
Time bar (total: 9.8s)
| 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)
| 3.2s | 5 768× | 2 | valid |
| 2.4s | 26 294× | 0 | invalid |
| 906.0ms | 2 442× | 1 | valid |
| 5.0ms | 46× | 0 | valid |
ival-cos: 2.6s (53.6% of total)ival-sub!: 719.0ms (15% of total)ival-fabs: 476.0ms (10% of total)adjust: 401.0ms (8.4% of total)ival-mult!: 199.0ms (4.2% of total)ival-add!: 174.0ms (3.6% of total)ival-<: 173.0ms (3.6% of total)ival-and: 61.0ms (1.3% of total)ival-assert: 13.0ms (0.3% of total)Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 48 |
| 1 | 106 | 48 |
| 2 | 654 | 44 |
| 3 | 3750 | 44 |
| 1× | node-limit |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 53.9% | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
Compiled 14 to 12 computations (14.3% saved)
| Inputs |
|---|
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(cos.f64 x) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps)))))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))))) |
#s(approx (+ x eps) #s(hole binary64 eps)) |
#s(approx (+ x eps) #s(hole binary64 (+ eps x))) |
#s(approx x #s(hole binary64 x)) |
#s(approx (cos x) #s(hole binary64 1)) |
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2))))) |
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))) |
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x)))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x)))) |
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x))))) |
#s(approx (cos x) #s(hole binary64 (cos x))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x)))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x))))) |
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x)))))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))) |
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x)))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps))))) |
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | 0 | ((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x)) |
| 1.0ms | eps | @ | inf | ((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x)) |
| 1.0ms | eps | @ | -inf | ((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x)) |
| 1.0ms | x | @ | -inf | ((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x)) |
| 1.0ms | eps | @ | 0 | ((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 145 | 529 |
| 0 | 150 | 513 |
| 1 | 880 | 510 |
| 0 | 8196 | 489 |
| 1× | iter-limit |
| 1× | node-limit |
| 1× | iter-limit |
| Inputs |
|---|
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
(cos.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(cos.f64 x) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps)))))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))))) |
#s(approx (+ x eps) #s(hole binary64 eps)) |
#s(approx (+ x eps) #s(hole binary64 (+ eps x))) |
#s(approx x #s(hole binary64 x)) |
#s(approx (cos x) #s(hole binary64 1)) |
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2))))) |
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))) |
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x)))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x)))) |
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x))))) |
#s(approx (cos x) #s(hole binary64 (cos x))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x)))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x))))) |
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x)))))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))) |
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x)))) |
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps))))) |
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1))))) |
| Outputs |
|---|
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) |
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) #s(literal -2 binary64)) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))))) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))))) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64))))) |
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))))) |
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (neg.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))))))) |
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) |
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (-.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x))) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x))) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x))) |
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))) |
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))))))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))) |
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) |
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (cos.f64 x))) |
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x))) |
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps)))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps)))))) |
(sin.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 eps x))) |
(fma.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))) |
(fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) |
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) |
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (sin.f64 x)))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 eps)))) |
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 eps))) |
(cos.f64 (neg.f64 (neg.f64 (+.f64 eps x)))) |
(cos.f64 (neg.f64 (+.f64 eps x))) |
(cos.f64 (+.f64 eps x)) |
(+.f64 (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))) |
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x))) |
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) |
(+.f64 (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) |
(/.f64 (neg.f64 (*.f64 (-.f64 eps x) (+.f64 eps x))) (neg.f64 (-.f64 eps x))) |
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (neg.f64 (fma.f64 eps eps (*.f64 x (-.f64 x eps))))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) |
(/.f64 (*.f64 (-.f64 eps x) (+.f64 eps x)) (-.f64 eps x)) |
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps)) |
(/.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) |
(/.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) |
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x))) |
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) |
(-.f64 (/.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) (/.f64 (*.f64 (neg.f64 x) (*.f64 x x)) (fma.f64 eps eps (*.f64 x (-.f64 x eps))))) |
(-.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) (neg.f64 eps)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) |
(-.f64 eps (neg.f64 x)) |
(-.f64 x (neg.f64 eps)) |
(+.f64 (/.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 eps eps (*.f64 x (-.f64 x eps))))) |
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) |
(+.f64 eps (*.f64 (neg.f64 x) #s(literal -1 binary64))) |
(+.f64 eps x) |
(+.f64 x (*.f64 (neg.f64 eps) #s(literal -1 binary64))) |
(+.f64 x eps) |
x |
eps |
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) |
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))) |
(cos.f64 (neg.f64 x)) |
(cos.f64 x) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 x (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 x (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x) (sin.f64 eps)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))) |
#s(approx (cos (+ x eps)) (cos.f64 eps)) |
#s(approx (cos (+ x eps)) (-.f64 (cos.f64 eps) (*.f64 (sin.f64 eps) x))) |
#s(approx (cos (+ x eps)) (fma.f64 x (-.f64 (*.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/2 binary64)) (sin.f64 eps)) (cos.f64 eps))) |
#s(approx (cos (+ x eps)) (fma.f64 x (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) x) (sin.f64 eps)) (cos.f64 eps))) |
#s(approx (+ x eps) eps) |
#s(approx (+ x eps) (+.f64 eps x)) |
#s(approx x x) |
#s(approx (cos x) #s(literal 1 binary64)) |
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx (cos x) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x))) |
#s(approx (+ x eps) (fma.f64 (/.f64 eps x) x x)) |
#s(approx (cos x) (cos.f64 x)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x))) |
#s(approx (+ x eps) (*.f64 (-.f64 (/.f64 eps (neg.f64 x)) #s(literal 1 binary64)) (neg.f64 x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/2 binary64) (*.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps)) eps) (sin.f64 x)) eps)) |
#s(approx (cos (+ x eps)) (-.f64 (cos.f64 x) (*.f64 (sin.f64 x) eps))) |
#s(approx (cos (+ x eps)) (fma.f64 eps (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) (cos.f64 x))) |
#s(approx (cos (+ x eps)) (fma.f64 eps (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) (cos.f64 x))) |
#s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x))) |
#s(approx (+ x eps) (*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)) (neg.f64 eps))) |
Compiled 2 015 to 429 computations (78.7% saved)
3 alts after pruning (3 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 99 | 3 | 102 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 100 | 3 | 103 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 53.7% | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
| ▶ | 99.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)) |
| ▶ | 81.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
Compiled 44 to 34 computations (22.7% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
(*.f64 (neg.f64 eps) (sin.f64 x)) |
(neg.f64 eps) |
eps |
(sin.f64 x) |
x |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps) |
(-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 #s(literal -1/2 binary64) (cos.f64 x)) |
#s(literal -1/2 binary64) |
(cos.f64 x) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(cos.f64 eps) |
#s(literal 1 binary64) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x)))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))))) |
