
Time bar (total: 8.3s)
| 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)
| 2.4s | 26 021× | 0 | invalid |
| 642.0ms | 5 555× | 1 | valid |
| 256.0ms | 2 701× | 0 | valid |
ival-sin: 759.0ms (34.9% of total)ival-add!: 545.0ms (25.1% of total)ival-fabs: 234.0ms (10.8% of total)ival-<: 205.0ms (9.4% of total)adjust: 136.0ms (6.3% of total)ival-mult!: 119.0ms (5.5% of total)ival-sub!: 94.0ms (4.3% of total)ival-and: 68.0ms (3.1% of total)ival-assert: 13.0ms (0.6% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 221 | 1 | (3.180295040117063e-265 2.0031290455432023e-267) | 4 | (-4.8513959543983726e-144 7.799302704606162e-146) | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 0 | 0 | - | 0 | - | (sin.f64 (+.f64 x eps)) |
| 0 | 0 | - | 0 | - | eps |
| 0 | 0 | - | 0 | - | (+.f64 x eps) |
| 0 | 0 | - | 0 | - | (sin.f64 x) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) | cancellation | 218 | 6 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 217 | 4 |
| - | 1 | 34 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 217 | 4 | 0 |
| - | 1 | 2 | 32 |
| number | freq |
|---|---|
| 0 | 38 |
| 1 | 218 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 28.0ms | 310× | 1 | valid |
| 9.0ms | 200× | 0 | valid |
| 1.0ms | 2× | 3 | valid |
Compiled 47 to 22 computations (53.2% saved)
ival-sin: 12.0ms (55.1% of total)adjust: 6.0ms (27.6% of total)ival-sub!: 2.0ms (9.2% of total)ival-add!: 2.0ms (9.2% of total)Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 50 |
| 1 | 25 | 50 |
| 2 | 32 | 50 |
| 3 | 40 | 50 |
| 4 | 53 | 50 |
| 5 | 81 | 50 |
| 6 | 140 | 50 |
| 7 | 385 | 50 |
| 8 | 1451 | 50 |
| 9 | 5230 | 50 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 11 | 7 |
| 0 | 11 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Outputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 65.8% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(sin.f64 x) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps))))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos 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 (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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x)))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x)))) |
#s(approx (+ x eps) #s(hole binary64 x)) |
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x))))) |
#s(approx (sin x) #s(hole binary64 (sin x))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x)))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x))))) |
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x))))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))) |
#s(approx eps #s(hole binary64 eps)) |
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x)))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- 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 | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x)) |
| 1.0ms | eps | @ | inf | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x)) |
| 1.0ms | x | @ | -inf | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x)) |
| 1.0ms | eps | @ | -inf | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x)) |
| 1.0ms | eps | @ | 0 | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 150 | 538 |
| 0 | 155 | 526 |
| 1 | 931 | 520 |
| 0 | 8567 | 489 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(sin.f64 x) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps))))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos 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 (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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x)))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x)))) |
#s(approx (+ x eps) #s(hole binary64 x)) |
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x))))) |
#s(approx (sin x) #s(hole binary64 (sin x))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x)))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x))))) |
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x))))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))) |
#s(approx eps #s(hole binary64 eps)) |
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x)))) |
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- 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 (+.f64 eps x) x) #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) |
(*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) |
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))) |
(fma.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))) |
(fma.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) |
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))))) |
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x) (sin.f64 x))) |
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x))) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))) |
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))) |
(+.f64 (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x))) (*.f64 (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))) (fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps)))) |
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x)))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (sin.f64 x)))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x)) (-.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps)))))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (sin.f64 x))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (sin.f64 x)))))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x)))) |
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (cos.f64 eps) (sin.f64 x))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps)))) |
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x)))) |
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps)))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(sin.f64 (+.f64 eps x)) |
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps))) |
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))) |
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 eps)) (sin.f64 x))) |
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps))) |
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps)))) |
(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps))) |
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x)))) |
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (sin.f64 x))) |
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps))) |
(/.f64 (neg.f64 (*.f64 (-.f64 eps x) (+.f64 eps x))) (neg.f64 (-.f64 eps x))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps eps (*.f64 x (-.f64 x eps))))) |
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps)) |
(/.f64 (*.f64 (-.f64 eps x) (+.f64 eps x)) (-.f64 eps x)) |
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) |
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) |
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) |
(-.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 eps eps (*.f64 x (-.f64 x eps))))) |
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) |
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x))) |
(-.f64 eps (neg.f64 x)) |
(-.f64 x (neg.f64 eps)) |
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) |
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps eps (*.f64 x (-.f64 x eps))))) |
(+.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 x) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) |
#s(approx (sin (+ x eps)) (sin.f64 eps)) |
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 eps) x (sin.f64 eps))) |
