.f64 x (-.f64 eps x)) |
eps |
x |
(-.f64 eps x) |
eps |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(fma.f64 x #s(literal 2 binary64) eps) |
(+.f64 eps (+.f64 x x)) |
#s(literal 2 binary64) |
(*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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 (sin.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 eps (*.f64 (+.f64 eps x) (+.f64 eps (+.f64 x x))) (*.f64 eps (*.f64 x x)))) (fma.f64 eps eps (*.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)))))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 eps (*.f64 (+.f64 eps x) (+.f64 eps (+.f64 x x))) (*.f64 eps (*.f64 x x)))) (fma.f64 eps eps (*.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x))))))) |
(sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #s(literal 1/2 binary64))) |
(sin.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 eps (*.f64 (+.f64 eps x) (+.f64 eps (+.f64 x x))) (*.f64 eps (*.f64 x x)))) (fma.f64 eps eps (*.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)))))) |
(*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #s(literal 1/2 binary64)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 eps (*.f64 (+.f64 eps x) (+.f64 eps (+.f64 x x))) (*.f64 eps (*.f64 x x)))) (fma.f64 eps eps (*.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x))))) |
(/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) |
(/.f64 (fma.f64 eps (*.f64 (+.f64 eps x) (+.f64 eps (+.f64 x x))) (*.f64 eps (*.f64 x x))) (fma.f64 eps eps (*.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x))))) |
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) |
(fma.f64 eps (*.f64 (+.f64 eps x) (+.f64 eps (+.f64 x x))) (*.f64 eps (*.f64 x x))) |
(pow.f64 (+.f64 x eps) #s(literal 3 binary64)) |
(*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) |
(+.f64 x eps) |
(+.f64 eps x) |
x |
eps |
#s(literal 3 binary64) |
(*.f64 x (*.f64 x x)) |
(*.f64 x x) |
(fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))) |
(fma.f64 eps eps (*.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)))) |
(fma.f64 x x (*.f64 (+.f64 x eps) x)) |
(*.f64 x (+.f64 eps (+.f64 x x))) |
(*.f64 (+.f64 x eps) x) |
(*.f64 x (+.f64 eps x)) |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(fma.f64 x #s(literal 2 binary64) eps) |
(+.f64 eps (+.f64 x x)) |
#s(literal 2 binary64) |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.8% | (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))) |
| ✓ | accuracy | 99.6% | (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) |
| ✓ | accuracy | 89.1% | (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) |
| ✓ | accuracy | 33.7% | (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) |
| ✓ | accuracy | 100.0% | (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 99.9% | (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 63.7% | (+.f64 x (-.f64 eps x)) |
| ✓ | accuracy | 100.0% | (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 100.0% | (*.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)))) |
| ✓ | accuracy | 99.9% | (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 99.4% | (*.f64 eps #s(literal -1/48 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/2 binary64) eps) |
| ✓ | 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 | 99.9% | (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
| 78.0ms | 256× | 0 | valid |
Compiled 473 to 45 computations (90.5% saved)
ival-mult: 29.0ms (51.5% of total)ival-add: 7.0ms (12.4% of total)ival-sin: 5.0ms (8.9% of total)ival-pow: 4.0ms (7.1% of total)ival-cos: 3.0ms (5.3% of total)const: 3.0ms (5.3% of total)ival-div: 2.0ms (3.6% of total)ival-sub: 2.0ms (3.6% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt (*.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))> |
#<alt (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))> |
#<alt (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))> |
#<alt (*.f64 #s(literal 1/2 binary64) eps)> |
#<alt (*.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))> |
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))> |
#<alt (*.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))))> |
#<alt (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))> |
#<alt (+.f64 x (-.f64 eps x))> |
#<alt (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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))> |
#<alt (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))> |
#<alt (pow.f64 (+.f64 x eps) #s(literal 3 binary64))> |
#<alt (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))> |
#<alt (fma.f64 x x (*.f64 (+.f64 x eps) x))> |
#<alt (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))> |
#<alt (*.f64 eps #s(literal -1/48 binary64))> |
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))> |
#<alt (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64)))> |
#<alt (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))))> |
#<alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x)))> |
| 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 (* 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 (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 (* -1/24 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))> |
#<alt (* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))> |
#<alt (* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))> |
#<alt (* -1/24 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))> |
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))> |
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (* 1/2 eps)> |
#<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 (* 1/2 (* eps (cos x)))> |
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))> |
#<alt (* -1/48 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x))))))> |
#<alt (* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))> |
#<alt (* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))> |
#<alt (* -1/48 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))> |
#<alt (* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))> |
#<alt (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))> |
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))> |
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))))> |
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* -1/48 (pow eps 3))> |
#<alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))> |
#<alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))> |
#<alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))> |
#<alt (* -1/48 (pow eps 3))> |
#<alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))> |
#<alt eps> |
#<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 eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt 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 (* 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 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))> |
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* 1/2 (* eps (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 (pow eps 3)> |
#<alt (+ (* x (+ (* 2 (pow eps 2)) (pow eps 2))) (pow eps 3))> |
#<alt (+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))> |
#<alt (+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (+ x (* 2 eps)))) (pow eps 2)))) (pow eps 3))> |
#<alt (pow x 3)> |
#<alt (* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (/ eps x))))> |
#<alt (* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (+ (* 2 (/ (pow eps 2) (pow x 2))) (+ (/ eps x) (/ (pow eps 2) (pow x 2)))))))> |
#<alt (* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (+ (* 2 (/ (pow eps 2) (pow x 2))) (+ (/ eps x) (+ (/ (pow eps 2) (pow x 2)) (/ (pow eps 3) (pow x 3))))))))> |
#<alt (pow x 3)> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ eps (* 2 eps)) x)) 1)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps))) x)) 1)))> |
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))) x)) 1)))> |
#<alt (pow x 3)> |
#<alt (+ (* eps (+ (* 2 (pow x 2)) (pow x 2))) (pow x 3))> |
#<alt (+ (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2)))) (pow x 3))> |
#<alt (+ (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))) (pow x 3))> |
#<alt (pow eps 3)> |
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))> |
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))> |
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (+ (/ (pow x 2) (pow eps 2)) (/ (pow x 3) (pow eps 3))))))))> |
#<alt (pow eps 3)> |
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1)))> |
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))> |
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (+ (* -1 (/ (pow x 3) eps)) (* -1 (pow x 2)))) eps)) (* 2 x))) eps)) 1)))> |
#<alt (pow eps 2)> |
#<alt (+ (* x (+ eps (* 2 eps))) (pow eps 2))> |
#<alt (+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2))> |
#<alt (+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2))> |
#<alt (* 3 (pow x 2))> |
#<alt (* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (/ eps x))))> |
#<alt (* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))> |
#<alt (* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))> |
#<alt (* 3 (pow x 2))> |
#<alt (* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (* -1 eps)) x))))> |
#<alt (* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x))))> |
#<alt (* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x))))> |
#<alt (+ (* 2 (pow x 2)) (pow x 2))> |
#<alt (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2)))> |
#<alt (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))> |
#<alt (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))> |
#<alt (pow eps 2)> |
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))> |
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))> |
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))> |
#<alt (pow eps 2)> |
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 x)) eps))))> |
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps))))> |
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps))))> |
#<alt (* eps x)> |
#<alt (* x (+ eps (* 2 x)))> |
#<alt (* x (+ eps (* 2 x)))> |
#<alt (* x (+ eps (* 2 x)))> |
#<alt (* 2 (pow x 2))> |
#<alt (* (pow x 2) (+ 2 (/ eps x)))> |
#<alt (* (pow x 2) (+ 2 (/ eps x)))> |
#<alt (* (pow x 2) (+ 2 (/ eps x)))> |
#<alt (* 2 (pow x 2))> |
#<alt (* (pow x 2) (+ 2 (/ eps x)))> |
#<alt (* (pow x 2) (+ 2 (/ eps x)))> |
#<alt (* (pow x 2) (+ 2 (/ eps x)))> |
#<alt (* 2 (pow x 2))> |
#<alt (+ (* 2 (pow x 2)) (* eps x))> |
#<alt (+ (* 2 (pow x 2)) (* eps x))> |
#<alt (+ (* 2 (pow x 2)) (* eps x))> |
#<alt (* eps x)> |
#<alt (* eps (+ x (* 2 (/ (pow x 2) eps))))> |
#<alt (* eps (+ x (* 2 (/ (pow x 2) eps))))> |
#<alt (* eps (+ x (* 2 (/ (pow x 2) eps))))> |
#<alt (* eps x)> |
#<alt (* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x))))> |
#<alt (* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x))))> |
#<alt (* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x))))> |
#<alt (cos x)> |
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))> |
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))> |
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (- x (* -1/2 eps)))> |
#<alt (cos (- x (* -1/2 eps)))> |
#<alt (cos (- x (* -1/2 eps)))> |
#<alt (cos (- x (* -1/2 eps)))> |
#<alt (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 (* -1/48 eps)> |
#<alt (* -1/48 eps)> |
#<alt (* -1/48 eps)> |
#<alt (* -1/48 eps)> |
#<alt (* -1/48 eps)> |
#<alt (* -1/48 eps)> |
#<alt (* -1/48 eps)> |
#<alt (* -1/48 eps)> |
#<alt (* -1/48 eps)> |
#<alt (* -1/48 eps)> |
#<alt (* -1/48 eps)> |
#<alt (* -1/48 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 (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 (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (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 eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt (* 1/3 (+ eps (* 2 eps)))> |
#<alt (- (+ (* 1/3 (+ eps (* 2 eps))) (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x))) (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)))> |
#<alt (- (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2))))))> |
#<alt (- (+ (* -1 (/ (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))))) (pow x 3))) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2))))))> |
#<alt (* 1/3 (+ eps (* 2 eps)))> |
#<alt (+ (* -1 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))> |
#<alt (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))> |
#<alt (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* 1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))))))) x)) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))) x)) (* 1/3 (pow eps 3)))) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps))))> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (pow x 2)) (+ (/ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) eps) (/ (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))) eps)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))> |
#<alt (pow eps 3)> |
#<alt (+ (* x (+ (* 2 (pow eps 2)) (pow eps 2))) (pow eps 3))> |
#<alt (+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))> |
#<alt (+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3))> |
#<alt (* (pow x 2) (+ eps (* 2 eps)))> |
#<alt (* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (/ (pow eps 2) x)))))> |
#<alt (* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2)))))))> |
#<alt (* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2)))))))> |
#<alt (* (pow x 2) (+ eps (* 2 eps)))> |
#<alt (* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps))))> |
#<alt (* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))))> |
#<alt (* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))))> |
#<alt (* eps (+ (* 2 (pow x 2)) (pow x 2)))> |
#<alt (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2))))> |
#<alt (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))))> |
#<alt (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))))> |
#<alt (pow eps 3)> |
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))> |
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))> |
#<alt (* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))> |
#<alt (pow eps 3)> |
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1)))> |
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))> |
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1)))> |
108 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | x | @ | 0 | (* (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) |
| 3.0ms | x | @ | 0 | (sin (* (+ x (- eps x)) 1/2)) |
| 2.0ms | eps | @ | 0 | (/ (- (pow (+ x eps) 3) (* x (* x x))) (+ (* (+ x eps) (+ x eps)) (+ (* x x) (* (+ x eps) x)))) |
| 2.0ms | eps | @ | inf | (/ (- (pow (+ x eps) 3) (* x (* x x))) (+ (* (+ x eps) (+ x eps)) (+ (* x x) (* (+ x eps) x)))) |
| 1.0ms | x | @ | inf | (* (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2) |
| 1× | batch-egg-rewrite |
| 5 254× | lower-*.f32 |
| 5 226× | lower-*.f64 |
| 3 716× | lower-/.f32 |
| 3 714× | lower-/.f64 |
| 3 626× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 35 | 205 |
| 0 | 67 | 178 |
| 1 | 257 | 178 |
| 2 | 1964 | 178 |
| 0 | 8141 | 177 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 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 (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 #s(literal 1/2 binary64) eps) |
(*.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)) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(*.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)))) |
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(+.f64 x (-.f64 eps x)) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(pow.f64 (+.f64 x eps) #s(literal 3 binary64)) |
(fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x))) |
(fma.f64 x x (*.f64 (+.f64 x eps) x)) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(*.f64 eps #s(literal -1/48 binary64)) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) |
(/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) |
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) |
| Outputs |
|---|
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps 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 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps 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 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps 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 2 binary64) (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))))) |
(/.f64 (neg.f64 (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps 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 2 binary64) (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (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 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps 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)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(*.f64 eps (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))) |
(*.f64 eps (*.f64 (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64))) |
(*.f64 #s(literal 2 binary64) (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))) |
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))) |
(*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))) |
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #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 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 #s(literal 2 binary64) eps) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.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))) (*.f64 #s(literal 1/2 binary64) eps)) |
(+.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) eps)) |
(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 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps)) |
(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 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) eps)) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps)))) (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64)))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps))) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 8 binary64) (*.f64 eps (*.f64 eps eps))) #s(literal 1/2 binary64)) (fma.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))) (*.f64 (*.f64 x x) #s(literal 4 binary64)))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)) |
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(+.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (*.f64 #s(literal 1/2 binary64) eps))) |
(+.f64 (*.f64 (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))) |
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (*.f64 #s(literal 1/2 binary64) eps))) |
(fma.f64 (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))) |
(*.f64 eps (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))) |
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))) |
(*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) eps) |
(*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) eps) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) |
(+.f64 (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (*.f64 #s(literal 1/2 binary64) eps)) |
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) |
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) |
(fma.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) (*.f64 #s(literal 1/2 binary64) eps)) |
(fma.f64 (*.f64 eps #s(literal -1/48 binary64)) (*.f64 eps eps) (*.f64 #s(literal 1/2 binary64) eps)) |
(fma.f64 (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)) eps (*.f64 #s(literal 1/2 binary64) eps)) |
(fma.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/48 binary64) (*.f64 #s(literal 1/2 binary64) eps)) |
(fma.f64 (*.f64 eps eps) (*.f64 eps #s(literal -1/48 binary64)) (*.f64 #s(literal 1/2 binary64) eps)) |
(/.f64 (fma.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/110592 binary64))) (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (fma.f64 (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (*.f64 #s(literal 1/2 binary64) eps))))) |
(/.f64 (-.f64 (*.f64 (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) (-.f64 (*.f64 eps (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))) (*.f64 #s(literal 1/2 binary64) eps))) |
(/.f64 (*.f64 eps (fma.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/110592 binary64)) #s(literal 1/8 binary64))) (fma.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/2304 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/96 binary64))))) |
(/.f64 (*.f64 eps (fma.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal -1/4 binary64))) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal -1/2 binary64))) |