#s(approx (sin x) #s(hole binary64 x)) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2)))))) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2)))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 eps))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps)))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2)))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps)))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2)))))))))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 -1/2)) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))) |
#s(approx (cos x) #s(hole binary64 1)) |
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2))))) |
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))) |
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x)))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x))))) |
#s(approx (sin x) #s(hole binary64 (sin x))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x)))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (* -1/2 (* eps (cos x))))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x)))) |
#s(approx (cos x) #s(hole binary64 (cos x))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))))) |
#s(approx (neg eps) #s(hole binary64 (* -1 eps))) |
#s(approx eps #s(hole binary64 eps)) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (sin x)))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2)))) |
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2))))) |
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))) |
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))) |
#s(approx (cos eps) #s(hole binary64 (cos eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x)))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 7.0ms | eps | @ | 0 | ((- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) eps (sin x) x (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1) |
| 3.0ms | x | @ | -inf | ((- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) eps (sin x) x (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1) |
| 2.0ms | eps | @ | inf | ((- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) eps (sin x) x (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1) |
| 2.0ms | eps | @ | -inf | ((- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) eps (sin x) x (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1) |
| 2.0ms | x | @ | 0 | ((- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) eps (sin x) x (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) -1/2 (cos x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 288 | 1167 |
| 0 | 306 | 1149 |
| 1 | 1741 | 1149 |
| 0 | 8659 | 1099 |
| 1× | iter-limit |
| 1× | node-limit |
| 1× | iter-limit |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
(*.f64 (neg.f64 eps) (sin.f64 x)) |
(neg.f64 eps) |
eps |
(sin.f64 x) |
x |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps) |
(-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 #s(literal -1/2 binary64) (cos.f64 x)) |
#s(literal -1/2 binary64) |
(cos.f64 x) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(cos.f64 eps) |
#s(literal 1 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x)))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))))) |
#s(approx (sin x) #s(hole binary64 x)) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2)))))) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2)))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 eps))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps)))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2)))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps)))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2)))))))))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 -1/2)) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))) |
#s(approx (cos x) #s(hole binary64 1)) |
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2))))) |
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))) |
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x)))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x))))) |
#s(approx (sin x) #s(hole binary64 (sin x))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x)))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (* -1/2 (* eps (cos x))))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x)))) |
#s(approx (cos x) #s(hole binary64 (cos x))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))))) |
#s(approx (neg eps) #s(hole binary64 (* -1 eps))) |
#s(approx eps #s(hole binary64 eps)) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (sin x)))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2)))) |
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2))))) |
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))) |
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))) |
#s(approx (cos eps) #s(hole binary64 (cos eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x)))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
(*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1 binary64)) |
(*.f64 (neg.f64 eps) (sin.f64 x)) |
(*.f64 (sin.f64 x) (neg.f64 eps)) |
(*.f64 #s(literal -1 binary64) (*.f64 (sin.f64 x) eps)) |
(neg.f64 (*.f64 (sin.f64 x) eps)) |
(*.f64 #s(literal -1 binary64) eps) |
(*.f64 eps #s(literal -1 binary64)) |
(neg.f64 eps) |
eps |
(sin.f64 x) |
x |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps) |
(*.f64 eps (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (neg.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (sin.f64 x)))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (sin.f64 x))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x))))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (sin.f64 x))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (sin.f64 x)))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)))))) |
(-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) |
(*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) |
(*.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x)) |
(*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps)) |
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
(*.f64 #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 (cos.f64 x) #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))) |
(cos.f64 (neg.f64 (neg.f64 x))) |
(cos.f64 (neg.f64 x)) |
(cos.f64 x) |
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))))) (neg.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (expm1.f64 (*.f64 (log.f64 (cos.f64 eps)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 1 binary64)))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps))))) (+.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(/.f64 (expm1.f64 (*.f64 (log.f64 (cos.f64 eps)) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 1 binary64))))) |
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (+.f64 (cos.f64 eps) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 eps) #s(literal 1 binary64)))) |
(-.f64 (/.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 1 binary64)))))) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(sin.f64 (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(fma.f64 (sin.f64 eps) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 eps) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))) |
(cos.f64 (neg.f64 (neg.f64 eps))) |
(cos.f64 (neg.f64 eps)) |
(cos.f64 eps) |
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 eps) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64))))) |
#s(literal 1 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps)) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 x (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) (cos.f64 eps)) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (fma.f64 x (-.f64 (*.f64 (+.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (*.f64 (cos.f64 eps) #s(literal -1/2 binary64))) #s(literal 1/2 binary64)) x) (sin.f64 eps)) (cos.f64 eps)) #s(literal 1 binary64))) |
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)) |
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)) |
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (neg.f64 eps)) x)) |
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)) |
#s(approx (sin x) x) |
#s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) |
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) |
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps x)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) |
#s(approx (* (* -1/2 (cos x)) eps) (fma.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps))) |
#s(approx (* (* -1/2 (cos x)) eps) (fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/4 binary64) eps)) (*.f64 #s(literal -1/2 binary64) eps))) |
#s(approx (* (* -1/2 (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/1440 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/48 binary64) eps)) (*.f64 #s(literal 1/4 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps))) |
#s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) |
#s(approx (cos x) #s(literal 1 binary64)) |
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
#s(approx (sin x) (sin.f64 x)) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x))) |
#s(approx (* (* -1/2 (cos x)) eps) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (* -1/2 (cos x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
#s(approx (cos x) (cos.f64 x)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 eps (neg.f64 x))) (cos.f64 x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 eps (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)) |
#s(approx (neg eps) (neg.f64 eps)) |
#s(approx eps eps) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps)) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (neg.f64 (sin.f64 x))) |
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps))) |
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps))) |
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/40320 binary64) (*.f64 eps eps)) #s(literal 1/720 binary64)) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps))) |