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps))) |
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (cos.f64 eps)) x (sin.f64 eps))) |
#s(approx (+ x eps) eps) |
#s(approx (+ x eps) (+.f64 eps x)) |
#s(approx x x) |
#s(approx (sin x) x) |
#s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)) |
#s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x)) |
#s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) |
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x))) |
#s(approx (+ x eps) x) |
#s(approx (+ x eps) (fma.f64 (/.f64 eps x) x x)) |
#s(approx (sin x) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) |
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x))) |
#s(approx (+ x eps) (*.f64 (neg.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 eps x) #s(literal -1 binary64)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (sin (+ x eps)) (sin.f64 x)) |
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 x) eps (sin.f64 x))) |
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x))) |
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (sin.f64 x))) |
#s(approx eps eps) |
#s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) |
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x))) |
#s(approx (+ x eps) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1 binary64)))) |
Compiled 1 964 to 373 computations (81% saved)
6 alts after pruning (5 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 98 | 5 | 103 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 98 | 6 | 104 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 65.8% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| ▶ | 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) |
| ▶ | 100.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
| ▶ | 99.9% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| ▶ | 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| ▶ | 98.2% | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
Compiled 179 to 128 computations (28.5% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
x |
eps |
#s(literal -1/6 binary64) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
#s(literal -1/2 binary64) |
(sin.f64 x) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(sin.f64 eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 (sin.f64 x) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(*.f64 (sin.f64 eps) x) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(cos.f64 eps) |
#s(literal 1 binary64) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2)))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2)))))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps)))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2))))) |
#s(approx (* (cos x) eps) #s(hole binary64 eps)) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2)))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))))) |
#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 x #s(hole binary64 x)) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 x))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)))) |
#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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (sin eps))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1))))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (- (cos eps) 1))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
#s(approx (* (sin eps) x) #s(hole binary64 (* x (sin eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x)))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x)))) |
#s(approx (cos x) #s(hole binary64 (cos x))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 (sin x)))) |
#s(approx (sin x) #s(hole binary64 (sin x))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x)))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x)))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* -1/2 (* (pow x 2) (sin eps))))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x))))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x))))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1/2 (* x (sin eps))))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x)))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps)))))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x)))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x)))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x)))) |
#s(approx eps #s(hole binary64 eps)) |
#s(approx (sin eps) #s(hole binary64 eps)) |
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2)))))) |
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))))) |
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x)))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2)))))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6))))))))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1/2 (* eps x)))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 eps) (* -1/2 x))))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2)))))) |
#s(approx (* (sin eps) x) #s(hole binary64 (* eps x))) |
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* -1/6 (* (pow eps 2) x)))))) |
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x)))))))) |
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x))))))))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2)))) |
#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)) |
#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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 (* eps (cos x))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (sin eps) #s(hole binary64 (sin eps))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1))) |
#s(approx (cos eps) #s(hole binary64 (cos eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x)))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x)))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | eps | @ | 0 | ((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) x eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (- (cos eps) 1) (cos eps) 1) |
| 5.0ms | x | @ | inf | ((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) x eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (- (cos eps) 1) (cos eps) 1) |
| 4.0ms | x | @ | -inf | ((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) x eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (- (cos eps) 1) (cos eps) 1) |
| 4.0ms | eps | @ | -inf | ((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) x eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (- (cos eps) 1) (cos eps) 1) |
| 4.0ms | x | @ | 0 | ((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) x eps -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (- (cos eps) 1) (cos eps) 1) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 527 | 2906 |
| 0 | 567 | 2858 |
| 1 | 3196 | 2858 |
| 0 | 8137 | 2749 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
x |
eps |
#s(literal -1/6 binary64) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
#s(literal -1/2 binary64) |
(sin.f64 x) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(sin.f64 eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 (sin.f64 x) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(*.f64 (sin.f64 eps) x) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(cos.f64 eps) |
#s(literal 1 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2)))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2))))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2)))))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps)))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2))))) |