(/.f64 (*.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/110592 binary64)) #s(literal 1/8 binary64)) eps) (fma.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/2304 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/96 binary64))))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal -1/4 binary64)) eps) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal -1/2 binary64))) |
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) eps) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (-.f64 eps x)))) #s(literal -1 binary64))) |
(+.f64 eps (+.f64 (neg.f64 x) x)) |
(+.f64 eps (-.f64 x x)) |
(+.f64 x (-.f64 eps x)) |
(+.f64 (-.f64 eps x) x) |
(+.f64 (+.f64 eps x) (neg.f64 x)) |
(+.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) |
(-.f64 eps (-.f64 x x)) |
(-.f64 (+.f64 eps x) x) |
(-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) |
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(-.f64 (/.f64 (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))))) (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))))))) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))))))) |
(-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))))) (/.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) |
(fma.f64 x (neg.f64 (*.f64 x x)) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) |
(fma.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)) (neg.f64 (*.f64 x (*.f64 x x)))) |
(fma.f64 (*.f64 x x) (neg.f64 x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) |
(fma.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (+.f64 eps x) (neg.f64 (*.f64 x (*.f64 x x)))) |
(fma.f64 (neg.f64 x) (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) |
(fma.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (neg.f64 (*.f64 x (*.f64 x x)))) |
(fma.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x)) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) |
(fma.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) #s(literal 3 binary64)) (neg.f64 (*.f64 x (*.f64 x x)))) |
(fma.f64 (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (-.f64 x eps) (*.f64 (-.f64 x eps) (-.f64 x eps)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) #s(literal 3 binary64)) (neg.f64 (*.f64 x (*.f64 x x)))) |
(fma.f64 (neg.f64 (*.f64 x x)) x (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) |
(fma.f64 (*.f64 (neg.f64 x) x) x (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) |
(/.f64 (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (neg.f64 (*.f64 x (*.f64 x x))))) (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))))))) |
(/.f64 (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (neg.f64 (*.f64 x (*.f64 x x))))) (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (neg.f64 (*.f64 x (*.f64 x x))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (neg.f64 (*.f64 x (*.f64 x x))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x)))))) |
(/.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x)))) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))))) |
(/.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x)))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (neg.f64 (*.f64 x (*.f64 x x))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (neg.f64 (*.f64 x (*.f64 x x)))))) (neg.f64 (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x))))) (neg.f64 (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))))) (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))))))) (*.f64 (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))))) (*.f64 (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))))) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) |
(pow.f64 (/.f64 (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (neg.f64 (*.f64 x (*.f64 x x)))))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x))))) #s(literal -1 binary64)) |
(*.f64 (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))) (+.f64 x (-.f64 eps x))) |
(*.f64 (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (neg.f64 (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))))))) |
(*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) |
| 1× | egg-herbie |
| 11 836× | lower-fma.f64 |
| 11 836× | lower-fma.f32 |
| 5 620× | lower-*.f64 |
| 5 620× | lower-*.f32 |
| 3 700× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 576 | 5604 |
| 1 | 1959 | 5182 |
| 2 | 7243 | 4885 |
| 0 | 8407 | 4503 |
| 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)) |
(* 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 (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(* -1/24 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x)))))) |
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))) |
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))) |
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))) |
(* -1/24 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(* 1/2 eps) |
(+ 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))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(* -1/48 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x)))))) |
(* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))) |
(* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))) |
(* -1/48 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps)))))) |
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))) |
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) |
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) |
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))))) |
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* -1/48 (pow eps 3)) |
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) |
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) |
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) |
(* -1/48 (pow eps 3)) |
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2)))))) |
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2)))))) |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
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)))) |
(* 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)))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* 1/2 (* eps (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))) |
(pow eps 3) |
(+ (* x (+ (* 2 (pow eps 2)) (pow eps 2))) (pow eps 3)) |
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3)) |
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (+ x (* 2 eps)))) (pow eps 2)))) (pow eps 3)) |
(pow x 3) |
(* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (/ eps x)))) |
(* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (+ (* 2 (/ (pow eps 2) (pow x 2))) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))) |
(* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (+ (* 2 (/ (pow eps 2) (pow x 2))) (+ (/ eps x) (+ (/ (pow eps 2) (pow x 2)) (/ (pow eps 3) (pow x 3)))))))) |
(pow x 3) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ eps (* 2 eps)) x)) 1))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps))) x)) 1))) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))) x)) 1))) |
(pow x 3) |
(+ (* eps (+ (* 2 (pow x 2)) (pow x 2))) (pow x 3)) |
(+ (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2)))) (pow x 3)) |
(+ (* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))) (pow x 3)) |
(pow eps 3) |
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps)))) |
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) |
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (+ (/ (pow x 2) (pow eps 2)) (/ (pow x 3) (pow eps 3)))))))) |
(pow eps 3) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (+ (* -1 (/ (pow x 3) eps)) (* -1 (pow x 2)))) eps)) (* 2 x))) eps)) 1))) |
(pow eps 2) |
(+ (* x (+ eps (* 2 eps))) (pow eps 2)) |
(+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2)) |
(+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2)) |
(* 3 (pow x 2)) |
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (/ eps x)))) |
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2)))))) |
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2)))))) |
(* 3 (pow x 2)) |
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (* -1 eps)) x)))) |
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x)))) |
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x)))) |
(+ (* 2 (pow x 2)) (pow x 2)) |
(+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2))) |
(+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))) |
(+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))) |
(pow eps 2) |
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ x eps)))) |
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) |
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) |
(pow eps 2) |
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 x)) eps)))) |
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps)))) |
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps)))) |
(* eps x) |
(* x (+ eps (* 2 x))) |
(* x (+ eps (* 2 x))) |
(* x (+ eps (* 2 x))) |
(* 2 (pow x 2)) |
(* (pow x 2) (+ 2 (/ eps x))) |
(* (pow x 2) (+ 2 (/ eps x))) |
(* (pow x 2) (+ 2 (/ eps x))) |
(* 2 (pow x 2)) |
(* (pow x 2) (+ 2 (/ eps x))) |
(* (pow x 2) (+ 2 (/ eps x))) |
(* (pow x 2) (+ 2 (/ eps x))) |
(* 2 (pow x 2)) |
(+ (* 2 (pow x 2)) (* eps x)) |
(+ (* 2 (pow x 2)) (* eps x)) |
(+ (* 2 (pow x 2)) (* eps x)) |
(* eps x) |
(* eps (+ x (* 2 (/ (pow x 2) eps)))) |
(* eps (+ x (* 2 (/ (pow x 2) eps)))) |
(* eps (+ x (* 2 (/ (pow x 2) eps)))) |
(* eps x) |
(* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x)))) |
(* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x)))) |
(* -1 (* eps (+ (* -2 (/ (pow x 2) eps)) (* -1 x)))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x))))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (- x (* -1/2 eps))) |
(cos (- x (* -1/2 eps))) |
(cos (- x (* -1/2 eps))) |
(cos (- x (* -1/2 eps))) |
(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))) |
(* -1/48 eps) |
(* -1/48 eps) |
(* -1/48 eps) |
(* -1/48 eps) |
(* -1/48 eps) |
(* -1/48 eps) |
(* -1/48 eps) |
(* -1/48 eps) |
(* -1/48 eps) |
(* -1/48 eps) |
(* -1/48 eps) |
(* -1/48 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)))) |
(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)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(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)) |
eps |
eps |
eps |
eps |
(* 1/3 (+ eps (* 2 eps))) |
(- (+ (* 1/3 (+ eps (* 2 eps))) (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x))) (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x))) |
(- (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2)))))) |
(- (+ (* -1 (/ (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))))) (pow x 3))) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2)))))) |
(* 1/3 (+ eps (* 2 eps))) |
(+ (* -1 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps)))) |
(+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps)))) |
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* 1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))))))) x)) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))) x)) (* 1/3 (pow eps 3)))) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps)))) |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
(* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (pow x 2)) (+ (/ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) eps) (/ (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))) eps)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
(pow eps 3) |
(+ (* x (+ (* 2 (pow eps 2)) (pow eps 2))) (pow eps 3)) |
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3)) |
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3)) |
(* (pow x 2) (+ eps (* 2 eps))) |
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (/ (pow eps 2) x))))) |
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2))))))) |
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2))))))) |
(* (pow x 2) (+ eps (* 2 eps))) |
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps)))) |
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps)))) |
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps)))) |
(* eps (+ (* 2 (pow x 2)) (pow x 2))) |
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2)))) |
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))) |
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))) |
(pow eps 3) |
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps)))) |
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) |
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) |
(pow eps 3) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1))) |
| Outputs |
|---|
(* 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)) (* 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 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(fma.f64 x (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) |
(+ (* 2 (* (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 x (fma.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 x)) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) |
(+ (* 2 (* (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 (*.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x #s(literal 1/3 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))) |
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) 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 eps (*.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)))))))) |
(*.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))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(-.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(fma.f64 x (-.f64 (*.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)))) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+ (* 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 (fma.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x #s(literal 1/6 binary64)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (neg.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #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 (- (* 1/2 eps) (* -1 x))) (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 (- (* 1/2 eps) (* -1 x))) (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 (- (* 1/2 eps) (* -1 x))) (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 (- (* 1/2 eps) (* -1 x))) (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))) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 eps (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 eps (fma.f64 (*.f64 eps 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 (*.f64 eps 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 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
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(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
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(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
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(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
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(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
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(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
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(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))) |
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(* 1/2 eps) |
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(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
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(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
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(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
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(* -1/48 (pow eps 3)) |
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(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48)) |
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eps |
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(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
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(* 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)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
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(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
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(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
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(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
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(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(-.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) |
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(fma.f64 x (-.f64 (*.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)))) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+ (* 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 (fma.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x #s(literal 1/6 binary64)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (neg.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (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 (* 1/2 (+ eps (* 2 x)))) (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 (* 1/2 (+ eps (* 2 x)))) (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 (* 1/2 (- eps (* -2 x)))) (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 (* 1/2 (- eps (* -2 x)))) (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 (* 1/2 (- eps (* -2 x)))) (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 (* 1/2 (- eps (* -2 x)))) (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))) |
(* 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 eps (*.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)))))))) |
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(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(*.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 (* 1/2 (+ eps (* 2 x)))) (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 (* 1/2 (+ eps (* 2 x)))) (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 (* 1/2 (+ eps (* 2 x)))) (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 (* 1/2 (+ eps (* 2 x)))) (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 (* 1/2 (- (* 2 x) (* -1 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 (* 1/2 (- (* 2 x) (* -1 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 (* 1/2 (- (* 2 x) (* -1 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 (* 1/2 (- (* 2 x) (* -1 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))) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(+ (* x (+ (* 2 (pow eps 2)) (pow eps 2))) (pow eps 3)) |
(fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 eps (*.f64 eps #s(literal 3 binary64))))) |
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3)) |
(fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 3 binary64)) (*.f64 x (*.f64 eps #s(literal 3 binary64)))) (*.f64 eps (*.f64 eps eps))) |
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (+ x (* 2 eps)))) (pow eps 2)))) (pow eps 3)) |
(fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 3 binary64) x) (*.f64 eps (*.f64 eps #s(literal 3 binary64)))) (*.f64 eps (*.f64 eps eps))) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (/ eps x)))) |
(*.f64 (*.f64 x (*.f64 x x)) (fma.f64 #s(literal 3 binary64) (/.f64 eps x) #s(literal 1 binary64))) |
(* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (+ (* 2 (/ (pow eps 2) (pow x 2))) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (fma.f64 eps (/.f64 eps (*.f64 x x)) (/.f64 (*.f64 eps #s(literal 3 binary64)) x))))) |
(* (pow x 3) (+ 1 (+ (* 2 (/ eps x)) (+ (* 2 (/ (pow eps 2) (pow x 2))) (+ (/ eps x) (+ (/ (pow eps 2) (pow x 2)) (/ (pow eps 3) (pow x 3)))))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 1 binary64) (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (fma.f64 eps (/.f64 eps (*.f64 x x)) (/.f64 (*.f64 eps #s(literal 3 binary64)) x))) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))))) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ eps (* 2 eps)) x)) 1))) |
(*.f64 (fma.f64 eps (/.f64 #s(literal -3 binary64) x) #s(literal -1 binary64)) (*.f64 (*.f64 x (neg.f64 x)) x)) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps))) x)) 1))) |
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal 3 binary64) (fma.f64 eps (/.f64 eps x) eps)) x)) (*.f64 (*.f64 x (neg.f64 x)) x)) |
(* -1 (* (pow x 3) (- (* -1 (/ (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps))) x)) 1))) |