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
#s(approx (cos eps) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))) |
#s(approx (cos eps) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) #s(literal -1/2 binary64))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps)) |
#s(approx (cos eps) (cos.f64 eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (cos.f64 x))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (neg.f64 eps) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))) |
Compiled 2 651 to 553 computations (79.1% saved)
16 alts after pruning (14 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 86 | 14 | 100 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 2 | 3 |
| Done | 0 | 0 | 0 |
| Total | 87 | 16 | 103 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 53.7% | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
| ✓ | 99.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)) |
| ▶ | 99.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
| 99.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) | |
| 99.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) | |
| ✓ | 81.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
| ▶ | 80.9% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
| ▶ | 80.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
| 80.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) | |
| ▶ | 80.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x))) |
| 99.3% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) | |
| 99.1% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) | |
| 54.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) | |
| 99.5% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) | |
| 99.3% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) | |
| 98.8% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps)))) |
Compiled 810 to 548 computations (32.3% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps) |
(-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) |
(*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) |
(-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) |
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) |
(fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) |
(-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) |
(*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) |
#s(literal 1/1440 binary64) |
(*.f64 x x) |
x |
#s(literal 1/48 binary64) |
#s(literal 1/4 binary64) |
#s(literal 1/2 binary64) |
eps |
(sin.f64 x) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x))) |
(*.f64 (neg.f64 eps) #s(approx (sin x) x)) |
(neg.f64 eps) |
#s(approx (sin x) x) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
(-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(*.f64 eps eps) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
(*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) |
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) |
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) |
(fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) |
(*.f64 #s(literal 1/120 binary64) (*.f64 x x)) |
#s(literal 1/120 binary64) |
#s(literal 1/6 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
(*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) |
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) |
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) |
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) |
(*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) |
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) |
#s(literal -1/5040 binary64) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2)))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 eps))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps)))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2)))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps)))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2)))))))))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 -1/2)) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))) |
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* 1/4 (pow x 2)))) |
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))))) |
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))))) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 1/4)) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (+ 1/4 (* -1/48 (pow x 2))))) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) |
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(hole binary64 -1/48)) |
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(hole binary64 (- (* 1/1440 (pow x 2)) 1/48))) |
#s(approx (* 1/1440 (* x x)) #s(hole binary64 (* 1/1440 (pow x 2)))) |
#s(approx (* x x) #s(hole binary64 (pow x 2))) |
#s(approx x #s(hole binary64 x)) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2)))))) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x)))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 1)) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 -1/6)) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6))) |
#s(approx (* 1/120 (* x x)) #s(hole binary64 (* 1/120 (pow x 2)))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) |
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))))) |
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 1/120)) |
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (+ 1/120 (* -1/5040 (pow x 2))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x)))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x)))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (* -1/2 (* eps (cos x))))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x)))) |
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* 1/1440 (pow x 6)))) |
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (- 1/1440 (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (* 1/1440 (pow x 4)))) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (* (pow x 4) (- 1/1440 (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (* (pow x 4) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(hole binary64 (* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (sin x) #s(hole binary64 (sin x))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* 1/120 (pow x 5)))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* 1/120 (pow x 4)))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1/5040 (pow x 7)))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* -1/5040 (pow x 6)))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))) |
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (* -1/5040 (pow x 4)))) |
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))) |
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))) |
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* -1/5040 (pow x 2)))) |
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x)))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (sin x)))) |
#s(approx eps #s(hole binary64 eps)) |
#s(approx (neg eps) #s(hole binary64 (* -1 eps))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2)))) |
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2))))) |
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))) |
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))) |
#s(approx (* eps eps) #s(hole binary64 (pow eps 2))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))) |
#s(approx (cos eps) #s(hole binary64 (cos eps))) |
#s(approx (+ (* (* eps eps) -1/2) 1) #s(hole binary64 (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/2)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x)))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | x | @ | inf | ((- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (- (* 1/1440 (* x x)) 1/48) (* 1/1440 (* x x)) 1/1440 (* x x) x 1/48 1/4 1/2 eps (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (+ (* (* eps eps) -1/2) 1) (* eps eps) -1/2 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 1/6 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) (+ (* -1/5040 (* x x)) 1/120) -1/5040) |
| 4.0ms | x | @ | -inf | ((- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (- (* 1/1440 (* x x)) 1/48) (* 1/1440 (* x x)) 1/1440 (* x x) x 1/48 1/4 1/2 eps (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (+ (* (* eps eps) -1/2) 1) (* eps eps) -1/2 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 1/6 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) (+ (* -1/5040 (* x x)) 1/120) -1/5040) |
| 2.0ms | x | @ | 0 | ((- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (- (* 1/1440 (* x x)) 1/48) (* 1/1440 (* x x)) 1/1440 (* x x) x 1/48 1/4 1/2 eps (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (+ (* (* eps eps) -1/2) 1) (* eps eps) -1/2 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 1/6 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) (+ (* -1/5040 (* x x)) 1/120) -1/5040) |
| 2.0ms | eps | @ | inf | ((- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (- (* 1/1440 (* x x)) 1/48) (* 1/1440 (* x x)) 1/1440 (* x x) x 1/48 1/4 1/2 eps (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (+ (* (* eps eps) -1/2) 1) (* eps eps) -1/2 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 1/6 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) (+ (* -1/5040 (* x x)) 1/120) -1/5040) |
| 2.0ms | eps | @ | -inf | ((- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (- (* 1/1440 (* x x)) 1/48) (* 1/1440 (* x x)) 1/1440 (* x x) x 1/48 1/4 1/2 eps (sin x) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (+ (* (* eps eps) -1/2) 1) (* eps eps) -1/2 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 1/6 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) (+ (* -1/5040 (* x x)) 1/120) -1/5040) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 447 | 2957 |
| 0 | 496 | 2855 |
| 1 | 2451 | 2855 |
| 0 | 8775 | 2807 |
| 1× | iter-limit |
| 1× | node-limit |
| 1× | iter-limit |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps) |
(-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) |