#s(approx (* (cos x) eps) #s(hole binary64 eps)) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2)))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))))) |
#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 x #s(hole binary64 x)) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 x))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)))) |
#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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (sin eps))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1))))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (- (cos eps) 1))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
#s(approx (* (sin eps) x) #s(hole binary64 (* x (sin eps)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x)))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x)))) |
#s(approx (cos x) #s(hole binary64 (cos x))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 (sin x)))) |
#s(approx (sin x) #s(hole binary64 (sin x))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x)))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x)))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* -1/2 (* (pow x 2) (sin eps))))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x))))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x))))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1/2 (* x (sin eps))))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x)))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps)))))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x)))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x)))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x)))) |
#s(approx eps #s(hole binary64 eps)) |
#s(approx (sin eps) #s(hole binary64 eps)) |
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2)))))) |
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))))) |
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x)))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2)))))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6))))))))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* -1/2 (* eps x)))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 eps) (* -1/2 x))))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2)))))) |
#s(approx (* (sin eps) x) #s(hole binary64 (* eps x))) |
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* -1/6 (* (pow eps 2) x)))))) |
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x)))))))) |
#s(approx (* (sin eps) x) #s(hole binary64 (* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x))))))))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2)))) |
#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)) |
#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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 (* eps (cos x))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (sin eps) #s(hole binary64 (sin eps))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))))) |
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1))) |
#s(approx (cos eps) #s(hole binary64 (cos eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x)))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x)))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 eps (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))) |
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)) |
(fma.f64 (cos.f64 x) eps (*.f64 eps (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps))) |
(fma.f64 eps (cos.f64 x) (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)) |
(fma.f64 eps (cos.f64 x) (*.f64 eps (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps))) |
(+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)) |
(+.f64 (*.f64 (cos.f64 x) eps) (*.f64 eps (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 (cos.f64 x) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))) |
(/.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64))) (-.f64 (cos.f64 x) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))) |
(/.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps))))) |
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(*.f64 (sin.f64 eps) x) |
(*.f64 x (sin.f64 eps)) |
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) (neg.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 1 binary64)))))) |
(/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (+.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(/.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 1 binary64))))) |
(-.f64 (/.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (+.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)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 1 binary64)))))) |
(-.f64 (cos.f64 eps) #s(literal 1 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))))) |
(sin.f64 (fma.f64 #s(literal -1 binary64) eps (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 eps (/.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 (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps (*.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 eps x (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) |
#s(approx (* (cos x) eps) eps) |
#s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps)) |
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) |
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) |
#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 x x) |
#s(approx (* -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) x)) |
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) |
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x)) |
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/10080 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x)) |
#s(approx (sin 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 (*.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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) |
#s(approx (* (sin x) eps) (*.f64 eps x)) |
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)) |
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x)) |
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x)) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (sin.f64 eps)) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))) |
#s(approx (* (sin eps) x) (*.f64 (sin.f64 eps) x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps)) |
#s(approx (cos x) (cos.f64 x)) |
#s(approx (* -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
#s(approx (sin x) (sin.f64 x)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))) |
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps)) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sin.f64 eps))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) (*.f64 x x))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (-.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (+.f64 (/.f64 (sin.f64 eps) (*.f64 x x)) (/.f64 (cos.f64 eps) x))) (pow.f64 x #s(literal -1 binary64))) (*.f64 x x))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x))) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 eps) x) #s(literal -1 binary64) (neg.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)))) x))) (*.f64 x x))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (neg.f64 x) (fma.f64 #s(literal 1/2 binary64) (sin.f64 eps) (/.f64 (neg.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (cos.f64 x) eps)) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (cos.f64 x)) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
#s(approx eps eps) |
#s(approx (sin eps) eps) |
#s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) |