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(pow x 3) |
(*.f64 x (*.f64 x x)) |
(+ (* eps (+ (* 2 (pow x 2)) (pow x 2))) (pow x 3)) |
(fma.f64 eps (*.f64 x (*.f64 x #s(literal 3 binary64))) (*.f64 x (*.f64 x x))) |
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(fma.f64 eps (*.f64 x (*.f64 #s(literal 3 binary64) (+.f64 eps x))) (*.f64 x (*.f64 x x))) |
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(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps)))) |
(*.f64 eps (*.f64 eps (*.f64 eps (fma.f64 x (/.f64 #s(literal 3 binary64) eps) #s(literal 1 binary64))))) |
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(pow eps 3) |
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(pow eps 2) |
(*.f64 eps eps) |
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(* 3 (pow x 2)) |
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(pow eps 2) |
(*.f64 eps eps) |
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(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps)))) |
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(* eps x) |
(*.f64 eps x) |
(* x (+ eps (* 2 x))) |
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(* x (+ eps (* 2 x))) |
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(* x (+ eps (* 2 x))) |
(*.f64 x (fma.f64 x #s(literal 2 binary64) eps)) |
(* 2 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 2 binary64))) |
(* (pow x 2) (+ 2 (/ eps x))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 eps x))) |
(* (pow x 2) (+ 2 (/ eps x))) |
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(*.f64 eps x) |
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(cos x) |
(cos.f64 x) |
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(cos (+ x (* 1/2 eps))) |
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(cos (* 1/2 eps)) |
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(cos (+ x (* 1/2 eps))) |
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(cos (+ x (* 1/2 eps))) |
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(cos (+ x (* 1/2 eps))) |
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(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal 1/6 binary64)))) (neg.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(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)))) |
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(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos x) |
(cos.f64 x) |
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(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) |
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/8 binary64))) (cos.f64 x)) |
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin 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 (- (* 2 x) (* -1 eps)))) |
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(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
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(sin (* 1/2 eps)) |
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(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 eps (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 eps (fma.f64 (*.f64 eps 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 (*.f64 eps 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 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
eps |
eps |
eps |
eps |
(* 1/3 (+ eps (* 2 eps))) |
eps |
(- (+ (* 1/3 (+ eps (* 2 eps))) (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x))) (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x))) |
eps |
(- (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2)))))) |
(-.f64 (+.f64 (fma.f64 eps (/.f64 eps x) eps) #s(literal 0 binary64)) (fma.f64 eps (/.f64 eps x) (*.f64 eps #s(literal 0 binary64)))) |
(- (+ (* -1 (/ (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))))) (pow x 3))) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))) (+ (* 1/9 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* 1/9 (/ (pow (+ eps (* 2 eps)) 2) x)) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (* 1/9 (pow (+ eps (* 2 eps)) 2)))) (pow x 2)))))) |
(-.f64 (-.f64 (+.f64 (fma.f64 eps (/.f64 eps x) eps) #s(literal 0 binary64)) (fma.f64 eps (/.f64 eps x) (*.f64 eps #s(literal 0 binary64)))) (/.f64 (fma.f64 eps (neg.f64 (*.f64 eps #s(literal 0 binary64))) (*.f64 eps (*.f64 eps #s(literal 0 binary64)))) (*.f64 x (*.f64 x x)))) |
(* 1/3 (+ eps (* 2 eps))) |
eps |
(+ (* -1 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps)))) |
eps |
(+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps)))) |
(-.f64 eps (/.f64 (/.f64 (neg.f64 (*.f64 eps #s(literal 0 binary64))) (neg.f64 x)) x)) |
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* 1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))))))) x)) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps)))))) x)) (* 1/3 (pow eps 3)))) (+ (* 1/9 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (* 1/9 (* (+ eps (* 2 eps)) (+ (* -2 eps) (* -1 eps))))) x)) (* 1/3 (+ eps (* 2 eps)))) |
(-.f64 eps (/.f64 (/.f64 (fma.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 (*.f64 eps #s(literal -3 binary64)) (neg.f64 (*.f64 eps #s(literal 0 binary64)))) x) (neg.f64 (*.f64 eps #s(literal 0 binary64)))) (neg.f64 x)) x)) |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
(* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
eps |
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
(fma.f64 (neg.f64 eps) (/.f64 (+.f64 (-.f64 x (/.f64 (neg.f64 (*.f64 x #s(literal 0 binary64))) eps)) (neg.f64 x)) (neg.f64 eps)) eps) |
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (pow x 2)) (+ (/ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) eps) (/ (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))) eps)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
(fma.f64 (neg.f64 eps) (/.f64 (+.f64 (-.f64 x (/.f64 (-.f64 (fma.f64 x (*.f64 x #s(literal -3 binary64)) (fma.f64 (neg.f64 (*.f64 x #s(literal 0 binary64))) (/.f64 (*.f64 x #s(literal -3 binary64)) eps) (*.f64 (*.f64 x x) #s(literal 0 binary64)))) (fma.f64 x (*.f64 x #s(literal -3 binary64)) (*.f64 x #s(literal 0 binary64)))) eps)) (neg.f64 x)) (neg.f64 eps)) eps) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(+ (* x (+ (* 2 (pow eps 2)) (pow eps 2))) (pow eps 3)) |
(fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 eps (*.f64 eps #s(literal 3 binary64))))) |
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3)) |
(fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 3 binary64)) (*.f64 x (*.f64 eps #s(literal 3 binary64)))) (*.f64 eps (*.f64 eps eps))) |
(+ (* x (+ (* 2 (pow eps 2)) (+ (* x (+ eps (* 2 eps))) (pow eps 2)))) (pow eps 3)) |
(fma.f64 x (fma.f64 eps (*.f64 eps #s(literal 3 binary64)) (*.f64 x (*.f64 eps #s(literal 3 binary64)))) (*.f64 eps (*.f64 eps eps))) |
(* (pow x 2) (+ eps (* 2 eps))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal 3 binary64)))) |
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (/ (pow eps 2) x))))) |
(*.f64 (*.f64 x x) (*.f64 #s(literal 3 binary64) (fma.f64 eps (/.f64 eps x) eps))) |
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2))))))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal 3 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x x)))) |
(* (pow x 2) (+ eps (+ (* 2 eps) (+ (* 2 (/ (pow eps 2) x)) (+ (/ (pow eps 2) x) (/ (pow eps 3) (pow x 2))))))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal 3 binary64) (fma.f64 eps (/.f64 eps x) eps) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x x)))) |
(* (pow x 2) (+ eps (* 2 eps))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal 3 binary64)))) |
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))) x)) (* 2 eps)))) |
(*.f64 (*.f64 x x) (*.f64 #s(literal 3 binary64) (fma.f64 eps (/.f64 eps x) eps))) |
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps)))) |
(*.f64 (*.f64 x x) (-.f64 (*.f64 eps #s(literal 3 binary64)) (/.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal -3 binary64)) (/.f64 (*.f64 eps (*.f64 eps eps)) x)) x))) |
(* (pow x 2) (+ eps (+ (* -1 (/ (+ (* -2 (pow eps 2)) (+ (* -1 (/ (pow eps 3) x)) (* -1 (pow eps 2)))) x)) (* 2 eps)))) |
(*.f64 (*.f64 x x) (-.f64 (*.f64 eps #s(literal 3 binary64)) (/.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal -3 binary64)) (/.f64 (*.f64 eps (*.f64 eps eps)) x)) x))) |
(* eps (+ (* 2 (pow x 2)) (pow x 2))) |
(*.f64 eps (*.f64 x (*.f64 x #s(literal 3 binary64)))) |
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2)))) |
(*.f64 eps (*.f64 x (*.f64 #s(literal 3 binary64) (+.f64 eps x)))) |
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))) |
(*.f64 eps (fma.f64 eps (fma.f64 x #s(literal 3 binary64) eps) (*.f64 x (*.f64 x #s(literal 3 binary64))))) |
(* eps (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))) |
(*.f64 eps (fma.f64 eps (fma.f64 x #s(literal 3 binary64) eps) (*.f64 x (*.f64 x #s(literal 3 binary64))))) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (/ x eps)))) |
(*.f64 eps (*.f64 eps (*.f64 eps (fma.f64 x (/.f64 #s(literal 3 binary64) eps) #s(literal 1 binary64))))) |
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 x (/.f64 x (*.f64 eps eps)) (/.f64 x eps)) (fma.f64 x (/.f64 x (*.f64 eps eps)) (/.f64 x eps))))) |
(* (pow eps 3) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 x (/.f64 x (*.f64 eps eps)) (/.f64 x eps)) (fma.f64 x (/.f64 x (*.f64 eps eps)) (/.f64 x eps))))) |
(pow eps 3) |
(*.f64 eps (*.f64 eps eps)) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (* 2 x)) eps)) 1))) |
(*.f64 (fma.f64 x (/.f64 #s(literal -3 binary64) eps) #s(literal -1 binary64)) (*.f64 (*.f64 eps (neg.f64 eps)) eps)) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1))) |
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (fma.f64 x #s(literal -3 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -3 binary64)) eps)) eps)) (*.f64 (*.f64 eps (neg.f64 eps)) eps)) |
(* -1 (* (pow eps 3) (- (* -1 (/ (+ x (+ (* -1 (/ (+ (* -2 (pow x 2)) (* -1 (pow x 2))) eps)) (* 2 x))) eps)) 1))) |
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (fma.f64 x #s(literal -3 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -3 binary64)) eps)) eps)) (*.f64 (*.f64 eps (neg.f64 eps)) eps)) |
Compiled 57 226 to 4 436 computations (92.2% saved)
25 alts after pruning (21 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 093 | 15 | 1 108 |
| Fresh | 5 | 6 | 11 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 2 | 2 |
| Total | 1 101 | 25 | 1 126 |
| Status | Accuracy | Program |
|---|---|---|
| 99.6% | (fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))) | |
| ▶ | 96.8% | (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
| 98.4% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))) | |
| ✓ | 63.5% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 98.9% | (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))) | |
| 98.9% | (*.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64))) | |
| 99.1% | (*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps 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))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) | |
| ▶ | 98.9% | (*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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)) |
| 98.6% | (*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) | |
| 11.0% | (*.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 x (+.f64 x (+.f64 eps x))))))) (fma.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (-.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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)) | |
| 21.8% | (*.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 (+.f64 eps x) (/.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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)) | |
| 21.0% | (*.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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)) | |
| 21.3% | (*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (fma.f64 (*.f64 (neg.f64 x) x) x (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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)) | |
| 35.5% | (*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x)) (+.f64 x (+.f64 eps x))) #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)) | |
| ▶ | 21.1% | (*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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)) |
| 35.5% | (*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 (-.f64 x eps) x)) (/.f64 (*.f64 (-.f64 eps x) (-.f64 eps x)) (+.f64 (-.f64 x eps) x))) #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)) | |
| 63.6% | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) | |
| ▶ | 53.0% | (*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #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)) |
| ▶ | 100.0% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64)) |
| ✓ | 99.9% | (*.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)) |
| 30.7% | (*.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 eps eps)))) | |
| 98.7% | (*.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)))) | |
| 98.2% | (*.f64 eps (cos.f64 x)) | |
| ✓ | 96.8% | (sin.f64 eps) |
| ✓ | 5.5% | #s(literal 0 binary64) |
Compiled 1 420 to 650 computations (54.2% saved)
| 1× | egg-herbie |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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)) |
| ✓ | cost-diff | 256 | (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))) |
| ✓ | cost-diff | 320 | (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 1920 | (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #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)) |
| ✓ | cost-diff | 320 | (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 1344 | (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) |
| ✓ | cost-diff | 0 | (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
| ✓ | cost-diff | 128 | (*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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)) |
| ✓ | cost-diff | 0 | (*.f64 eps eps) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
| ✓ | cost-diff | 0 | (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) eps) |
| ✓ | 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)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) |
| ✓ | cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64)) |
| 15 314× | lower-fma.f32 |
| 15 300× | lower-fma.f64 |
| 5 238× | lower-*.f32 |
| 5 194× | lower-*.f64 |
| 2 718× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 52 | 669 |
| 0 | 102 | 586 |
| 1 | 200 | 574 |
| 2 | 494 | 547 |
| 3 | 1247 | 539 |
| 4 | 3313 | 482 |
| 5 | 5954 | 478 |
| 0 | 8434 | 468 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
eps |
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(cos.f64 x) |
x |
(*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)) |
(neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin.f64 x) |
#s(literal 2 binary64) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
eps |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
#s(literal -1/6 binary64) |
(*.f64 eps eps) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
eps |
(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) |
(*.f64 eps eps) |
(fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) |
(*.f64 eps #s(literal 1/3840 binary64)) |
#s(literal 1/3840 binary64) |
#s(literal -1/48 binary64) |
#s(literal 1/2 binary64) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
x |
#s(literal 2 binary64) |
(*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #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 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) |
(*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) |
(*.f64 eps eps) |
eps |
(/.f64 #s(literal 1 binary64) eps) |
#s(literal 1 binary64) |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal 2 binary64) |
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))) |
(*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64)) |
(-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) |
(/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) |
(*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) |
(+.f64 eps x) |
eps |
x |
(*.f64 (+.f64 eps x) (+.f64 eps x)) |
(fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))) |
(+.f64 x (+.f64 eps x)) |
(/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) |
(*.f64 x (*.f64 x x)) |
(*.f64 x x) |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 2 binary64) eps) |
#s(literal 2 binary64) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64)) |
(*.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (cos.f64 x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
eps |
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))) |
(-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(cos.f64 x) |
x |
(*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)) |
(neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) |
(neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) |
(sin.f64 x) |
#s(literal 2 binary64) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(fma.f64 eps (*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) eps) |
eps |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(*.f64 eps (*.f64 eps #s(literal -1/6 binary64))) |
#s(literal -1/6 binary64) |
(*.f64 eps eps) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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 (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (+.f64 eps eps))) |
(*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
eps |
(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) |
(*.f64 eps eps) |
(fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) |
(*.f64 eps #s(literal 1/3840 binary64)) |
#s(literal 1/3840 binary64) |
#s(literal -1/48 binary64) |
#s(literal 1/2 binary64) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
x |
#s(literal 2 binary64) |
(*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #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 (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)))) |
(*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 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 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) eps) |
(*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) |
eps |
(*.f64 eps eps) |
eps |
(/.f64 #s(literal 1 binary64) eps) |
#s(literal 1 binary64) |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(fma.f64 x #s(literal 2 binary64) eps) |
(+.f64 x (+.f64 eps x)) |
x |
#s(literal 2 binary64) |
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 #s(literal 2 binary64) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x))))))) |
(*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x)))))) |
(sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x))))) |
(*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps))) (-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x)))) |
(-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) |
(-.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (/.f64 (+.f64 eps x) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps))))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps)))) |
(/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) |
(*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (/.f64 (+.f64 eps x) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps))))) |
(*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) |
(+.f64 eps x) |
eps |
x |
(*.f64 (+.f64 eps x) (+.f64 eps x)) |
(fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))) |
(fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps)) |
(+.f64 x (+.f64 eps x)) |
(/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) |
(/.f64 (*.f64 x (*.f64 x x)) (fma.f64 #s(literal 3 binary64) (*.f64 x (+.f64 eps x)) (*.f64 eps eps))) |
(*.f64 x (*.f64 x x)) |
(*.f64 x x) |
#s(literal 1/2 binary64) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal 1/2 binary64) eps x) |
(fma.f64 x #s(literal 2 binary64) eps) |
(+.f64 x (+.f64 eps x)) |
#s(literal 2 binary64) |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.6% | (*.f64 (+.f64 eps x) (+.f64 eps x)) |
| ✓ | accuracy | 65.4% | (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) |
| ✓ | accuracy | 34.1% | (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) |
| ✓ | accuracy | 34.1% | (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) |
| ✓ | accuracy | 100.0% | (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 99.9% | (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 53.1% | (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) |