(*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) |
(-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) |
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) |
(fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) |
(-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) |
(*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) |
#s(literal 1/1440 binary64) |
(*.f64 x x) |
x |
#s(literal 1/48 binary64) |
#s(literal 1/4 binary64) |
#s(literal 1/2 binary64) |
eps |
(sin.f64 x) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x))) |
(*.f64 (neg.f64 eps) #s(approx (sin x) x)) |
(neg.f64 eps) |
#s(approx (sin x) x) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
(-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(*.f64 eps eps) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
(*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) |
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) |
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) |
(fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) |
(*.f64 #s(literal 1/120 binary64) (*.f64 x x)) |
#s(literal 1/120 binary64) |
#s(literal 1/6 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
(*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) |
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) |
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) |
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) |
(*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) |
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) |
#s(literal -1/5040 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2)))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 eps))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps)))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2)))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps)))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2)))))))))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 -1/2)) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))) |
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* 1/4 (pow x 2)))) |
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))))) |
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))))) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 1/4)) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (+ 1/4 (* -1/48 (pow x 2))))) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) |
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(hole binary64 -1/48)) |
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(hole binary64 (- (* 1/1440 (pow x 2)) 1/48))) |
#s(approx (* 1/1440 (* x x)) #s(hole binary64 (* 1/1440 (pow x 2)))) |
#s(approx (* x x) #s(hole binary64 (pow x 2))) |
#s(approx x #s(hole binary64 x)) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2)))))) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x)))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 1)) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 -1/6)) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6))) |
#s(approx (* 1/120 (* x x)) #s(hole binary64 (* 1/120 (pow x 2)))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) |
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) |
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))))) |
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 1/120)) |
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (+ 1/120 (* -1/5040 (pow x 2))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x)))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x)))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (* -1/2 (* eps (cos x))))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x)))) |
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* 1/1440 (pow x 6)))) |
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (- 1/1440 (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) #s(hole binary64 (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (* 1/1440 (pow x 4)))) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (* (pow x 4) (- 1/1440 (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(hole binary64 (* (pow x 4) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(hole binary64 (* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (sin x) #s(hole binary64 (sin x))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* 1/120 (pow x 5)))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* 1/120 (pow x 4)))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1/5040 (pow x 7)))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* -1/5040 (pow x 6)))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))) |
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (* -1/5040 (pow x 4)))) |
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))) |
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))) |
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* -1/5040 (pow x 2)))) |
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x)))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (sin x)))) |
#s(approx eps #s(hole binary64 eps)) |
#s(approx (neg eps) #s(hole binary64 (* -1 eps))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2)))) |
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2))))) |
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))) |
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))) |
#s(approx (* eps eps) #s(hole binary64 (pow eps 2))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))) |
#s(approx (cos eps) #s(hole binary64 (cos eps))) |
#s(approx (+ (* (* eps eps) -1/2) 1) #s(hole binary64 (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/2)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x)))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps) |
(*.f64 eps (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (neg.f64 (fma.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps (sin.f64 x)))) |
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x |
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eps |
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#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) (*.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64)))) |
#s(approx (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x)) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) #s(literal 1/4 binary64)) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (fma.f64 (*.f64 x x) #s(literal -1/48 binary64) #s(literal 1/4 binary64))) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64))) |
#s(approx (- (* 1/1440 (* x x)) 1/48) #s(literal -1/48 binary64)) |
#s(approx (- (* 1/1440 (* x x)) 1/48) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64))) |
#s(approx (* 1/1440 (* x x)) (*.f64 (*.f64 x x) #s(literal 1/1440 binary64))) |
#s(approx (* x x) (*.f64 x x)) |
#s(approx x x) |
#s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)) |
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) |
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x)) |
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)) |
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) (*.f64 x x) (neg.f64 eps)) x)) |
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal -1/120 binary64) eps) (*.f64 x x) (*.f64 #s(literal 1/6 binary64) eps)) (neg.f64 eps)) x)) |
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 #s(literal 1/5040 binary64) eps) (*.f64 x x) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(literal 1 binary64)) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) |
#s(approx (- (* 1/120 (* x x)) 1/6) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64))) |
#s(approx (* 1/120 (* x x)) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64))) |
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64))) |
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x)) |
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64)) |
#s(approx (+ (* -1/5040 (* x x)) 1/120) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x))) |
#s(approx (* (* -1/2 (cos x)) eps) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (* -1/2 (cos x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal 1/1440 binary64))) |
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (-.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 x x))))) |
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (+.f64 #s(literal 1/1440 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/48 binary64) (*.f64 x x)))))) |
#s(approx (- (* (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (* x x)) 1/2) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (-.f64 (+.f64 #s(literal 1/1440 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/48 binary64) (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))))) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/1440 binary64))) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 x x))))) |
#s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (*.f64 (+.f64 #s(literal 1/1440 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/48 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x)))) |
#s(approx (- (* 1/1440 (* x x)) 1/48) (*.f64 (-.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 x x))) (*.f64 x x))) |
#s(approx (sin x) (sin.f64 x)) |
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/120 binary64))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (*.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (*.f64 (+.f64 #s(literal 1/120 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64)))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/120 binary64))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (*.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x)))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (*.f64 (+.f64 #s(literal 1/120 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x)))) |