#s(approx (sin eps) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 eps eps)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) |
#s(approx (sin eps) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) (*.f64 eps eps)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (cos.f64 x) eps)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (cos.f64 x)) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps)) |
#s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (*.f64 (+.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) x)) eps (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps)) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) eps)) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps)) |
#s(approx (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal 1/12 binary64) x)) eps) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps)) |
#s(approx (* (sin eps) x) (*.f64 eps x)) |
#s(approx (* (sin eps) x) (*.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/6 binary64) x) eps)) |
#s(approx (* (sin eps) x) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 eps eps)) x (*.f64 #s(literal -1/6 binary64) x)) (*.f64 eps eps) x) eps)) |
#s(approx (* (sin eps) x) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 eps eps)) x (*.f64 #s(literal 1/120 binary64) x)) (*.f64 eps eps) (*.f64 #s(literal -1/6 binary64) x)) (*.f64 eps eps) x) eps)) |
#s(approx (- (cos eps) 1) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
#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) #s(literal 1 binary64)) |
#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 (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (*.f64 #s(literal -1/6 binary64) (pow.f64 eps #s(literal 3 binary64))) (cos.f64 x))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)))) (pow.f64 eps #s(literal 3 binary64)))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) (cos.f64 x))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 eps eps))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)))) (*.f64 eps eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)) |
#s(approx (sin eps) (sin.f64 eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (*.f64 eps eps))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) |
#s(approx (- (cos eps) 1) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
#s(approx (cos eps) (cos.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (cos.f64 x) #s(literal 1/6 binary64))))) |
#s(approx (* (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) #s(literal 1/6 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))))) |
#s(approx (+ (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps))) eps))) (*.f64 eps eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (cos.f64 x) #s(literal 1/6 binary64))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps))))) |
Compiled 12 033 to 1 542 computations (87.2% saved)
19 alts after pruning (17 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 354 | 17 | 371 |
| Fresh | 0 | 0 | 0 |
| Picked | 3 | 2 | 5 |
| Done | 1 | 0 | 1 |
| Total | 358 | 19 | 377 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))) |
| 100.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) | |
| 100.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) | |
| ✓ | 99.9% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| 99.8% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| ▶ | 99.8% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| 99.8% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| 99.6% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| 99.6% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) | |
| ✓ | 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) | |
| 99.3% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) | |
| 99.2% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) | |
| 98.9% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) | |
| ▶ | 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
| ▶ | 98.2% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
| ▶ | 99.3% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
| 99.2% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) | |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
Compiled 972 to 634 computations (34.8% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))) |
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)) |
(cos.f64 x) |
x |
eps |
(*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps) |
(*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) |
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(*.f64 (cos.f64 x) eps) |
#s(literal -1/6 binary64) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
#s(literal -1/2 binary64) |
(sin.f64 x) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps) |
(*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) |
(fma.f64 eps x (*.f64 eps eps)) |
(*.f64 eps eps) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps) |
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) |
(fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) |
#s(literal -1/720 binary64) |
(*.f64 (*.f64 x x) eps) |
(*.f64 x x) |
(*.f64 #s(literal 1/24 binary64) eps) |
#s(literal 1/24 binary64) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 #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)) 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 (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(literal 1 binary64) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (* -1/6 (pow eps 3))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3)))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (pow eps 3)))))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (+ (* 1/12 (* (pow eps 2) x)) (* 1/12 (pow eps 3))))))))))) |
#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 x #s(hole binary64 x)) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1/6 (pow eps 3)))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 3) x))))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* 1/12 (pow eps 3))))))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* -1/6 (pow eps 2)))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps)))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2))))) |
#s(approx (* (cos x) eps) #s(hole binary64 eps)) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2)))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 x))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)))) |
#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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 eps)) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* -1/2 (pow eps 2)))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (pow eps 2))) |
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (+ (* eps x) (pow eps 2)))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 eps)) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2)))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) #s(hole binary64 (* 1/24 eps))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) #s(hole binary64 (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))) |
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2)))) |
#s(approx (* x x) #s(hole binary64 (pow x 2))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 x)) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2)))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))) |
#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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x)))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ (* eps (cos x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