| ✓ | accuracy | 100.0% | (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 100.0% | (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
| ✓ | accuracy | 99.9% | (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
| ✓ | accuracy | 99.8% | (*.f64 eps #s(literal 1/3840 binary64)) |
| ✓ | accuracy | 100.0% | (*.f64 eps eps) |
| ✓ | accuracy | 100.0% | (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
| ✓ | accuracy | 99.7% | (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
| ✓ | accuracy | 100.0% | (cos.f64 x) |
| ✓ | accuracy | 100.0% | (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))) |
| ✓ | accuracy | 100.0% | (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) |
| ✓ | accuracy | 100.0% | (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)) |
| 108.0ms | 256× | 0 | valid |
Compiled 711 to 60 computations (91.6% saved)
ival-mult: 39.0ms (47.2% of total)ival-sin: 12.0ms (14.5% of total)ival-add: 9.0ms (10.9% of total)const: 9.0ms (10.9% of total)ival-cos: 6.0ms (7.3% of total)ival-div: 5.0ms (6.1% of total)ival-sub: 1.0ms (1.2% of total)ival-neg: 1.0ms (1.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64))> |
#<alt (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))))> |
#<alt (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))> |
#<alt (*.f64 #s(literal 1/2 binary64) eps)> |
#<alt (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps)> |
#<alt (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps))> |
#<alt (*.f64 eps eps)> |
#<alt (*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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))> |
#<alt (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))> |
#<alt (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))> |
#<alt (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))> |
#<alt (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))> |
#<alt (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))> |
#<alt (*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #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))> |
#<alt (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))> |
#<alt (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))> |
#<alt (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))> |
#<alt (*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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))> |
#<alt (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))> |
#<alt (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))> |
#<alt (cos.f64 x)> |
#<alt (*.f64 eps #s(literal 1/3840 binary64))> |
#<alt (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))> |
#<alt (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))> |
#<alt (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64)))> |
#<alt (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))> |
#<alt (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))> |
#<alt (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))> |
#<alt (*.f64 (+.f64 eps x) (+.f64 eps x))> |
| 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 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))> |
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))> |
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))> |
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))> |
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))> |
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))> |
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))> |
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 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 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))> |
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))> |
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))> |
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))> |
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))> |
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))> |
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))))> |
#<alt (* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 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 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 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 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))> |
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (sin (* 1/2 eps))> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt eps> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))> |
#<alt (* -1/6 (pow eps 3))> |
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (* -1/6 (pow eps 2))> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<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 (* 1/1920 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))> |
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/1920 (cos (+ x (* 1/2 eps))))))> |
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))> |
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))> |
#<alt (* 1/1920 (* (pow eps 5) (cos (- x (* -1/2 eps)))))> |
#<alt (* -1 (* (pow eps 5) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))> |
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))> |
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))> |
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))> |
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))> |
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))> |
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))> |
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))> |
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))> |
#<alt (* 1/2 (* eps (cos x)))> |
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))> |
#<alt (* 1/3840 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))> |
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#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))))> |
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))))> |
#<alt (* 1/3840 (* (pow eps 5) (cos (- x (* -1/2 eps)))))> |
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#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))> |
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))> |
#<alt (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))> |
#<alt (+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))> |
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))> |
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))> |
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))> |
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))> |
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))> |
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))> |
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#<alt (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))> |
#<alt (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))> |
#<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) (- (* 1/3840 (pow eps 2)) 1/48))))> |
#<alt (* 1/3840 (pow eps 5))> |
#<alt (* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))> |
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#<alt (* 1/3840 (pow eps 5))> |
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#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))> |
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))> |
#<alt 1/2> |
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#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))> |
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))> |
#<alt (* 1/3840 (pow eps 4))> |
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))> |
#<alt (* 1/3840 (pow eps 4))> |
#<alt (* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))> |
#<alt (* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 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 (+ 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 (cos x))> |
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))> |
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))> |
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))> |
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))> |
#<alt (* 1/2 (* eps (cos x)))> |
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))> |
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))> |
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (* 1/2 (* eps (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))))))))> |
#<alt (* eps (+ 1/2 (* eps (+ (* 1/2 (* eps (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))))) (* 1/2 (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))))> |
#<alt (* eps (+ 1/2 (* eps (+ (* 1/2 (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (+ (* 1/2 (* eps (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (+ (* 2 (/ x (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (+ (/ x (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (/ (* (+ x (* 2 x)) (- (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* 2 (pow x 2)) (pow x 2)))))))) (* 1/2 (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))))))))))> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* -1 (* eps (- (* -1/2 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1/2)))> |
#<alt (* -1 (* eps (- (* -1 (/ (+ (* -1/2 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 1/2 (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))) eps)) 1/2)))> |
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#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/6 (+ eps (* 2 eps)))> |
#<alt (+ (* 1/6 (+ eps (* 2 eps))) (* 1/2 (/ (- (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))) x)))> |
#<alt (+ (* 1/6 (+ eps (* 2 eps))) (+ (* 1/2 (/ (- (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (pow eps 3)))) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))) (pow x 2))) (* 1/2 (/ (- (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))) x))))> |
#<alt (+ (* 1/6 (+ eps (* 2 eps))) (+ (* 1/2 (/ (- (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ eps (* 2 eps))))))) (* -1/3 (* (pow eps 2) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))))) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))))) (pow x 3))) (+ (* 1/2 (/ (- (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (pow eps 3)))) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))) (pow x 2))) (* 1/2 (/ (- (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))) x)))))> |
#<alt (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))))> |
#<alt (+ (* -1/2 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))))> |
#<alt (+ (* -1 (/ (+ (* -1/2 (/ (- (* 1/3 (pow eps 3)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/2 (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))))) x)) (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))))> |
#<alt (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (- (* 1/3 (pow eps 3)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))))) (* 1/2 (/ (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps))))))) (+ (* -1/3 (* (pow eps 2) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))))))) x))) x)) (* 1/2 (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))))) x)) (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))))> |
#<alt (pow eps 2)> |
#<alt (+ (* x (+ eps (* 2 eps))) (pow eps 2))> |
#<alt (+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2))> |
#<alt (+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2))> |
#<alt (* 3 (pow x 2))> |
#<alt (* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (/ eps x))))> |
#<alt (* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))> |
#<alt (* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2))))))> |
#<alt (* 3 (pow x 2))> |
#<alt (* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (* -1 eps)) x))))> |
#<alt (* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x))))> |
#<alt (* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x))))> |
#<alt (+ (* 2 (pow x 2)) (pow x 2))> |
#<alt (+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2)))> |
#<alt (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))> |
#<alt (+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2)))> |
#<alt (pow eps 2)> |
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ x eps))))> |
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))> |
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))))> |
#<alt (pow eps 2)> |
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 x)) eps))))> |
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps))))> |
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps))))> |
#<alt (* eps (cos x))> |
#<alt (* eps (+ (cos x) (* 2 (* eps (+ (* -1/4 (sin x)) (* 1/2 (* (cos x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))))))> |
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#<alt (+ (* -1 (/ (+ (* -1 (/ (+ (* -2 (/ (* (cos (* 1/2 (- eps (* -2 x)))) (+ (* -1/4 (* (sin (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))))) (* (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (- (* 1/3 (pow eps 3)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))))))) (* (cos (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))))) (+ (* -1/2 (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps))))))) (+ (* -1/3 (* (pow eps 2) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))))))) (* -1/48 (pow (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) 3)))))) x)) (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (+ (* -1/8 (* (sin (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))))) (pow (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) 2))) (* 1/2 (* (cos (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))))) (- (* 1/3 (pow eps 3)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))))))))) x)) (* (cos (* 1/2 (- eps (* -2 x)))) (* (cos (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))))) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))))))) x)) (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))))))))> |
#<alt (* -1/2 (* eps (sin x)))> |
#<alt (* eps (+ (* -1/2 (sin x)) (* 1/48 (* (pow eps 2) (sin x)))))> |
#<alt (* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/3840 (* (pow eps 2) (sin x))) (* 1/48 (sin x))))))> |
#<alt (* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/48 (sin x)) (* (pow eps 2) (+ (* -1/3840 (sin x)) (* 1/645120 (* (pow eps 2) (sin x)))))))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* x (sin (* 1/2 eps))))> |
#<alt (* x (+ (* -1 (sin (* 1/2 eps))) (* 1/6 (* (pow x 2) (sin (* 1/2 eps))))))> |
#<alt (* x (+ (* -1 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/6 (sin (* 1/2 eps)))))))> |
#<alt (* x (+ (* -1 (sin (* 1/2 eps))) (* (pow x 2) (+ (* 1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/120 (sin (* 1/2 eps))) (* 1/5040 (* (pow x 2) (sin (* 1/2 eps))))))))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (* -1 (* (sin x) (sin (* 1/2 eps))))> |
#<alt (cos x)> |
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#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x))))))> |
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))))))> |
#<alt (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))> |
#<alt (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))> |
#<alt (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))> |
#<alt (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))> |
#<alt (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))> |
#<alt (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))> |
#<alt (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))> |
#<alt (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 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 (sin (* 1/2 eps))) (* -1/2 (* x (cos (* 1/2 eps)))))))> |
#<alt (+ (cos (* 1/2 eps)) (* x (+ (* -1 (sin (* 1/2 eps))) (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))))))> |
#<alt (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))> |
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#<alt (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))> |
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#<alt (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))> |
#<alt (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))> |
#<alt 1> |
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#<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 (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (* 1/3840 eps)> |
#<alt (cos x)> |
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#<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)))))> |
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#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (+ x (* 1/2 eps)))> |
#<alt (cos (- (* 1/2 eps) (* -1 x)))> |
#<alt (cos (- (* 1/2 eps) (* -1 x)))> |
#<alt (cos (- (* 1/2 eps) (* -1 x)))> |
#<alt (cos (- (* 1/2 eps) (* -1 x)))> |
#<alt (cos (* 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))))> |
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#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos (* 1/2 (- eps (* -2 x))))> |
#<alt (cos x)> |
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#<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))))> |
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#<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 (* 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 (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))> |
#<alt (+ (* eps (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))> |
#<alt (+ (* eps (- (+ 1 (* eps (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))> |
#<alt (+ (* eps (- (+ 1 (* eps (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* eps (- (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))> |
#<alt eps> |
#<alt (* eps (+ 1 (/ (pow x 3) (pow eps 3))))> |
#<alt (* eps (+ 1 (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow eps 4))) (/ (pow x 3) (pow eps 3)))))> |
#<alt (* eps (- (+ 1 (+ (* -1 (/ (+ (* -1 (* (pow x 3) (pow (+ x (* 2 x)) 2))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))) (pow eps 5))) (/ (pow x 3) (pow eps 3)))) (/ (* (pow x 3) (+ x (* 2 x))) (pow eps 4))))> |
#<alt eps> |
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (/ (- (pow x 3) (+ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* -1 (pow x 2)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))> |
#<alt eps> |
#<alt eps> |
#<alt (+ eps (/ (pow x 3) (pow eps 2)))> |
#<alt (+ eps (* (pow x 3) (+ (* -3 (/ x (pow eps 3))) (/ 1 (pow eps 2)))))> |
#<alt (* 1/3 x)> |
#<alt (* x (- (+ 1/3 (* 1/3 (/ (+ eps (* 2 eps)) x))) (* 1/9 (/ (+ eps (* 2 eps)) x))))> |
#<alt (* x (- (+ 1/3 (+ (* 1/3 (/ (+ eps (* 2 eps)) x)) (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow x 2))))) (+ (* 1/9 (/ (+ eps (* 2 eps)) x)) (+ (* 1/9 (/ (pow eps 2) (pow x 2))) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2)))))))> |
#<alt (* x (- (+ 1/3 (+ (* 1/3 (/ (+ eps (* 2 eps)) x)) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow x 2))) (* 1/3 (/ (pow eps 3) (pow x 3)))))) (+ (* 1/9 (/ (+ eps (* 2 eps)) x)) (+ (* 1/9 (/ (pow eps 2) (pow x 2))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 3))) (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 3)))))))))> |
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#<alt (+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))))) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))> |
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#<alt eps> |
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#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (pow x 2)) (+ (/ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) eps) (/ (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))) eps)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1)))> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt (* 1/3 (+ eps (* 2 eps)))> |
#<alt (- (+ (* -1/27 (/ (pow (+ eps (* 2 eps)) 2) x)) (+ (* 1/3 (+ eps (* 2 eps))) (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)))) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) x)))> |
#<alt (- (+ (* -1/3 (/ (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))) (pow x 2))) (+ (* -1/27 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* -1/27 (/ (pow (+ eps (* 2 eps)) 2) x)) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) x)) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 2))) (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2))))))> |