#s(approx (- (* 1/120 (* x x)) 1/6) (*.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) (*.f64 x x))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/5040 binary64))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (*.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (pow.f64 x #s(literal 7 binary64)))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64)))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (*.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) (pow.f64 x #s(literal -6 binary64))) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64)))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal -1/5040 binary64))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (-.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
#s(approx (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) (pow.f64 x #s(literal -6 binary64))) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/5040 binary64))) |
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (*.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) |
#s(approx (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x)))) |
#s(approx (+ (* -1/5040 (* x x)) 1/120) (*.f64 (*.f64 x x) #s(literal -1/5040 binary64))) |
#s(approx (+ (* -1/5040 (* x x)) 1/120) (*.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64)) (*.f64 x x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 eps (neg.f64 x))) (cos.f64 x))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (neg.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal 1/120 binary64)) (pow.f64 x #s(literal 5 binary64))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (neg.f64 (*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal 1/120 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64))))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (neg.f64 (*.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (*.f64 x x))) (pow.f64 x #s(literal 7 binary64))))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (neg.f64 (*.f64 (+.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.f64 x #s(literal 7 binary64))))) |
#s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (neg.f64 (*.f64 (-.f64 (+.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.f64 x #s(literal -6 binary64))) (pow.f64 x #s(literal 7 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps)) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (neg.f64 (sin.f64 x))) |
#s(approx eps eps) |
#s(approx (neg eps) (neg.f64 eps)) |
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps))) |
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps))) |
#s(approx (- (cos eps) 1) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/40320 binary64) (*.f64 eps eps)) #s(literal 1/720 binary64)) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps))) |
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
#s(approx (cos eps) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))) |
#s(approx (cos eps) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))) |
#s(approx (* eps eps) (*.f64 eps eps)) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) #s(literal -1/2 binary64))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps)) |
#s(approx (cos eps) (cos.f64 eps)) |
#s(approx (+ (* (* eps eps) -1/2) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (cos.f64 x))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (neg.f64 eps) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))) |
Compiled 16 041 to 2 537 computations (84.2% saved)
18 alts after pruning (13 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 354 | 7 | 361 |
| Fresh | 3 | 6 | 9 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 2 | 2 |
| Total | 359 | 18 | 377 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 53.7% | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
| ✓ | 99.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)) |
| ▶ | 99.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
| ▶ | 99.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
| 99.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/1440 binary64))) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) | |
| 99.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) | |
| ✓ | 81.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
| ✓ | 80.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
| 80.9% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x)))) | |
| ▶ | 80.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
| 53.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) #s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/5040 binary64)))))) | |
| ✓ | 80.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x))) |
| 99.3% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) | |
| 99.1% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) | |
| ▶ | 54.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
| ▶ | 99.5% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
| 99.3% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) | |
| 98.8% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps)))) |
Compiled 944 to 638 computations (32.4% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps) |
(-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) |
(*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) |
(-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) |
(*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) |
(fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) |
(-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) |
(*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) |
(*.f64 x x) |
x |
#s(literal 1/1440 binary64) |
#s(literal 1/48 binary64) |
#s(literal 1/4 binary64) |
#s(literal 1/2 binary64) |
eps |
(sin.f64 x) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
(*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(literal -1/2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
(*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) |
(neg.f64 eps) |
#s(approx (sin x) (*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) |
(*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) |
(fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
(fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) |
(fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) |
(*.f64 eps x) |
#s(literal 1/6 binary64) |
(*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) |
(*.f64 eps eps) |
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps) |
(-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) |
(*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) |
(-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 x x) #s(literal 1/4 binary64)) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2)))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 eps))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps)))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2)))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps)))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2)))))))))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 -1/2)) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))) |
#s(approx (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) #s(hole binary64 (* 1/4 (pow x 2)))) |
#s(approx (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) #s(hole binary64 (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))))) |
#s(approx (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) #s(hole binary64 (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* 1/4 x))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* x (+ 1/4 (* -1/48 (pow x 2)))))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* x (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))))) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) #s(hole binary64 1/4)) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) #s(hole binary64 (+ 1/4 (* -1/48 (pow x 2))))) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) #s(hole binary64 (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) |
#s(approx (- (* (* x x) 1/1440) 1/48) #s(hole binary64 -1/48)) |
#s(approx (- (* (* x x) 1/1440) 1/48) #s(hole binary64 (- (* 1/1440 (pow x 2)) 1/48))) |
#s(approx (* (* x x) 1/1440) #s(hole binary64 (* 1/1440 (pow x 2)))) |
#s(approx (* x x) #s(hole binary64 (pow x 2))) |
#s(approx x #s(hole binary64 x)) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2)))))) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x)))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 1)) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 -1/6)) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* -1 eps))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (- (* 1/4 (* (pow eps 2) x)) eps))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) #s(hole binary64 (* 1/4 (pow eps 2)))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) #s(hole binary64 (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))) |
#s(approx (* eps x) #s(hole binary64 (* eps x))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x)))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x)))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (* -1/2 (* eps (cos x))))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x)))) |
#s(approx (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) #s(hole binary64 (* 1/1440 (pow x 6)))) |