#s(approx (cos x) #s(hole binary64 (cos x))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 (sin x)))) |
#s(approx (sin x) #s(hole binary64 (sin x))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x)))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2))))))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* -1/2 (* eps x)))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x)))))) |
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* eps x))) |
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* x (+ eps (/ (pow eps 2) x))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* -1/720 (* eps (pow x 6))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6)))))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (* -1/720 (* eps (pow x 4))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) #s(hole binary64 (* -1/720 (* eps (pow x 2))))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x)))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* 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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x)))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps))))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x))))))) |
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) 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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* eps (cos x)))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))) |
#s(approx eps #s(hole binary64 eps)) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* -1/2 (* eps (sin x))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x)))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x)))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2)))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* eps (+ (* -1/2 eps) (* -1/2 x))))) |
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* eps (+ eps x)))) |
#s(approx (* eps eps) #s(hole binary64 (pow eps 2))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) #s(hole binary64 (* eps (+ 1/24 (* -1/720 (pow x 2)))))) |
#s(approx (* 1/24 eps) #s(hole binary64 (* 1/24 eps))) |
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 (* eps (cos x))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x)))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2)))) |
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x)))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) #s(hole binary64 (* -1 (* eps (- (* 1/720 (pow x 2)) 1/24))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 10.0ms | eps | @ | inf | ((- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (cos x) x eps (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* -1/2 (+ (* eps x) (* eps eps))) (+ (* eps x) (* eps eps)) (* eps eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) -1/720 (* (* x x) eps) (* x x) (* 1/24 eps) 1/24 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) 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) (* 1/120 (* x x)) 1/120 1/6 1) |
| 8.0ms | x | @ | inf | ((- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (cos x) x eps (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* -1/2 (+ (* eps x) (* eps eps))) (+ (* eps x) (* eps eps)) (* eps eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) -1/720 (* (* x x) eps) (* x x) (* 1/24 eps) 1/24 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) 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) (* 1/120 (* x x)) 1/120 1/6 1) |
| 6.0ms | eps | @ | -inf | ((- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (cos x) x eps (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* -1/2 (+ (* eps x) (* eps eps))) (+ (* eps x) (* eps eps)) (* eps eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) -1/720 (* (* x x) eps) (* x x) (* 1/24 eps) 1/24 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) 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) (* 1/120 (* x x)) 1/120 1/6 1) |
| 5.0ms | x | @ | -inf | ((- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (cos x) x eps (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* -1/2 (+ (* eps x) (* eps eps))) (+ (* eps x) (* eps eps)) (* eps eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) -1/720 (* (* x x) eps) (* x x) (* 1/24 eps) 1/24 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) 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) (* 1/120 (* x x)) 1/120 1/6 1) |
| 5.0ms | eps | @ | 0 | ((- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (cos x) x eps (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) -1/6 (* -1/2 (sin x)) -1/2 (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* -1/2 (+ (* eps x) (* eps eps))) (+ (* eps x) (* eps eps)) (* eps eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) -1/720 (* (* x x) eps) (* x x) (* 1/24 eps) 1/24 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) 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) (* 1/120 (* x x)) 1/120 1/6 1) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 605 | 4346 |
| 0 | 660 | 4166 |
| 1 | 3374 | 4164 |
| 0 | 8169 | 3983 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))) |
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)) |
(cos.f64 x) |
x |
eps |
(*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps) |
(*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) |
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(*.f64 (cos.f64 x) eps) |
#s(literal -1/6 binary64) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
#s(literal -1/2 binary64) |
(sin.f64 x) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps)) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps) |
(*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) |
(fma.f64 eps x (*.f64 eps eps)) |
(*.f64 eps eps) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps) |
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) |
(fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) |
#s(literal -1/720 binary64) |
(*.f64 (*.f64 x x) eps) |
(*.f64 x x) |
(*.f64 #s(literal 1/24 binary64) eps) |
#s(literal 1/24 binary64) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 #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)) 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 (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(literal 1 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (* -1/6 (pow eps 3))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3)))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (pow eps 3)))))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (+ (* 1/12 (* (pow eps 2) x)) (* 1/12 (pow eps 3))))))))))) |
#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 x #s(hole binary64 x)) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1/6 (pow eps 3)))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 3) x))))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* 1/12 (pow eps 3))))))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* -1/6 (pow eps 2)))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps)))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2))))) |
#s(approx (* (cos x) eps) #s(hole binary64 eps)) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2)))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 x))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)))) |
#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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 eps)) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* -1/2 (pow eps 2)))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (pow eps 2))) |