#<alt (- (+ (* -1/3 (/ (* (+ eps (* 2 eps)) (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ eps (* 2 eps)))))) (pow x 3))) (+ (* -1/3 (/ (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))) (pow x 2))) (+ (* -1/3 (/ (* (pow eps 2) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))) (pow x 3))) (+ (* -1/27 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* -1/27 (/ (pow (+ eps (* 2 eps)) 2) x)) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))))))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) x)) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 2))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 3))) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2))) (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 3))))))))> |
#<alt (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))> |
#<alt (- (+ (* -1 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))> |
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#<alt (- (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))))) x)) (+ (* -1/3 (/ (* (pow eps 2) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2)))) x)) (+ (* 1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))) x)) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (pow eps 3)))))) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))> |
#<alt (pow x 2)> |
#<alt (+ (* 2 (* eps x)) (pow x 2))> |
#<alt (+ (* eps (+ eps (* 2 x))) (pow x 2))> |
#<alt (+ (* eps (+ eps (* 2 x))) (pow x 2))> |
#<alt (pow eps 2)> |
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))> |
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))> |
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))> |
#<alt (pow eps 2)> |
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))> |
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))> |
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))> |
#<alt (pow eps 2)> |
#<alt (+ (* 2 (* eps x)) (pow eps 2))> |
#<alt (+ (* x (+ x (* 2 eps))) (pow eps 2))> |
#<alt (+ (* x (+ x (* 2 eps))) (pow eps 2))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* 2 (/ eps x))))> |
#<alt (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* 2 (/ eps x))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))> |
141 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 25.0ms | x | @ | inf | (* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (+ (* 1/2 eps) x))) |
| 23.0ms | x | @ | 0 | (* (- (/ (* (+ eps x) (* (+ eps x) (+ eps x))) (+ (* x (+ x (+ eps x))) (* (+ eps x) (+ eps x)))) (/ (* x (* x x)) (+ (* x (+ x (+ eps x))) (* (+ eps x) (+ eps x))))) 1/2) |
| 9.0ms | eps | @ | inf | (* (- (/ (* (+ eps x) (* (+ eps x) (+ eps x))) (+ (* x (+ x (+ eps x))) (* (+ eps x) (+ eps x)))) (/ (* x (* x x)) (+ (* x (+ x (+ eps x))) (* (+ eps x) (+ eps x))))) 1/2) |
| 6.0ms | x | @ | inf | (* (* (sin (* 1/2 eps)) (+ (* (cos (* 1/2 eps)) (cos x)) (* (neg (sin (* 1/2 eps))) (sin x)))) 2) |
| 5.0ms | eps | @ | 0 | (- (/ (* (+ eps x) (* (+ eps x) (+ eps x))) (+ (* x (+ x (+ eps x))) (* (+ eps x) (+ eps x)))) (/ (* x (* x x)) (+ (* x (+ x (+ eps x))) (* (+ eps x) (+ eps x))))) |
| 1× | batch-egg-rewrite |
| 7 394× | lower-fma.f32 |
| 7 380× | lower-fma.f64 |
| 5 278× | lower-*.f32 |
| 5 234× | lower-*.f64 |
| 4 654× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 52 | 453 |
| 0 | 102 | 360 |
| 1 | 356 | 307 |
| 2 | 2834 | 307 |
| 0 | 10220 | 306 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 #s(literal 1/2 binary64) eps) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) |
(*.f64 eps eps) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) |
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #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 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) |
(*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64)) |
(fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (neg.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 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x))) |
(cos.f64 x) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) |
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) |
(/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) |
(-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) |
(*.f64 (+.f64 eps x) (+.f64 eps x)) |
| Outputs |
|---|
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))) |
(+.f64 (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64))) |
(fma.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64))) |
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64)))))) |
(*.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)))) |
(*.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 (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 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (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 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) |
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 2 binary64)) (-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.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)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal 2 binary64)) (-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))))) |
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) |
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) |
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) |
(fma.f64 (cos.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) |
(fma.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) |
(fma.f64 (sin.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) |
(fma.f64 (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) |
(fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) |
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))) |
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(*.f64 (/.f64 (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 (*.f64 x (+.f64 eps (+.f64 x x))) (*.f64 x (*.f64 (+.f64 eps (+.f64 x x)) (*.f64 x (+.f64 eps (+.f64 x x))))) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) (/.f64 (-.f64 (+.f64 eps x) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 (+.f64 eps (+.f64 x x)) (*.f64 x (+.f64 eps (+.f64 x x)))) (*.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x (+.f64 eps (+.f64 x x))))))))) |
(*.f64 (/.f64 (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))) (-.f64 (*.f64 x (+.f64 eps (+.f64 x x))) (*.f64 (+.f64 eps x) (+.f64 eps x))))) (/.f64 (-.f64 (+.f64 eps x) x) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (+.f64 eps (+.f64 x x))) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) |
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (+.f64 eps x)))) |
(+.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (+.f64 eps x))) |
(+.f64 (*.f64 eps (+.f64 eps x)) (*.f64 x (+.f64 eps x))) |
(-.f64 (/.f64 (*.f64 (*.f64 eps (+.f64 eps x)) (*.f64 eps (+.f64 eps x))) (-.f64 (*.f64 eps (+.f64 eps x)) (*.f64 x (+.f64 eps x)))) (/.f64 (*.f64 (*.f64 x x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (-.f64 (*.f64 eps (+.f64 eps x)) (*.f64 x (+.f64 eps x))))) |
(fma.f64 eps (+.f64 eps x) (*.f64 x (+.f64 eps x))) |
(fma.f64 x (+.f64 eps x) (*.f64 eps (+.f64 eps x))) |
(fma.f64 (+.f64 eps x) eps (*.f64 x (+.f64 eps x))) |
(fma.f64 (+.f64 eps x) x (*.f64 eps (+.f64 eps x))) |
(/.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))) |
(/.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 eps x) (-.f64 eps x))) (*.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) (-.f64 eps x))) |
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x)))) (*.f64 (-.f64 eps x) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))) |
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (*.f64 (+.f64 eps x) (-.f64 eps x))) (*.f64 (-.f64 eps x) (-.f64 eps x))) |
(/.f64 (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x)))) (fma.f64 (*.f64 eps (+.f64 eps x)) (*.f64 eps (+.f64 eps x)) (-.f64 (*.f64 (*.f64 x x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 eps (+.f64 eps x)) (*.f64 x (+.f64 eps x)))))) |
(/.f64 (-.f64 (*.f64 (*.f64 eps (+.f64 eps x)) (*.f64 eps (+.f64 eps x))) (*.f64 (*.f64 x x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (-.f64 (*.f64 eps (+.f64 eps x)) (*.f64 x (+.f64 eps x)))) |
(/.f64 (*.f64 (+.f64 eps x) (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x)))) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))) |
(/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) (-.f64 eps x)) |
(/.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (+.f64 eps x)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))) |
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (+.f64 eps x)) (-.f64 eps x)) |
(/.f64 (neg.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))))) (neg.f64 (*.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 eps x) (-.f64 eps x)))) (neg.f64 (*.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) (-.f64 eps x)))) |
(/.f64 (neg.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))))) (neg.f64 (*.f64 (-.f64 eps x) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))) |
(/.f64 (neg.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (*.f64 (+.f64 eps x) (-.f64 eps x)))) (neg.f64 (*.f64 (-.f64 eps x) (-.f64 eps x)))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x))))) (neg.f64 (fma.f64 (*.f64 eps (+.f64 eps x)) (*.f64 eps (+.f64 eps x)) (-.f64 (*.f64 (*.f64 x x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 eps (+.f64 eps x)) (*.f64 x (+.f64 eps x))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 eps (+.f64 eps x)) (*.f64 eps (+.f64 eps x))) (*.f64 (*.f64 x x) (*.f64 (+.f64 eps x) (+.f64 eps x))))) (neg.f64 (-.f64 (*.f64 eps (+.f64 eps x)) (*.f64 x (+.f64 eps x))))) |
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))))) (neg.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))) |
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x)))) (neg.f64 (-.f64 eps x))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (+.f64 eps x))) (neg.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))) |
(/.f64 (neg.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (+.f64 eps x))) (neg.f64 (-.f64 eps x))) |
(/.f64 (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 x (*.f64 x x)) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 eps (*.f64 eps eps)))) (fma.f64 (*.f64 x x) (*.f64 (+.f64 eps x) (+.f64 eps x)) (-.f64 (*.f64 (*.f64 eps (+.f64 eps x)) (*.f64 eps (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 eps x)) (*.f64 eps (+.f64 eps x)))))) |
(pow.f64 (+.f64 eps x) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 (log.f64 (+.f64 eps x))) #s(literal 2 binary64)) |
(*.f64 (+.f64 eps x) (+.f64 eps x)) |
(*.f64 (*.f64 (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x))) (fma.f64 eps (*.f64 eps eps) (*.f64 x (*.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))) #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (*.f64 (+.f64 eps x) (-.f64 eps x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps x)) #s(literal 2 binary64))) |
(*.f64 (exp.f64 (log.f64 (+.f64 eps x))) (exp.f64 (log.f64 (+.f64 eps x)))) |
| 1× | egg-herbie |
| 10 464× | lower-fma.f64 |
| 10 464× | lower-fma.f32 |
| 6 204× | lower-+.f64 |
| 6 204× | lower-+.f32 |
| 5 248× | lower-*.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1240 | 15067 |
| 1 | 4206 | 14389 |
| 0 | 8325 | 13528 |
| 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 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 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 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 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)))))))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 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)))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* -1/6 (pow eps 3)) |
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)) |
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)) |
(* -1/6 (pow eps 3)) |
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))) |
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))) |
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(* -1/6 (pow eps 2)) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(* 1/1920 (* (pow eps 5) (cos (+ x (* 1/2 eps))))) |
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/1920 (cos (+ x (* 1/2 eps)))))) |
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))) |
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))) |
(* 1/1920 (* (pow eps 5) (cos (- x (* -1/2 eps))))) |
(* -1 (* (pow eps 5) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))) |
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))) |
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))) |
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))))) |
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(* 1/3840 (* (pow eps 5) (cos (+ x (* 1/2 eps))))) |
(* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/3840 (cos (+ x (* 1/2 eps)))))) |
(* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))) |
(* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))) |
(* 1/3840 (* (pow eps 5) (cos (- x (* -1/2 eps))))) |
(* -1 (* (pow eps 5) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))) |
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))) |
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))) |
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) |
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))))) |
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))))))) |
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) |
(* 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) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* 1/3840 (pow eps 5)) |
(* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2))))) |
(* 1/3840 (pow eps 5)) |
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840))) |
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4)))))) |
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4)))))) |
1/2 |
(+ 1/2 (* -1/48 (pow eps 2))) |
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))) |
(+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))) |
(* 1/3840 (pow eps 4)) |
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2))))) |
(* 1/3840 (pow eps 4)) |
(* (pow eps 4) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 4) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2))))) |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
(* 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 (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))) |
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2)))))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 1/2 (* eps (cos x))) |
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))) |
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* 1/2 (* eps (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))) |
(* eps (+ 1/2 (* eps (+ (* 1/2 (* eps (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))))) (* 1/2 (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))))))))) |
(* eps (+ 1/2 (* eps (+ (* 1/2 (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (+ (* 1/2 (* eps (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (+ (* 2 (/ x (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (+ (/ x (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (/ (* (+ x (* 2 x)) (- (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* 2 (pow x 2)) (pow x 2)))))))) (* 1/2 (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))))))))) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* -1 (* eps (- (* -1/2 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ (+ (* -1/2 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 1/2 (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))) eps)) 1/2))) |
(* -1 (* eps (- (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) (* 1/2 (/ (+ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))) eps))) eps)) (* 1/2 (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))) eps)) 1/2))) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/6 (+ eps (* 2 eps))) |
(+ (* 1/6 (+ eps (* 2 eps))) (* 1/2 (/ (- (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))) x))) |
(+ (* 1/6 (+ eps (* 2 eps))) (+ (* 1/2 (/ (- (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (pow eps 3)))) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))) (pow x 2))) (* 1/2 (/ (- (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))) x)))) |
(+ (* 1/6 (+ eps (* 2 eps))) (+ (* 1/2 (/ (- (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ eps (* 2 eps))))))) (* -1/3 (* (pow eps 2) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))))) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))))) (pow x 3))) (+ (* 1/2 (/ (- (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (pow eps 3)))) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))) (pow x 2))) (* 1/2 (/ (- (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))) x))))) |
(* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps)))))) |
(+ (* -1/2 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))))) |
(+ (* -1 (/ (+ (* -1/2 (/ (- (* 1/3 (pow eps 3)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/2 (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))))) x)) (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))))) |
(+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (- (* 1/3 (pow eps 3)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))))) (* 1/2 (/ (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps))))))) (+ (* -1/3 (* (pow eps 2) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))))))) x))) x)) (* 1/2 (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))))) x)) (* 1/2 (- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))))) |
(pow eps 2) |
(+ (* x (+ eps (* 2 eps))) (pow eps 2)) |
(+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2)) |
(+ (* x (+ eps (+ (* 2 eps) (* 3 x)))) (pow eps 2)) |
(* 3 (pow x 2)) |
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (/ eps x)))) |
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2)))))) |
(* (pow x 2) (+ 3 (+ (* 2 (/ eps x)) (+ (/ eps x) (/ (pow eps 2) (pow x 2)))))) |
(* 3 (pow x 2)) |
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (* -1 eps)) x)))) |
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x)))) |
(* (pow x 2) (+ 3 (* -1 (/ (+ (* -2 eps) (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))) x)))) |
(+ (* 2 (pow x 2)) (pow x 2)) |
(+ (* 2 (pow x 2)) (+ (* eps (+ x (* 2 x))) (pow x 2))) |
(+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))) |
(+ (* 2 (pow x 2)) (+ (* eps (+ eps (+ x (* 2 x)))) (pow x 2))) |
(pow eps 2) |
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ x eps)))) |
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) |
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (/ x eps) (/ (pow x 2) (pow eps 2))))))) |
(pow eps 2) |
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 x)) eps)))) |
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps)))) |
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps)))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* 2 (* eps (+ (* -1/4 (sin x)) (* 1/2 (* (cos x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))))))))))) |
(* eps (+ (cos x) (* eps (+ (* 2 (* eps (+ (* -1/4 (* (sin x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))) (+ (* -1/16 (cos x)) (* (cos x) (- (* 1/2 (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) 1/48)))))) (* 2 (+ (* -1/4 (sin x)) (* 1/2 (* (cos x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))))))) |