#s(approx (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) #s(hole binary64 (* (pow x 6) (- 1/1440 (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) #s(hole binary64 (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) #s(hole binary64 (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* 1/1440 (pow x 5)))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* (pow x 5) (- 1/1440 (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* (pow x 5) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) #s(hole binary64 (* 1/1440 (pow x 4)))) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) #s(hole binary64 (* (pow x 4) (- 1/1440 (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) #s(hole binary64 (* (pow x 4) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (- (* (* x x) 1/1440) 1/48) #s(hole binary64 (* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (sin x) #s(hole binary64 (sin x))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* 1/120 (pow x 5)))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* 1/120 (pow x 4)))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (* 1/120 (pow x 2)))) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* 1/6 (* eps (pow x 3))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow x 3) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow x 3) (- (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))) (/ eps (pow x 2)))))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* 1/6 (* eps (pow x 2))))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* (pow x 2) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) #s(hole binary64 (* 1/6 (* eps x)))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) #s(hole binary64 (* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))) |
#s(approx (- (* (* x x) 1/4) 1/2) #s(hole binary64 (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x)))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/48 (/ 1 (pow x 2))) 1/1440))))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/1440 (/ 1/4 (pow x 4)))))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps)))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps)))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps)))))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (pow eps 2)) (/ eps x)) x)) (* 1/6 eps))))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) #s(hole binary64 (* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (sin x)))) |
#s(approx eps #s(hole binary64 eps)) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* eps (* x (- (* 1/6 (pow x 2)) 1))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* eps (- (* 1/6 (pow x 2)) 1)))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) #s(hole binary64 (* eps (+ (* 1/6 x) (* 1/4 eps))))) |
#s(approx (* eps eps) #s(hole binary64 (pow eps 2))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2)))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2)))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* 1/4 (* (pow eps 2) x)))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps))))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) #s(hole binary64 (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x)))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2)))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 11.0ms | x | @ | -inf | ((- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) (- (* (* x x) 1/1440) 1/48) (* (* x x) 1/1440) (* x x) x 1/1440 1/48 1/4 1/2 eps (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) (* eps x) 1/6 (* (* eps eps) 1/4) (* eps eps) (* (* eps eps) -1/2) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (* x x) 1/4) 1/2) (* (* x x) 1/4)) |
| 4.0ms | x | @ | inf | ((- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) (- (* (* x x) 1/1440) 1/48) (* (* x x) 1/1440) (* x x) x 1/1440 1/48 1/4 1/2 eps (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) (* eps x) 1/6 (* (* eps eps) 1/4) (* eps eps) (* (* eps eps) -1/2) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (* x x) 1/4) 1/2) (* (* x x) 1/4)) |
| 4.0ms | eps | @ | -inf | ((- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) (- (* (* x x) 1/1440) 1/48) (* (* x x) 1/1440) (* x x) x 1/1440 1/48 1/4 1/2 eps (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) (* eps x) 1/6 (* (* eps eps) 1/4) (* eps eps) (* (* eps eps) -1/2) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (* x x) 1/4) 1/2) (* (* x x) 1/4)) |
| 4.0ms | eps | @ | inf | ((- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) (- (* (* x x) 1/1440) 1/48) (* (* x x) 1/1440) (* x x) x 1/1440 1/48 1/4 1/2 eps (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) (* eps x) 1/6 (* (* eps eps) 1/4) (* eps eps) (* (* eps eps) -1/2) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (* x x) 1/4) 1/2) (* (* x x) 1/4)) |
| 3.0ms | eps | @ | 0 | ((- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) (- (* (* x x) 1/1440) 1/48) (* (* x x) 1/1440) (* x x) x 1/1440 1/48 1/4 1/2 eps (sin x) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) (* eps x) 1/6 (* (* eps eps) 1/4) (* eps eps) (* (* eps eps) -1/2) (- (cos (+ x eps)) (cos x)) (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (- (* (* -1/2 (cos x)) eps) (sin x)) (* (* -1/2 (cos x)) eps) (* -1/2 (cos x)) (- (* (* x x) 1/4) 1/2) (* (* x x) 1/4)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 514 | 3547 |
| 0 | 563 | 3420 |
| 1 | 2830 | 3420 |
| 0 | 9915 | 3302 |
| 1× | iter-limit |
| 1× | node-limit |
| 1× | iter-limit |
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps) |
(-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) |
(*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) |
(-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) |
(*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) |
(fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) |
(-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) |
(*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) |
(*.f64 x x) |
x |
#s(literal 1/1440 binary64) |
#s(literal 1/48 binary64) |
#s(literal 1/4 binary64) |
#s(literal 1/2 binary64) |
eps |
(sin.f64 x) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
(*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(literal -1/2 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
(*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) |
(neg.f64 eps) |
#s(approx (sin x) (*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) |
(*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x) |
(fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) |
#s(literal -1/6 binary64) |
#s(literal 1 binary64) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
(fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) |
(fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) |
(*.f64 eps x) |
#s(literal 1/6 binary64) |
(*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) |
(*.f64 eps eps) |
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps) |
(-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) |
(*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) |
(-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 x x) #s(literal 1/4 binary64)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (pow eps 2)))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x))))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1/2 eps))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1 x) (* -1/2 eps)))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2)))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps)))))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2)))))))))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 -1/2)) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* 1/4 (pow x 2)) 1/2))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2))) |
#s(approx (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) #s(hole binary64 (* 1/4 (pow x 2)))) |
#s(approx (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) #s(hole binary64 (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))))) |
#s(approx (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) #s(hole binary64 (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* 1/4 x))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* x (+ 1/4 (* -1/48 (pow x 2)))))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* x (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))))) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) #s(hole binary64 1/4)) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) #s(hole binary64 (+ 1/4 (* -1/48 (pow x 2))))) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) #s(hole binary64 (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48))))) |
#s(approx (- (* (* x x) 1/1440) 1/48) #s(hole binary64 -1/48)) |
#s(approx (- (* (* x x) 1/1440) 1/48) #s(hole binary64 (- (* 1/1440 (pow x 2)) 1/48))) |
#s(approx (* (* x x) 1/1440) #s(hole binary64 (* 1/1440 (pow x 2)))) |
#s(approx (* x x) #s(hole binary64 (pow x 2))) |
#s(approx x #s(hole binary64 x)) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2)))))) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))) |
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps x)))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2))))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps))))))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2))))))))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 1)) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 -1/6)) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* -1 eps))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (- (* 1/4 (* (pow eps 2) x)) eps))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (- (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))) eps))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) #s(hole binary64 (* 1/4 (pow eps 2)))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) #s(hole binary64 (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2))))) |
#s(approx (* eps x) #s(hole binary64 (* eps x))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x)))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x)))) |
#s(approx (* (* -1/2 (cos x)) eps) #s(hole binary64 (* -1/2 (* eps (cos x))))) |
#s(approx (* -1/2 (cos x)) #s(hole binary64 (* -1/2 (cos x)))) |
#s(approx (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) #s(hole binary64 (* 1/1440 (pow x 6)))) |