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (+ (* eps x) (pow eps 2)))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 eps)) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2)))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) #s(hole binary64 (* 1/24 eps))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) #s(hole binary64 (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))) |
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2)))) |
#s(approx (* x x) #s(hole binary64 (pow x 2))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 x)) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2)))))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))) |
#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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x)))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ (* eps (cos x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
#s(approx (cos x) #s(hole binary64 (cos x))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 (sin x)))) |
#s(approx (sin x) #s(hole binary64 (sin x))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x)))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2))))))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* -1/2 (* eps x)))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x)))))) |
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* eps x))) |
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* x (+ eps (/ (pow eps 2) x))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* -1/720 (* eps (pow x 6))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6)))))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (* -1/720 (* eps (pow x 4))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) #s(hole binary64 (* -1/720 (* eps (pow x 2))))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x)))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* 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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x)))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps))))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x))))))) |
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) 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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* eps (cos x)))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))) |
#s(approx eps #s(hole binary64 eps)) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* -1/2 (* eps (sin x))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x)))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x)))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2)))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* eps (+ (* -1/2 eps) (* -1/2 x))))) |
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* eps (+ eps x)))) |
#s(approx (* eps eps) #s(hole binary64 (pow eps 2))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) #s(hole binary64 (* eps (+ 1/24 (* -1/720 (pow x 2)))))) |
#s(approx (* 1/24 eps) #s(hole binary64 (* 1/24 eps))) |
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 (* eps (cos x))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x)))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2)))) |
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x)))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) #s(hole binary64 (* -1 (* eps (- (* 1/720 (pow x 2)) 1/24))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 eps (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps) #s(literal 2 binary64))) (-.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))))) |
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x |
eps |
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(*.f64 eps (cos.f64 x)) |
#s(literal -1/6 binary64) |
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(*.f64 (sin.f64 x) #s(literal -1/2 binary64)) |
#s(literal -1/2 binary64) |
(sin.f64 x) |
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#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps) |
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#s(literal 1 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (+.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64))) eps)) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (pow.f64 eps #s(literal 3 binary64)) (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64))) eps)) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (fma.f64 (*.f64 eps eps) x (pow.f64 eps #s(literal 3 binary64))) (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64))) eps)) |
#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 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx x x) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (fma.f64 (fma.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 (*.f64 eps eps) x (pow.f64 eps #s(literal 3 binary64)))) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) x) (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 (+.f64 eps x) eps)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) |
#s(approx (* (cos x) eps) eps) |
#s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps)) |
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) |
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) |
#s(approx (* -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) x)) |
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) |
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x)) |
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/10080 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x)) |
#s(approx (sin 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 (*.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 (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) eps) -1/2) (cos x)) eps) eps) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) x) (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) eps) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64))) |
#s(approx (+ (* eps x) (* eps eps)) (*.f64 eps eps)) |
#s(approx (+ (* eps x) (* eps eps)) (*.f64 (+.f64 eps x) eps)) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) eps) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps)) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) eps))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps)) |
#s(approx (* (* x x) eps) (*.f64 (*.f64 x x) eps)) |
#s(approx (* x x) (*.f64 x x)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) |
#s(approx (* (sin x) eps) (*.f64 eps x)) |
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)) |
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x)) |
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x)) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) 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 (+ (* (- (* 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 (*.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 (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (cos x) (cos.f64 x)) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps)) |
#s(approx (* -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
#s(approx (sin x) (sin.f64 x)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 eps eps) x) eps)) (*.f64 x x))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 eps eps) x) eps) (/.f64 eps (*.f64 x x))) (*.f64 x x))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (*.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 eps eps) x) eps)) x)) |
#s(approx (+ (* eps x) (* eps eps)) (*.f64 eps x)) |