(* eps (+ (cos x) (* eps (+ (* 2 (+ (* -1/4 (sin x)) (* 1/2 (* (cos x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))) (* eps (+ (* 2 (* eps (+ (* -1/2 (* (sin x) (- (* 1/2 (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) 1/48))) (+ (* -1/16 (* (cos x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))) (+ (* 1/96 (sin x)) (* (cos x) (+ (* -1/16 (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))))) (* 1/2 (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (+ (* 2 (/ x (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (+ (/ x (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (/ (* (+ x (* 2 x)) (- (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* 2 (pow x 2)) (pow x 2)))))))))))))) (* 2 (+ (* -1/4 (* (sin x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))) (+ (* -1/16 (cos x)) (* (cos x) (- (* 1/2 (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) 1/48))))))))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow (+ eps x) 3) (+ (* x (+ eps (* 2 x))) (pow (+ eps x) 2))) (/ (pow x 3) (+ (* x (+ eps (* 2 x))) (pow (+ eps x) 2)))))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow (+ eps x) 3) (+ (* x (+ eps (* 2 x))) (pow (+ eps x) 2))) (/ (pow x 3) (+ (* x (+ eps (* 2 x))) (pow (+ eps x) 2)))))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow (+ eps x) 3) (+ (* x (+ eps (* 2 x))) (pow (+ eps x) 2))) (/ (pow x 3) (+ (* x (+ eps (* 2 x))) (pow (+ eps x) 2)))))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow (+ eps x) 3) (+ (* x (+ eps (* 2 x))) (pow (+ eps x) 2))) (/ (pow x 3) (+ (* x (+ eps (* 2 x))) (pow (+ eps x) 2)))))))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow (- x (* -1 eps)) 3) (+ (* x (- (* 2 x) (* -1 eps))) (pow (- x (* -1 eps)) 2))) (/ (pow x 3) (+ (* x (- (* 2 x) (* -1 eps))) (pow (- x (* -1 eps)) 2)))))))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow (- x (* -1 eps)) 3) (+ (* x (- (* 2 x) (* -1 eps))) (pow (- x (* -1 eps)) 2))) (/ (pow x 3) (+ (* x (- (* 2 x) (* -1 eps))) (pow (- x (* -1 eps)) 2)))))))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow (- x (* -1 eps)) 3) (+ (* x (- (* 2 x) (* -1 eps))) (pow (- x (* -1 eps)) 2))) (/ (pow x 3) (+ (* x (- (* 2 x) (* -1 eps))) (pow (- x (* -1 eps)) 2)))))))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 (- (/ (pow (- x (* -1 eps)) 3) (+ (* x (- (* 2 x) (* -1 eps))) (pow (- x (* -1 eps)) 2))) (/ (pow x 3) (+ (* x (- (* 2 x) (* -1 eps))) (pow (- x (* -1 eps)) 2)))))))) |
(* 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 (* 1/6 (+ eps (* 2 eps)))))) |
(+ (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/6 (+ eps (* 2 eps)))))) (/ (* (cos (* 1/6 (+ eps (* 2 eps)))) (* (cos (* 1/2 (+ eps (* 2 x)))) (- (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) x)) |
(+ (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/6 (+ eps (* 2 eps)))))) (+ (* 2 (/ (* (cos (* 1/2 (+ eps (* 2 x)))) (+ (* -1/8 (* (sin (* 1/6 (+ eps (* 2 eps)))) (pow (- (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))) 2))) (* 1/2 (* (cos (* 1/6 (+ eps (* 2 eps)))) (- (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ eps (* 2 eps)))) (* 1/3 (pow eps 3)))) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))))) (pow x 2))) (/ (* (cos (* 1/6 (+ eps (* 2 eps)))) (* (cos (* 1/2 (+ eps (* 2 x)))) (- (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2)))) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) x))) |
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(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (* 1/48 (* (pow eps 2) (sin x))))) |
(* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/3840 (* (pow eps 2) (sin x))) (* 1/48 (sin x)))))) |
(* eps (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/48 (sin x)) (* (pow eps 2) (+ (* -1/3840 (sin x)) (* 1/645120 (* (pow eps 2) (sin x))))))))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* x (sin (* 1/2 eps)))) |
(* x (+ (* -1 (sin (* 1/2 eps))) (* 1/6 (* (pow x 2) (sin (* 1/2 eps)))))) |
(* x (+ (* -1 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/120 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/6 (sin (* 1/2 eps))))))) |
(* x (+ (* -1 (sin (* 1/2 eps))) (* (pow x 2) (+ (* 1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/120 (sin (* 1/2 eps))) (* 1/5040 (* (pow x 2) (sin (* 1/2 eps)))))))))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(* -1 (* (sin x) (sin (* 1/2 eps)))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))) |
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))) |
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
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(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
(cos (* 1/2 eps)) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
(+ (cos (* 1/2 eps)) (* x (+ (* -1 (sin (* 1/2 eps))) (* -1/2 (* x (cos (* 1/2 eps))))))) |
(+ (cos (* 1/2 eps)) (* x (+ (* -1 (sin (* 1/2 eps))) (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps))))))))) |
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
(+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 eps) |
(* 1/3840 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))))) |
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(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (+ x (* 1/2 eps))) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos (* 1/2 eps)) |
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps))))) |
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(+ (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)))) |
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(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)))) |
(* 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)) |
(/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))) |
(+ (* eps (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))) |
(+ (* eps (- (+ 1 (* eps (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))) |
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eps |
(* eps (+ 1 (/ (pow x 3) (pow eps 3)))) |
(* eps (+ 1 (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow eps 4))) (/ (pow x 3) (pow eps 3))))) |
(* eps (- (+ 1 (+ (* -1 (/ (+ (* -1 (* (pow x 3) (pow (+ x (* 2 x)) 2))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))) (pow eps 5))) (/ (pow x 3) (pow eps 3)))) (/ (* (pow x 3) (+ x (* 2 x))) (pow eps 4)))) |
eps |
(* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (/ (- (pow x 3) (+ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* -1 (pow x 2)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
eps |
eps |
(+ eps (/ (pow x 3) (pow eps 2))) |
(+ eps (* (pow x 3) (+ (* -3 (/ x (pow eps 3))) (/ 1 (pow eps 2))))) |
(* 1/3 x) |
(* x (- (+ 1/3 (* 1/3 (/ (+ eps (* 2 eps)) x))) (* 1/9 (/ (+ eps (* 2 eps)) x)))) |
(* x (- (+ 1/3 (+ (* 1/3 (/ (+ eps (* 2 eps)) x)) (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow x 2))))) (+ (* 1/9 (/ (+ eps (* 2 eps)) x)) (+ (* 1/9 (/ (pow eps 2) (pow x 2))) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2))))))) |
(* x (- (+ 1/3 (+ (* 1/3 (/ (+ eps (* 2 eps)) x)) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (pow x 2))) (* 1/3 (/ (pow eps 3) (pow x 3)))))) (+ (* 1/9 (/ (+ eps (* 2 eps)) x)) (+ (* 1/9 (/ (pow eps 2) (pow x 2))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 3))) (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 3))))))))) |
(* 1/3 x) |
(* -1 (* x (- (* -1 (/ (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))) x)) 1/3))) |
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (* -1/9 (+ (* -2 eps) (* -1 eps)))) x)) 1/3))) |
(* -1 (* x (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (* -1/9 (+ (* -2 eps) (* -1 eps)))) x)) 1/3))) |
(/ (pow x 3) (pow eps 2)) |
(* (pow x 3) (+ (* -3 (/ x (pow eps 3))) (/ 1 (pow eps 2)))) |
(* (pow x 3) (+ (* x (- (* -1 (* x (+ (* -3 (/ (+ eps (* 2 eps)) (pow eps 5))) (* 3 (/ 1 (pow eps 4)))))) (* 3 (/ 1 (pow eps 3))))) (/ 1 (pow eps 2)))) |
(* (pow x 3) (+ (* x (- (* x (- (* x (- (* 9 (/ 1 (pow eps 5))) (* -1 (/ (* (+ eps (* 2 eps)) (+ (* -3 (/ (+ eps (* 2 eps)) (pow eps 5))) (* 3 (/ 1 (pow eps 4))))) (pow eps 2))))) (+ (* -3 (/ (+ eps (* 2 eps)) (pow eps 5))) (* 3 (/ 1 (pow eps 4)))))) (* 3 (/ 1 (pow eps 3))))) (/ 1 (pow eps 2)))) |
(* 1/3 x) |
(* x (+ 1/3 (* -1/9 (/ (+ eps (* 2 eps)) x)))) |
(* x (- (+ 1/3 (* -1 (/ (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))) (pow x 2)))) (* 1/9 (/ (+ eps (* 2 eps)) x)))) |
(* x (- (+ 1/3 (* -1 (/ (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ eps (* 2 eps))))) (pow x 3)))) (+ (* -1/27 (/ (pow (+ eps (* 2 eps)) 2) (pow x 2))) (+ (* 1/9 (/ (+ eps (* 2 eps)) x)) (* 1/9 (/ (pow eps 2) (pow x 2))))))) |
(* 1/3 x) |
(* -1 (* x (- (* -1/9 (/ (+ (* -2 eps) (* -1 eps)) x)) 1/3))) |
(* -1 (* x (- (* -1 (/ (- (+ (* -1/9 (/ (pow eps 2) x)) (* 1/27 (/ (pow (+ (* -2 eps) (* -1 eps)) 2) x))) (* -1/9 (+ (* -2 eps) (* -1 eps)))) x)) 1/3))) |
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/9 (pow eps 2)) (* 1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)))) x)) (* 1/27 (/ (* (pow eps 2) (+ (* -2 eps) (* -1 eps))) x))) (+ (* -1/9 (pow eps 2)) (* 1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)))) x)) (* -1/9 (+ (* -2 eps) (* -1 eps)))) x)) 1/3))) |
(/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))) |
(+ (* -1 (/ (* eps (* (pow x 3) (+ x (* 2 x)))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))) |
(+ (* eps (- (* -1 (* eps (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))) |
(+ (* eps (- (* eps (- (* -1 (* eps (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))))) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))) |
(/ (pow x 3) (pow eps 2)) |
(/ (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) eps)) (pow x 3)) (pow eps 2)) |
(/ (- (+ (* -1 (/ (+ (* -1 (* (pow x 3) (pow (+ x (* 2 x)) 2))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))) (pow eps 2))) (pow x 3)) (/ (* (pow x 3) (+ x (* 2 x))) eps)) (pow eps 2)) |
(/ (- (+ (* -1 (/ (+ (* -1 (* (+ x (* 2 x)) (+ (* -1 (* (pow x 3) (pow (+ x (* 2 x)) 2))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))))) (* -1 (* (pow x 3) (* (+ x (* 2 x)) (+ (* 2 (pow x 2)) (pow x 2)))))) (pow eps 3))) (pow x 3)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow eps 2))) (+ (/ (* (pow x 3) (+ x (* 2 x))) eps) (/ (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))) (pow eps 2))))) (pow eps 2)) |
(/ (pow x 3) (pow eps 2)) |
(/ (+ (/ (* (pow x 3) (+ (* -2 x) (* -1 x))) eps) (pow x 3)) (pow eps 2)) |
(/ (+ (* -1 (/ (- (+ (* -1 (/ (* (pow x 3) (pow (+ (* -2 x) (* -1 x)) 2)) eps)) (/ (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))) eps)) (* (pow x 3) (+ (* -2 x) (* -1 x)))) eps)) (pow x 3)) (pow eps 2)) |
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (+ (* -2 x) (* -1 x)) (+ (* -1 (* (pow x 3) (pow (+ (* -2 x) (* -1 x)) 2))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) eps)) (* -1 (/ (* (pow x 3) (* (+ (* -2 x) (* -1 x)) (+ (* 2 (pow x 2)) (pow x 2)))) eps))) (+ (* -1 (* (pow x 3) (pow (+ (* -2 x) (* -1 x)) 2))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) eps)) (* (pow x 3) (+ (* -2 x) (* -1 x)))) eps)) (pow x 3)) (pow eps 2)) |
eps |
(* eps (+ 1 (* eps (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))))))) |
(* eps (+ 1 (* eps (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* eps (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))))))) |
(* eps (+ 1 (* eps (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* eps (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* eps (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (+ (* 2 (/ x (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (+ (/ x (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (/ (* (+ x (* 2 x)) (- (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* 2 (pow x 2)) (pow x 2))))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))))))) |
eps |
eps |
eps |
eps |
eps |
(* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (pow x 2)) (+ (/ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) eps) (/ (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))) eps)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
eps |
eps |
eps |
eps |
(* 1/3 (+ eps (* 2 eps))) |
(- (+ (* -1/27 (/ (pow (+ eps (* 2 eps)) 2) x)) (+ (* 1/3 (+ eps (* 2 eps))) (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)))) (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) x))) |
(- (+ (* -1/3 (/ (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))) (pow x 2))) (+ (* -1/27 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* -1/27 (/ (pow (+ eps (* 2 eps)) 2) x)) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) x)) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 2))) (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2)))))) |
(- (+ (* -1/3 (/ (* (+ eps (* 2 eps)) (+ (* -1/3 (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ eps (* 2 eps)))))) (pow x 3))) (+ (* -1/3 (/ (* (+ eps (* 2 eps)) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))) (pow x 2))) (+ (* -1/3 (/ (* (pow eps 2) (+ (* -1/27 (pow (+ eps (* 2 eps)) 2)) (* 1/9 (pow eps 2)))) (pow x 3))) (+ (* -1/27 (/ (* (pow eps 2) (+ eps (* 2 eps))) (pow x 2))) (+ (* -1/27 (/ (pow (+ eps (* 2 eps)) 2) x)) (+ (* 1/3 (+ eps (* 2 eps))) (+ (* 1/3 (/ (+ (* 2 (pow eps 2)) (pow eps 2)) x)) (* 1/3 (/ (pow eps 3) (pow x 2)))))))))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) x)) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 2))) (+ (* 1/3 (/ (* (+ eps (* 2 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 3))) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))) (pow x 2))) (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* 2 (pow eps 2)) (pow eps 2))) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ eps (* 2 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* 1/9 (+ eps (* 2 eps))))))))) (pow x 3)))))))) |
(- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))) |
(- (+ (* -1 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))) |
(- (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (pow eps 3)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))) |
(- (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))))) x)) (+ (* -1/3 (/ (* (pow eps 2) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2)))) x)) (+ (* 1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))) x)) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (pow eps 3)))))) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))) |
(pow x 2) |
(+ (* 2 (* eps x)) (pow x 2)) |
(+ (* eps (+ eps (* 2 x))) (pow x 2)) |
(+ (* eps (+ eps (* 2 x))) (pow x 2)) |
(pow eps 2) |
(* (pow eps 2) (+ 1 (* 2 (/ x eps)))) |
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))) |
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))) |
(pow eps 2) |
(* (pow eps 2) (+ 1 (* 2 (/ x eps)))) |
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps)))) |
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps)))) |
(pow eps 2) |
(+ (* 2 (* eps x)) (pow eps 2)) |
(+ (* x (+ x (* 2 eps))) (pow eps 2)) |
(+ (* x (+ x (* 2 eps))) (pow eps 2)) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 2 (/ eps x)))) |
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2))))) |
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* 2 (/ eps x)))) |
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x)))) |
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) 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 (*.f64 eps #s(literal 2 binary64)) (*.f64 (cos.f64 x) #s(literal -1/12 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 eps (fma.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/24 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 x) #s(literal -1/12 binary64)))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.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))))) |
(fma.f64 #s(literal -2 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 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 x (fma.f64 x (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 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)) (* 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 (fma.f64 (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal 1/3 binary64) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 2 (* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps)))))) |
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* 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 (*.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 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 (*.f64 eps (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)))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(-.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(fma.f64 x (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (neg.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+ (* 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 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 #s(literal 1/6 binary64) x) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(* (sin (* 1/2 eps)) (+ (* -1 (* (sin x) (sin (* 1/2 eps)))) (* (cos x) (cos (* 1/2 eps))))) |
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1/2 |
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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)) |
(* 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 eps #s(literal 1/2 binary64)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 (+.f64 (/.f64 x (neg.f64 eps)) #s(literal -1/2 binary64)) (neg.f64 eps)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 (+.f64 (/.f64 x (neg.f64 eps)) #s(literal -1/2 binary64)) (neg.f64 eps)) |
(* -1 (* eps (- (* -1 (/ x eps)) 1/2))) |
(*.f64 (+.f64 (/.f64 x (neg.f64 eps)) #s(literal -1/2 binary64)) (neg.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)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))) |
(*.f64 eps (fma.f64 eps (fma.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (cos.f64 x) #s(literal -1/12 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 eps (fma.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/24 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 x) #s(literal -1/12 binary64)))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.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))))) |
(fma.f64 #s(literal -2 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 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 x (fma.f64 x (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 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)) (* 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 (fma.f64 (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) #s(literal 1/3 binary64) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (sin.f64 (*.f64 eps #s(literal 1/2 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 (*.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 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 (*.f64 eps (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 (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 eps)) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(-.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) |
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) |
(fma.f64 x (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (neg.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(+ (* 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 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (*.f64 #s(literal 1/6 binary64) x) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* eps (+ 1/2 (* 1/2 (* eps (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))) |
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(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 x)) eps)))) |
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 3 binary64)) eps))) |
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps)))) |
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal -3 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -3 binary64)) eps)) eps))) |
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (+ (* -1 x) (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps)))) eps)))) |
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal -3 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -3 binary64)) eps)) eps))) |
(* eps (cos x)) |
(*.f64 eps (cos.f64 x)) |
(* eps (+ (cos x) (* 2 (* eps (+ (* -1/4 (sin x)) (* 1/2 (* (cos x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))))))))))) |
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(* eps (+ (cos x) (* eps (+ (* 2 (* eps (+ (* -1/4 (* (sin x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))) (+ (* -1/16 (cos x)) (* (cos x) (- (* 1/2 (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) 1/48)))))) (* 2 (+ (* -1/4 (sin x)) (* 1/2 (* (cos x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))))))) |
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(* eps (+ (cos x) (* eps (+ (* 2 (+ (* -1/4 (sin x)) (* 1/2 (* (cos x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))))) (* eps (+ (* 2 (* eps (+ (* -1/2 (* (sin x) (- (* 1/2 (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) 1/48))) (+ (* -1/16 (* (cos x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))) (+ (* 1/96 (sin x)) (* (cos x) (+ (* -1/16 (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))))) (* 1/2 (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))))) (+ (* 2 (/ x (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))) (+ (/ x (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (/ (* (+ x (* 2 x)) (- (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* 2 (pow x 2)) (pow x 2)))))))))))))) (* 2 (+ (* -1/4 (* (sin x) (- (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))))) (+ (* -1/16 (cos x)) (* (cos x) (- (* 1/2 (- (+ (* -1 (/ (* (+ x (* 2 x)) (+ (* -1 (/ (* (pow x 3) (pow (+ x (* 2 x)) 2)) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)))) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) 1/48))))))))))) |