#s(approx (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) #s(hole binary64 (* (pow x 6) (- 1/1440 (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) #s(hole binary64 (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) #s(hole binary64 (* (pow x 6) (- (+ 1/1440 (/ 1/4 (pow x 4))) (+ (* 1/48 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* 1/1440 (pow x 5)))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* (pow x 5) (- 1/1440 (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* (pow x 5) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) #s(hole binary64 (* 1/1440 (pow x 4)))) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) #s(hole binary64 (* (pow x 4) (- 1/1440 (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) #s(hole binary64 (* (pow x 4) (- (+ 1/1440 (/ 1/4 (pow x 4))) (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (- (* (* x x) 1/1440) 1/48) #s(hole binary64 (* (pow x 2) (- 1/1440 (* 1/48 (/ 1 (pow x 2))))))) |
#s(approx (sin x) #s(hole binary64 (sin x))) |
#s(approx (* (neg eps) (sin x)) #s(hole binary64 (* -1 (* eps (sin x))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* 1/120 (pow x 5)))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* 1/120 (pow x 4)))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (* 1/120 (pow x 2)))) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* 1/6 (* eps (pow x 3))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow x 3) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow x 3) (- (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))) (/ eps (pow x 2)))))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* 1/6 (* eps (pow x 2))))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* (pow x 2) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) #s(hole binary64 (* 1/6 (* eps x)))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) #s(hole binary64 (* x (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))) |
#s(approx (- (* (* x x) 1/4) 1/2) #s(hole binary64 (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2))))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x)))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/48 (/ 1 (pow x 2))) 1/1440))))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/48 (/ 1 (pow x 2))) (+ 1/1440 (/ 1/4 (pow x 4)))))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps)))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps)))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps)))))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (pow eps 2)) (/ eps x)) x)) (* 1/6 eps))))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) #s(hole binary64 (* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (sin x)))) |
#s(approx eps #s(hole binary64 eps)) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* eps (* x (- (* 1/6 (pow x 2)) 1))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* eps (- (* 1/6 (pow x 2)) 1)))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) #s(hole binary64 (* eps (+ (* 1/6 x) (* 1/4 eps))))) |
#s(approx (* eps eps) #s(hole binary64 (pow eps 2))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x))))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2)))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2)))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* 1/4 (* (pow eps 2) x)))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* (pow eps 2) (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps))))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) #s(hole binary64 (* (pow eps 2) (+ 1/4 (* 1/6 (/ x eps)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x)))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2)))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x))))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
(*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps) |
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#s(approx (* (* -1/2 (cos x)) eps) (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/48 binary64) eps (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/1440 binary64))) (*.f64 #s(literal 1/4 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps))) |
#s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) |
#s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) |
#s(approx (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) |
#s(approx (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x))) |
#s(approx (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x)) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) (*.f64 #s(literal 1/4 binary64) x)) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64)) x)) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x)) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) #s(literal 1/4 binary64)) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/4 binary64))) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64))) |
#s(approx (- (* (* x x) 1/1440) 1/48) #s(literal -1/48 binary64)) |
#s(approx (- (* (* x x) 1/1440) 1/48) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64))) |
#s(approx (* (* x x) 1/1440) (*.f64 (*.f64 x x) #s(literal 1/1440 binary64))) |
#s(approx (* x x) (*.f64 x x)) |
#s(approx x x) |
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) |
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)) |
#s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) |
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)) |
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)) |
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (neg.f64 eps)) x)) |
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x) (neg.f64 eps)) x)) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(literal 1 binary64)) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) #s(literal 1 binary64))) |
#s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) |
#s(approx (- (* 1/120 (* x x)) 1/6) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (neg.f64 eps)) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (-.f64 (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64)) eps)) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps)) eps) x) eps)) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps)) eps)) |
#s(approx (* eps x) (*.f64 eps x)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x))) |
#s(approx (* (* -1/2 (cos x)) eps) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (* -1/2 (cos x)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) |
#s(approx (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) #s(literal 1/1440 binary64))) |
#s(approx (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (-.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 x x))))) |
#s(approx (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (+.f64 #s(literal 1/1440 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/48 binary64) (*.f64 x x)))))) |
#s(approx (- (* (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) x) 1/2) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (-.f64 (+.f64 #s(literal 1/1440 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/48 binary64) (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/1440 binary64))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 x x))))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 1/1440 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/48 binary64) (*.f64 x x)))))) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/1440 binary64))) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 x x))))) |
#s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) (*.f64 (+.f64 #s(literal 1/1440 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/48 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x)))) |
#s(approx (- (* (* x x) 1/1440) 1/48) (*.f64 (-.f64 #s(literal 1/1440 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 x x))) (*.f64 x x))) |
#s(approx (sin x) (sin.f64 x)) |
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/120 binary64))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (*.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (*.f64 (+.f64 #s(literal 1/120 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64)))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/120 binary64))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (*.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x)))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (*.f64 (+.f64 #s(literal 1/120 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x x)))) |
#s(approx (- (* 1/120 (* x x)) 1/6) (*.f64 (*.f64 x x) #s(literal 1/120 binary64))) |
#s(approx (- (* 1/120 (* x x)) 1/6) (*.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) (*.f64 x x))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) eps) #s(literal 1/6 binary64))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (/.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 (*.f64 x x) x))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (+.f64 (fma.f64 (/.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (/.f64 (neg.f64 eps) (*.f64 x x))) (*.f64 (*.f64 x x) x))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (-.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 #s(literal 1/6 binary64) eps))) (/.f64 eps (*.f64 x x))) (*.f64 (*.f64 x x) x))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (fma.f64 (/.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 x x))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (*.f64 x x) (+.f64 (fma.f64 (/.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 #s(literal 1/6 binary64) eps)) (/.f64 (neg.f64 eps) (*.f64 x x))))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) (*.f64 (*.f64 eps x) #s(literal 1/6 binary64))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) (*.f64 (fma.f64 (/.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 #s(literal 1/6 binary64) eps)) x)) |
#s(approx (- (* (* x x) 1/4) 1/2) (*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (*.f64 x x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 eps (neg.f64 x))) (cos.f64 x))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) (neg.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/48 binary64) (*.f64 x x)) #s(literal 1/1440 binary64)) (pow.f64 x #s(literal 5 binary64))))) |