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(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow (+ eps x) 3) (+ (* x (+ eps (* 2 x))) (pow (+ eps x) 2))) (/ (pow x 3) (+ (* x (+ eps (* 2 x))) (pow (+ eps x) 2)))))))) |
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(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 (- (/ (pow (+ eps x) 3) (+ (* x (+ eps (* 2 x))) (pow (+ eps x) 2))) (/ (pow x 3) (+ (* x (+ eps (* 2 x))) (pow (+ eps x) 2)))))))) |
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1 |
#s(literal 1 binary64) |
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(+ 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) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 binary64)) |
(* 1/3840 eps) |
(*.f64 eps #s(literal 1/3840 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) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x))))) |
(fma.f64 eps (fma.f64 (*.f64 eps (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 (fma.f64 (cos.f64 x) #s(literal -1/8 binary64) (*.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/48 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)) |
(cos (+ x (* 1/2 eps))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (+ x (* 1/2 eps))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (+ x (* 1/2 eps))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (+ x (* 1/2 eps))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
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(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (- x (* -1/2 eps))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (- x (* -1/2 eps))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (- x (* -1/2 eps))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(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))) (neg.f64 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))))) |
(fma.f64 x (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/6 binary64) x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (neg.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (+ x (* 1/2 eps))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (+ x (* 1/2 eps))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (+ x (* 1/2 eps))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (+ x (* 1/2 eps))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(cos (- (* 1/2 eps) (* -1 x))) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(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))) (neg.f64 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))))) |
(fma.f64 x (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps))))) |
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 #s(literal 1/6 binary64) x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (neg.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(cos (* 1/2 (- eps (* -2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(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 (*.f64 eps (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 (fma.f64 (cos.f64 x) #s(literal -1/8 binary64) (*.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/48 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(cos (* 1/2 (+ eps (* 2 x)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(cos (* 1/2 (- (* 2 x) (* -1 eps)))) |
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(*.f64 eps (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps 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 (*.f64 eps 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 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin (* 1/2 eps)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))) |
(/.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 3 binary64) (*.f64 x x))) |
(+ (* eps (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))) |
(fma.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 3 binary64) (*.f64 x x)))) |
(+ (* eps (- (+ 1 (* eps (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))) |
(fma.f64 eps (fma.f64 eps (-.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 #s(literal 3 binary64) (*.f64 x x)))) (fma.f64 (*.f64 x #s(literal 3 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (*.f64 #s(literal 3 binary64) (*.f64 x x))) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 3 binary64) (*.f64 x x)))) |
(+ (* eps (- (+ 1 (* eps (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* eps (- (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 3)) (/ (* (+ x (* 2 x)) (- (+ (* 2 (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (/ x (+ (* 2 (pow x 2)) (pow x 2)))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2))))) (/ x (+ (* 2 (pow x 2)) (pow x 2))))) (+ (/ (* (+ x (* 2 x)) (- 1 (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (+ (* 2 (pow x 2)) (pow x 2))) (/ (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))) (/ (* (pow x 3) (+ x (* 2 x))) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))) (/ (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))) |
(fma.f64 eps (fma.f64 eps (-.f64 (fma.f64 eps (fma.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 x #s(literal 3 binary64)) (*.f64 (*.f64 #s(literal 3 binary64) (*.f64 x x)) (*.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (/.f64 (*.f64 (*.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 #s(literal 3 binary64) (*.f64 x x)))) (fma.f64 (*.f64 x #s(literal 3 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (*.f64 #s(literal 3 binary64) (*.f64 x x))) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))) (*.f64 (*.f64 x x) #s(literal -3 binary64)))) (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 #s(literal 3 binary64) (*.f64 x x))))) (fma.f64 (*.f64 x #s(literal 3 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (*.f64 #s(literal 3 binary64) (*.f64 x x))) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 9 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 3 binary64) (*.f64 x x)))) |
eps |
(* eps (+ 1 (/ (pow x 3) (pow eps 3)))) |
(+.f64 eps (*.f64 eps (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) |
(* eps (+ 1 (+ (* -1 (/ (* (pow x 3) (+ x (* 2 x))) (pow eps 4))) (/ (pow x 3) (pow eps 3))))) |
(*.f64 eps (+.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (fma.f64 (neg.f64 (*.f64 x (*.f64 x x))) (/.f64 (*.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)))) |
(* eps (- (+ 1 (+ (* -1 (/ (+ (* -1 (* (pow x 3) (pow (+ x (* 2 x)) 2))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))) (pow eps 5))) (/ (pow x 3) (pow eps 3)))) (/ (* (pow x 3) (+ x (* 2 x))) (pow eps 4)))) |
(*.f64 eps (+.f64 (-.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 3 binary64) (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) #s(literal 9 binary64)))) (pow.f64 eps #s(literal 5 binary64)))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x #s(literal 3 binary64))) (pow.f64 eps #s(literal 4 binary64)))))) |
eps |
(* -1 (* eps (- (* -1 (/ (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
(*.f64 (neg.f64 eps) (+.f64 (neg.f64 (/.f64 (fma.f64 x #s(literal 3 binary64) (*.f64 x #s(literal -3 binary64))) eps)) #s(literal -1 binary64))) |
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
(*.f64 (neg.f64 eps) (+.f64 (/.f64 (+.f64 (fma.f64 x #s(literal 3 binary64) (/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal -3 binary64)) (fma.f64 (*.f64 x x) #s(literal -3 binary64) (*.f64 (*.f64 x #s(literal -3 binary64)) (fma.f64 x #s(literal 3 binary64) (*.f64 x #s(literal -3 binary64)))))) (neg.f64 eps))) (*.f64 x #s(literal -3 binary64))) (neg.f64 eps)) #s(literal -1 binary64))) |
(* -1 (* eps (- (* -1 (/ (- (+ x (+ (* -1 (/ (- (+ (* -2 (pow x 2)) (+ (* -1 (/ (- (pow x 3) (+ (* (+ (* -2 x) (* -1 x)) (- (+ (* -2 (pow x 2)) (* -1 (pow x 2))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x)))))))) (* (+ (* 2 (pow x 2)) (pow x 2)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* -1 (pow x 2)))) (+ (* -1 (+ (* 2 (pow x 2)) (pow x 2))) (* (+ (* -2 x) (* -1 x)) (- (+ x (* 2 x)) (* -1 (+ (* -2 x) (* -1 x))))))) eps)) (* 2 x))) (* -1 (+ (* -2 x) (* -1 x)))) eps)) 1))) |
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eps |
eps |
(+ eps (/ (pow x 3) (pow eps 2))) |
(+.f64 eps (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps eps))) |
(+ eps (* (pow x 3) (+ (* -3 (/ x (pow eps 3))) (/ 1 (pow eps 2))))) |
(fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 #s(literal -3 binary64) (/.f64 x (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) eps) |
(* 1/3 x) |
(*.f64 x #s(literal 1/3 binary64)) |
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(-.f64 (fma.f64 #s(literal -1/3 binary64) (/.f64 (*.f64 (*.f64 #s(literal 3 binary64) eps) (fma.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 eps eps) (*.f64 #s(literal 3 binary64) eps)) (*.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 #s(literal 3 binary64) eps)) (fma.f64 (*.f64 eps eps) #s(literal 1/9 binary64) (*.f64 #s(literal -1/27 binary64) (*.f64 #s(literal 9 binary64) (*.f64 eps eps))))))) (*.f64 x (*.f64 x x))) (fma.f64 #s(literal -1/3 binary64) (fma.f64 (*.f64 #s(literal 3 binary64) eps) (/.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/9 binary64) (*.f64 #s(literal -1/27 binary64) (*.f64 #s(literal 9 binary64) (*.f64 eps eps)))) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/9 binary64) (*.f64 #s(literal -1/27 binary64) (*.f64 #s(literal 9 binary64) (*.f64 eps eps))))) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/27 binary64) (fma.f64 (*.f64 eps eps) (/.f64 (*.f64 #s(literal 3 binary64) eps) (*.f64 x x)) (/.f64 (*.f64 #s(literal 9 binary64) (*.f64 eps eps)) x)) (*.f64 #s(literal 1/3 binary64) (+.f64 (fma.f64 #s(literal 3 binary64) eps (/.f64 (*.f64 #s(literal 3 binary64) (*.f64 eps eps)) x)) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x x))))))) (fma.f64 #s(literal 1/3 binary64) (fma.f64 (*.f64 #s(literal 3 binary64) eps) (/.f64 (*.f64 (*.f64 #s(literal 3 binary64) eps) #s(literal 2/9 binary64)) x) (/.f64 (*.f64 (*.f64 #s(literal 3 binary64) eps) (-.f64 (*.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 #s(literal 3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 #s(literal 3 binary64) eps) (*.f64 (*.f64 #s(literal 3 binary64) eps) #s(literal 2/9 binary64))))) (*.f64 (*.f64 eps eps) #s(literal 1/9 binary64)))) (*.f64 x x))) (*.f64 #s(literal 1/3 binary64) (fma.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 (*.f64 #s(literal 3 binary64) eps) #s(literal 2/9 binary64)) (*.f64 x x)) (/.f64 (-.f64 (*.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 #s(literal 3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 #s(literal 3 binary64) eps) (*.f64 (*.f64 #s(literal 3 binary64) eps) #s(literal 2/9 binary64))))) (*.f64 (*.f64 eps eps) #s(literal 1/9 binary64))) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 #s(literal 3 binary64) eps) (/.f64 (*.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 #s(literal 3 binary64) eps) (-.f64 (*.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 #s(literal 3 binary64) (*.f64 eps eps)) (*.f64 (*.f64 #s(literal 3 binary64) eps) (*.f64 (*.f64 #s(literal 3 binary64) eps) #s(literal 2/9 binary64))))) (*.f64 (*.f64 eps eps) #s(literal 1/9 binary64))) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 #s(literal 3 binary64) eps) #s(literal 2/9 binary64)))))) (*.f64 x (*.f64 x x)))))))) |
(- (* 1/3 (+ eps (* 2 eps))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))) |
(fma.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 3 binary64) eps) #s(literal 0 binary64)) |
(- (+ (* -1 (/ (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))) |
(+.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal -3 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps #s(literal -3 binary64))) (fma.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 3 binary64) eps) (*.f64 #s(literal 1/9 binary64) (*.f64 eps #s(literal -3 binary64)))) (fma.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 eps eps) #s(literal 9 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/9 binary64)))))) (neg.f64 x)) (fma.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 3 binary64) eps) #s(literal 0 binary64))) |
(- (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/3 (pow eps 3)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))) |
(+.f64 (/.f64 (-.f64 (-.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal -3 binary64))) (/.f64 (-.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps (*.f64 eps eps))) (fma.f64 #s(literal 1/3 binary64) (fma.f64 (*.f64 eps #s(literal -3 binary64)) (-.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal -3 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/9 binary64) (*.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps #s(literal -3 binary64))) (fma.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 3 binary64) eps) (*.f64 #s(literal 1/9 binary64) (*.f64 eps #s(literal -3 binary64))))))) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 3 binary64) eps) (*.f64 #s(literal 1/9 binary64) (*.f64 eps #s(literal -3 binary64)))))) (fma.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 eps #s(literal -3 binary64))) (fma.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 eps eps) #s(literal 9 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/9 binary64))) (*.f64 (*.f64 #s(literal -1/27 binary64) (*.f64 eps eps)) (*.f64 eps #s(literal -3 binary64)))))) x)) (fma.f64 (*.f64 eps eps) #s(literal -1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps #s(literal -3 binary64))) (fma.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 3 binary64) eps) (*.f64 #s(literal 1/9 binary64) (*.f64 eps #s(literal -3 binary64)))) (fma.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 eps eps) #s(literal 9 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/9 binary64)))))) (neg.f64 x)) (fma.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 3 binary64) eps) #s(literal 0 binary64))) |
(- (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))))) x)) (+ (* -1/3 (/ (* (pow eps 2) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2)))) x)) (+ (* 1/3 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (pow eps 3)) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))) x)) (+ (* 1/3 (/ (* (pow eps 2) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps))))))))) x)) (* 1/3 (pow eps 3)))))) (+ (* -1/3 (* (+ (* -2 eps) (* -1 eps)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (* 1/9 (pow eps 2))))) (+ (* -1/27 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (+ (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2)))) (+ (* -1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) (* 1/3 (* (pow eps 2) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ (* -2 (pow eps 2)) (* -1 (pow eps 2))))) (+ (* -1/9 (pow eps 2)) (+ (* -1/27 (pow (+ (* -2 eps) (* -1 eps)) 2)) (+ (* 1/9 (pow eps 2)) (* 1/3 (* (+ (* -2 eps) (* -1 eps)) (- (* 1/3 (+ eps (* 2 eps))) (* -1/9 (+ (* -2 eps) (* -1 eps)))))))))) x)) (* 1/3 (+ eps (* 2 eps)))) (+ (* -1/9 (+ (* -2 eps) (* -1 eps))) (* 1/9 (+ (* -2 eps) (* -1 eps))))) |
(+.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal -3 binary64)) (/.f64 (fma.f64 #s(literal -1/3 binary64) (fma.f64 (*.f64 eps #s(literal -3 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 eps #s(literal -3 binary64))) (fma.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 eps eps) #s(literal 9 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/9 binary64))) (*.f64 (*.f64 #s(literal -1/27 binary64) (*.f64 eps eps)) (*.f64 eps #s(literal -3 binary64)))) x) (/.f64 (*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 eps eps) #s(literal 9 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/9 binary64)))) x)) (fma.f64 #s(literal 1/3 binary64) (fma.f64 (*.f64 eps #s(literal -3 binary64)) (/.f64 (*.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 eps #s(literal -3 binary64)) (-.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal -3 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/9 binary64) (*.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps #s(literal -3 binary64))) (fma.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 3 binary64) eps) (*.f64 #s(literal 1/9 binary64) (*.f64 eps #s(literal -3 binary64))))))) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 3 binary64) eps) (*.f64 #s(literal 1/9 binary64) (*.f64 eps #s(literal -3 binary64)))))))) x) (*.f64 (*.f64 eps eps) (+.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal -3 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/9 binary64) (*.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps #s(literal -3 binary64))) (fma.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 3 binary64) eps) (*.f64 #s(literal 1/9 binary64) (*.f64 eps #s(literal -3 binary64))))))) x) eps))) (neg.f64 (fma.f64 #s(literal 1/3 binary64) (fma.f64 (*.f64 eps #s(literal -3 binary64)) (-.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 eps eps) #s(literal -3 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -1/9 binary64) (*.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps #s(literal -3 binary64))) (fma.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 3 binary64) eps) (*.f64 #s(literal 1/9 binary64) (*.f64 eps #s(literal -3 binary64))))))) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 3 binary64) eps) (*.f64 #s(literal 1/9 binary64) (*.f64 eps #s(literal -3 binary64)))))) (fma.f64 (*.f64 #s(literal -1/3 binary64) (*.f64 eps #s(literal -3 binary64))) (fma.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 eps eps) #s(literal 9 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/9 binary64))) (*.f64 (*.f64 #s(literal -1/27 binary64) (*.f64 eps eps)) (*.f64 eps #s(literal -3 binary64)))))))) (neg.f64 x))) (fma.f64 (*.f64 eps eps) #s(literal -1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps #s(literal -3 binary64))) (fma.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 3 binary64) eps) (*.f64 #s(literal 1/9 binary64) (*.f64 eps #s(literal -3 binary64)))) (fma.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 eps eps) #s(literal 9 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/9 binary64)))))) (neg.f64 x)) (fma.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 3 binary64) eps) #s(literal 0 binary64))) |
(pow x 2) |
(*.f64 x x) |
(+ (* 2 (* eps x)) (pow x 2)) |
(*.f64 x (fma.f64 eps #s(literal 2 binary64) x)) |
(+ (* eps (+ eps (* 2 x))) (pow x 2)) |
(fma.f64 eps (fma.f64 x #s(literal 2 binary64) eps) (*.f64 x x)) |
(+ (* eps (+ eps (* 2 x))) (pow x 2)) |
(fma.f64 eps (fma.f64 x #s(literal 2 binary64) eps) (*.f64 x x)) |
(pow eps 2) |
(*.f64 eps eps) |
(* (pow eps 2) (+ 1 (* 2 (/ x eps)))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal 2 binary64) (/.f64 x eps) #s(literal 1 binary64))) |
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) (fma.f64 #s(literal 2 binary64) (/.f64 x eps) #s(literal 1 binary64)))) |
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) (fma.f64 #s(literal 2 binary64) (/.f64 x eps) #s(literal 1 binary64)))) |
(pow eps 2) |
(*.f64 eps eps) |
(* (pow eps 2) (+ 1 (* 2 (/ x eps)))) |
(*.f64 (*.f64 eps eps) (fma.f64 #s(literal 2 binary64) (/.f64 x eps) #s(literal 1 binary64))) |
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps)))) |
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (/.f64 (*.f64 x x) eps)) eps))) |
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps)))) |
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (/.f64 (*.f64 x x) eps)) eps))) |
(pow eps 2) |
(*.f64 eps eps) |
(+ (* 2 (* eps x)) (pow eps 2)) |
(fma.f64 eps eps (*.f64 #s(literal 2 binary64) (*.f64 eps x))) |
(+ (* x (+ x (* 2 eps))) (pow eps 2)) |
(fma.f64 x (fma.f64 eps #s(literal 2 binary64) x) (*.f64 eps eps)) |
(+ (* x (+ x (* 2 eps))) (pow eps 2)) |
(fma.f64 x (fma.f64 eps #s(literal 2 binary64) x) (*.f64 eps eps)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2 (/ eps x)))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal 2 binary64) (/.f64 eps x) #s(literal 1 binary64))) |
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2))))) |
(*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) (fma.f64 #s(literal 2 binary64) (/.f64 eps x) #s(literal 1 binary64)))) |
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2))))) |
(*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) (fma.f64 #s(literal 2 binary64) (/.f64 eps x) #s(literal 1 binary64)))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* 2 (/ eps x)))) |
(*.f64 (*.f64 x x) (fma.f64 #s(literal 2 binary64) (/.f64 eps x) #s(literal 1 binary64))) |
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x)))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 eps #s(literal -2 binary64)) (/.f64 (*.f64 eps eps) x)) x))) |
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x)))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 eps #s(literal -2 binary64)) (/.f64 (*.f64 eps eps) x)) x))) |
Compiled 89 816 to 6 599 computations (92.7% saved)
29 alts after pruning (23 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 658 | 12 | 1 670 |
| Fresh | 5 | 11 | 16 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 4 | 4 |
| Total | 1 666 | 29 | 1 695 |
| Status | Accuracy | Program |
|---|---|---|
| 28.6% | (fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) | |
| 50.0% | (fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) | |
| 99.6% | (fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))) | |
| ✓ | 96.8% | (fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
| ✓ | 63.5% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 98.9% | (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))) | |
| 52.0% | (*.f64 (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (*.f64 eps eps) (*.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (*.f64 eps (*.f64 eps eps)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) | |
| 98.9% | (*.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64))) | |
| 99.1% | (*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps 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))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) | |
| ✓ | 98.9% | (*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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)) |
| 98.6% | (*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) | |
| 21.8% | (*.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (+.f64 eps x) (/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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)) | |
| 21.0% | (*.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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)) | |
| 21.6% | (*.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 (neg.f64 x) (/.f64 (*.f64 x x) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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)) | |
| 21.3% | (*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (fma.f64 (*.f64 (neg.f64 x) x) x (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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)) | |
| 35.5% | (*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x)) (+.f64 x (+.f64 eps x))) #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)) | |
| 21.1% | (*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) | |
| 20.9% | (*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x x) (+.f64 (fma.f64 #s(literal 3 binary64) (/.f64 eps x) #s(literal 3 binary64)) (/.f64 (*.f64 eps eps) (*.f64 x x))))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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)) | |
| 35.5% | (*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 (-.f64 x eps) x)) (/.f64 (*.f64 (-.f64 eps x) (-.f64 eps x)) (+.f64 (-.f64 x eps) x))) #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)) | |
| 63.6% | (*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) | |
| 99.2% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (*.f64 eps (fma.f64 (*.f64 eps 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.f64 x)))) #s(literal 2 binary64)) | |
| ✓ | 99.9% | (*.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)) |
| 99.4% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 #s(literal 3 binary64) eps))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) | |
| 28.7% | (*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64))) | |
| 98.7% | (*.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)))) | |
| 98.2% | (*.f64 eps (cos.f64 x)) | |
| 5.4% | (*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) | |
| ✓ | 96.8% | (sin.f64 eps) |
| ✓ | 5.5% | #s(literal 0 binary64) |
Compiled 2 189 to 680 computations (68.9% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64))) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 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 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #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 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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 (sin.f64 (+.f64 x eps)) (fma.f64 (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)) (*.f64 x (*.f64 x x)) x)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps 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))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps 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))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (*.f64 eps eps) (*.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (*.f64 eps (*.f64 eps eps)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(-.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)) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(*.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 (*.f64 (sin.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 #s(literal 3 binary64) eps))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.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)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #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 (*.f64 eps (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 eps eps)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x)) (+.f64 x (+.f64 eps x))) #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 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 (-.f64 x eps) x)) (/.f64 (*.f64 (-.f64 eps x) (-.f64 eps x)) (+.f64 (-.f64 x eps) x))) #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 (*.f64 (sin.f64 (*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 0 binary64)) eps (*.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 eps eps))) (*.f64 (fma.f64 x x #s(literal 0 binary64)) eps)) #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 (*.f64 (sin.f64 (*.f64 (/.f64 (fma.f64 (*.f64 (neg.f64 x) x) x (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (*.f64 (sin.f64 (*.f64 (fma.f64 (neg.f64 x) (/.f64 (*.f64 x x) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (*.f64 (sin.f64 (*.f64 (fma.f64 (+.f64 eps x) (/.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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 (*.f64 (sin.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (+.f64 eps x) (/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (*.f64 (sin.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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 (*.f64 (sin.f64 (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x x) (+.f64 (fma.f64 #s(literal 3 binary64) (/.f64 eps x) #s(literal 3 binary64)) (/.f64 (*.f64 eps eps) (*.f64 x x))))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 x (+.f64 x (+.f64 eps x))))))) (fma.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (-.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (*.f64 eps (fma.f64 (*.f64 eps 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.f64 x)))) #s(literal 2 binary64)) |
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.f64 x)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64)) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64)) |
3 calls:
| 16.0ms | eps |
| 16.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 14.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | eps |
| 100.0% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64))) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 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 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #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 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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 (sin.f64 (+.f64 x eps)) (fma.f64 (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)) (*.f64 x (*.f64 x x)) x)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps 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))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps 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))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (*.f64 eps eps) (*.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (*.f64 eps (*.f64 eps eps)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(-.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)) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) |
(*.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 (*.f64 (sin.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 #s(literal 3 binary64) eps))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.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)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 x (-.f64 eps x)) #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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (*.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #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 (*.f64 eps (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 eps eps)))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (*.f64 x x)) (+.f64 x (+.f64 eps x))) #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 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 x x) (+.f64 (-.f64 x eps) x)) (/.f64 (*.f64 (-.f64 eps x) (-.f64 eps x)) (+.f64 (-.f64 x eps) x))) #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 (*.f64 (sin.f64 (*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) #s(literal 0 binary64)) eps (*.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 eps eps))) (*.f64 (fma.f64 x x #s(literal 0 binary64)) eps)) #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 (*.f64 (sin.f64 (*.f64 (/.f64 (fma.f64 (*.f64 (neg.f64 x) x) x (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (*.f64 (sin.f64 (*.f64 (fma.f64 (neg.f64 x) (/.f64 (*.f64 x x) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (*.f64 (sin.f64 (*.f64 (fma.f64 (+.f64 eps x) (/.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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 (*.f64 (sin.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (+.f64 eps x) (+.f64 eps x)) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (+.f64 eps x) (/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (*.f64 (sin.f64 (*.f64 (fma.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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 (*.f64 (sin.f64 (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (/.f64 (neg.f64 (*.f64 x (*.f64 x x))) (fma.f64 x (+.f64 eps (+.f64 x x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (*.f64 (sin.f64 (*.f64 (-.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x x) (+.f64 (fma.f64 #s(literal 3 binary64) (/.f64 eps x) #s(literal 3 binary64)) (/.f64 (*.f64 eps eps) (*.f64 x x))))) (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x))))) #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 (*.f64 (sin.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (*.f64 x (*.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 (+.f64 x eps) x)))) #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 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) |
(*.f64 (*.f64 (sin.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (fma.f64 (+.f64 eps x) (*.f64 (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 x (+.f64 x (+.f64 eps x))))))) (fma.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x))) (*.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (-.f64 (*.f64 x (+.f64 x (+.f64 eps x))) (*.f64 (+.f64 eps x) (+.f64 eps x))))) (neg.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (+.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps x) (+.f64 eps x)))))) #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 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (*.f64 eps (fma.f64 (*.f64 eps 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.f64 x)))) #s(literal 2 binary64)) |
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (sin.f64 (neg.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:
| 19.0ms | eps |
| 15.0ms | x |
| 14.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
| 99.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64))) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 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 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #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 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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 (sin.f64 (+.f64 x eps)) (fma.f64 (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)) (*.f64 x (*.f64 x x)) x)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps 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))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps 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))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (*.f64 eps eps) (*.f64 (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) (*.f64 eps (*.f64 eps eps)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(-.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 (*.f64 eps 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))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
3 calls:
| 10.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 6.0ms | x |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.1% | 1 | x |
| 99.1% | 1 | eps |
| 99.1% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64))) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 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 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #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 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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 (sin.f64 (+.f64 x eps)) (fma.f64 (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)) (*.f64 x (*.f64 x x)) x)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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)) |
| Outputs |
|---|
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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:
| 21.0ms | x |
| 5.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 5.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 1 | x |
| 98.9% | 1 | eps |
| 98.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64))) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 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 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #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 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) |
(*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))) |
| Outputs |
|---|
(*.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)) |
3 calls:
| 5.0ms | x |
| 4.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 4.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 1 | x |
| 98.9% | 1 | eps |
| 98.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64))) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 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 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64))) |
| Outputs |
|---|
(*.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64))) |
3 calls:
| 4.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 4.0ms | x |
| 4.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 1 | x |
| 98.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 98.9% | 1 | eps |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64))) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 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 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
3 calls:
| 4.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 4.0ms | x |
| 4.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.6% | 1 | x |
| 98.6% | 1 | eps |
| 98.6% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64))) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(sin.f64 eps) |
(*.f64 eps (cos.f64 x)) |
| Outputs |
|---|
(*.f64 eps (cos.f64 x)) |
3 calls:
| 4.0ms | x |
| 3.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.2% | 1 | x |
| 98.2% | 1 | eps |
| 98.2% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(*.f64 (*.f64 eps (*.f64 eps eps)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/6 binary64))) |
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(fma.f64 (/.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (*.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))) |
(sin.f64 eps) |
| Outputs |
|---|
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
3 calls:
| 3.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 96.8% | 1 | x |
| 96.8% | 1 | eps |
| 96.8% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
Total -0.2b remaining (-0.3%)
Threshold costs -0.2b (-0.3%)
| Inputs |
|---|
#s(literal 0 binary64) |
(*.f64 #s(literal -1/6 binary64) (*.f64 eps (*.f64 eps eps))) |
| Outputs |
|---|
#s(literal 0 binary64) |
3 calls:
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 1.0ms | eps |
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 5.5% | 1 | x |
| 5.5% | 1 | eps |
| 5.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 15 to 10 computations (33.3% saved)
| 1× | egg-herbie |
| 58× | *-commutative_binary64 |
| 6× | +-commutative_binary64 |
| 6× | sub-neg_binary64 |
| 6× | neg-sub0_binary64 |
| 6× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 56 | 139 |
| 1 | 87 | 139 |
| 2 | 95 | 139 |
| 3 | 102 | 139 |
| 4 | 105 | 139 |
| 5 | 106 | 139 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #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 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps 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))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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 (*.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)) |
(*.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) |
(*.f64 eps (cos.f64 x)) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
#s(literal 0 binary64) |
| Outputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))) #s(literal 2 binary64)) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 x))))) #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 (*.f64 eps (fma.f64 (*.f64 eps 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))) (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 (*.f64 eps 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))))) |
(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #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 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 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)) |
(*.f64 #s(literal 2 binary64) (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))) |
(*.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (*.f64 eps #s(literal 2 binary64))) |
(*.f64 (*.f64 (*.f64 eps #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 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) |
(*.f64 eps (cos.f64 x)) |
(fma.f64 eps (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps) |
(fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) eps) |
#s(literal 0 binary64) |
| 16 678× | lower-fma.f64 |
| 16 678× | lower-fma.f32 |
| 11 836× | lower-fma.f64 |
| 11 836× | lower-fma.f32 |
| 8 230× | lower-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 35 | 205 |
| 0 | 67 | 178 |
| 1 | 257 | 178 |
| 2 | 1964 | 178 |
| 0 | 8141 | 177 |
| 0 | 576 | 5604 |
| 1 | 1959 | 5182 |
| 2 | 7243 | 4885 |
| 0 | 8407 | 4503 |
| 0 | 626 | 5677 |
| 1 | 1924 | 5339 |
| 2 | 5669 | 5205 |
| 0 | 8103 | 4828 |
| 0 | 107 | 496 |
| 1 | 314 | 496 |
| 2 | 775 | 489 |
| 3 | 2836 | 489 |
| 4 | 6173 | 489 |
| 0 | 8126 | 458 |
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 53 | 16 |
| 2 | 380 | 16 |
| 3 | 4766 | 16 |
| 0 | 8210 | 16 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 380 to 219 computations (42.4% saved)
Compiled 394 to 188 computations (52.3% saved)
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