#s(approx (* (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) x) (neg.f64 (*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/48 binary64) (*.f64 x x)) #s(literal 1/1440 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (neg.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal 1/120 binary64)) (pow.f64 x #s(literal 5 binary64))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (neg.f64 (*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal 1/120 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (neg.f64 x) (*.f64 x x)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 eps eps) x) (*.f64 #s(literal -1/6 binary64) eps)))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (neg.f64 x) (*.f64 x x)) (fma.f64 #s(literal -1/6 binary64) eps (neg.f64 (/.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (/.f64 (neg.f64 eps) x)) x))))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (neg.f64 x) (*.f64 x x)) (fma.f64 #s(literal -1/6 binary64) eps (neg.f64 (/.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/4 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) x) #s(literal 1/2 binary64) eps) x))) x))))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) eps (neg.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 eps eps) (/.f64 eps x)) x))) (*.f64 x x))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) (*.f64 (neg.f64 x) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 eps eps) x) (*.f64 #s(literal -1/6 binary64) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (neg.f64 (sin.f64 x))) eps)) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (neg.f64 (sin.f64 x))) |
#s(approx eps eps) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps)) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps)) eps)) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps x) #s(literal 1/4 binary64))) #s(literal 1 binary64)) eps)) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps)) eps)) |
#s(approx (* eps eps) (*.f64 eps eps)) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (*.f64 (*.f64 eps eps) (cos.f64 x)) #s(literal -1/2 binary64))) |
#s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps)) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps)) #s(literal 1/2 binary64)) (*.f64 eps eps))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (-.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) x)) (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps eps))) |
#s(approx (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)) (*.f64 eps eps))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (-.f64 x (neg.f64 eps))) (cos.f64 x))) |
#s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 (neg.f64 eps) (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))) |
#s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (neg.f64 (/.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) eps))) #s(literal 1/2 binary64)) (*.f64 eps eps))) |
#s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (fma.f64 #s(literal 1/4 binary64) x (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) (*.f64 eps eps))) |
Compiled 17 619 to 2 525 computations (85.7% saved)
20 alts after pruning (11 fresh and 9 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 343 | 5 | 348 |
| Fresh | 2 | 6 | 8 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 5 | 5 |
| Total | 346 | 20 | 366 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 53.7% | #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
| ✓ | 99.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)) |
| ✓ | 99.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
| 99.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 #s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/1440 binary64))) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) | |
| ✓ | 99.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
| 99.4% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps)) | |
| 99.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) | |
| ✓ | 81.2% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
| ✓ | 80.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
| 80.9% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x)))) | |
| ✓ | 80.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
| 53.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) #s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/5040 binary64)))))) | |
| ✓ | 80.7% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x))) |
| 99.1% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) | |
| ✓ | 54.8% | #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
| 99.3% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) | |
| 99.5% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) | |
| 98.8% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps)))) | |
| 80.8% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps)))) | |
| 53.5% | #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) eps) #s(literal 1/6 binary64))))) |
Compiled 1 611 to 685 computations (57.5% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) eps) #s(literal 1/6 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) #s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/5040 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/1440 binary64))) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 #s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/1440 binary64))) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (*.f64 eps eps)))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (sin.f64 x)) eps)) |
3 calls:
| 7.0ms | eps |
| 7.0ms | x |
| 6.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) eps) #s(literal 1/6 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) #s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/5040 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/1440 binary64))) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 #s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/1440 binary64))) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1440 binary64) (*.f64 x x)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/1440 binary64)) #s(literal 1/48 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
3 calls:
| 8.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 7.0ms | eps |
| 6.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) eps) #s(literal 1/6 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) #s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/5040 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(approx (+ (* (- (* 1/1440 (* x x)) 1/48) (* x x)) 1/4) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/1440 binary64))) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 #s(approx (+ (* (- (* (* x x) 1/1440) 1/48) (* x x)) 1/4) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/1440 binary64))) x) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)) |
3 calls:
| 16.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 6.0ms | x |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 99.7% | 1 | x |
| 99.7% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) eps) #s(literal 1/6 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) #s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/5040 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))) eps)) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (* -1/2 (cos x)) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)) |
3 calls:
| 19.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 5.0ms | eps |
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 99.7% | 1 | x |
| 99.7% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) eps) #s(literal 1/6 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) #s(approx (* (+ (* (- (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) 1/6) (* x x)) 1) x) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/5040 binary64)))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 (*.f64 #s(literal 1/6 binary64) eps) x)) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
3 calls:
| 5.0ms | eps |
| 5.0ms | x |
| 3.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 99.5% | 1 | x |
| 99.5% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) eps) #s(literal 1/6 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 #s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) (fma.f64 (neg.f64 eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))) |
3 calls:
| 3.0ms | x |
| 3.0ms | eps |
| 2.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.3% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 99.3% | 1 | x |
| 99.3% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))) |
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* -1/2 (cos x)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* eps x) 1/6) (* (* eps eps) 1/4)) x) (neg eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (*.f64 (*.f64 x x) x) eps) #s(literal 1/6 binary64))))) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps)) |
3 calls:
| 5.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 2.0ms | eps |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.1% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 99.1% | 1 | x |
| 99.1% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
Total -16.6b remaining (-134%)
Threshold costs -16.6b (-134%)
| Inputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x))) |
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (* -1/2 (cos x)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)) |
| Outputs |
|---|
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) x))) |
3 calls:
| 1.0ms | eps |
| 1.0ms | x |
| 1.0ms | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 80.7% | 1 | (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) |
| 80.7% | 1 | x |
| 80.7% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| 1× | fuel |
Compiled 227 to 81 computations (64.3% saved)
Compiled 264 to 112 computations (57.6% saved)
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