#s(approx (+ (* eps x) (* eps eps)) (*.f64 (+.f64 (/.f64 (*.f64 eps eps) x) eps) x)) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) (*.f64 (*.f64 #s(literal -1/720 binary64) eps) (pow.f64 x #s(literal 6 binary64)))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) (*.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) eps)))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) (*.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) eps))))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) (*.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/720 binary64) eps (fma.f64 (/.f64 #s(literal 1/24 binary64) x) (/.f64 eps x) (/.f64 eps (pow.f64 x #s(literal 6 binary64)))))))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) eps) #s(literal -1/720 binary64))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) eps)))) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) eps))) (pow.f64 x #s(literal 4 binary64)))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/720 binary64))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) eps)) (*.f64 x x))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))) |
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps)) |
#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 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/6 binary64))) (pow.f64 x #s(literal 5 binary64)))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/120 binary64)) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/6 binary64))) (pow.f64 x #s(literal 5 binary64)))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/120 binary64))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (*.f64 (-.f64 #s(literal 1/120 binary64) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/6 binary64))) (pow.f64 x #s(literal 4 binary64)))) |
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/120 binary64)) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/6 binary64))) (pow.f64 x #s(literal 4 binary64)))) |
#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 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/6 binary64))) (*.f64 x x))) |
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 eps eps) (/.f64 (neg.f64 eps) x)) x))) (*.f64 x x))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (*.f64 (neg.f64 x) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (*.f64 eps eps) x) eps)))) |
#s(approx (+ (* eps x) (* eps eps)) (*.f64 (neg.f64 x) (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (*.f64 eps eps) x) eps)))) |
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (neg.f64 (*.f64 (-.f64 (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/6 binary64)) #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 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/6 binary64)) #s(literal 1/120 binary64)) (pow.f64 x #s(literal -4 binary64))) (pow.f64 x #s(literal 5 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (sin.f64 x) eps) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (cos.f64 x) eps)) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx eps eps) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (cos.f64 x) eps)) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (*.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) eps)) |
#s(approx (+ (* eps x) (* eps eps)) (*.f64 (+.f64 eps x) eps)) |
#s(approx (* eps eps) (*.f64 eps eps)) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps)) |
#s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) eps)) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps)) |
#s(approx (* 1/24 eps) (*.f64 #s(literal 1/24 binary64) eps)) |
#s(approx (* -1/2 eps) (*.f64 #s(literal -1/2 binary64) eps)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (cos.f64 x)) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)) (cos.f64 x))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (*.f64 eps eps)))) (pow.f64 eps #s(literal 3 binary64)))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)) (cos.f64 x))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) (cos.f64 x))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 eps eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (*.f64 eps eps))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) (*.f64 eps eps))) |
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (*.f64 (-.f64 (*.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) |
#s(approx (+ (* eps x) (* eps eps)) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) (*.f64 eps eps))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal 1/6 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1 binary64)) eps))) (*.f64 eps eps))) |
#s(approx (+ (* (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (* x x)) eps) (*.f64 (neg.f64 eps) (-.f64 (*.f64 (fma.f64 (-.f64 (*.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 (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.f64 #s(literal 1/720 binary64) (*.f64 x x)) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)))) |
#s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 (neg.f64 eps) (-.f64 (*.f64 #s(literal 1/720 binary64) (*.f64 x x)) #s(literal 1/24 binary64)))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps))))) |
Compiled 24 031 to 3 026 computations (87.4% saved)
21 alts after pruning (17 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 584 | 10 | 594 |
| Fresh | 5 | 7 | 12 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 2 | 2 |
| Total | 592 | 21 | 613 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))) |
| 100.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) | |
| 100.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) | |
| ✓ | 99.9% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| 99.8% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| ✓ | 99.8% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) | |
| 99.3% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) | |
| ▶ | 99.8% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| 99.6% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) #s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| ✓ | 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) | |
| 99.3% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) | |
| ▶ | 99.2% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) | |
| ▶ | 5.0% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
| ✓ | 98.2% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
| 99.2% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) | |
| 99.3% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) | |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) | |
| ▶ | 99.3% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
Compiled 1 304 to 825 computations (36.7% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))) |
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)) |
(cos.f64 x) |
x |
eps |
(*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps) |
(*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) |
(fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) |
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(*.f64 x x) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
#s(literal -1/6 binary64) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(sin.f64 x) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) |
(*.f64 (*.f64 x x) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
(*.f64 #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))) eps) |
#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))) |
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/24 binary64) (*.f64 x x)) |
#s(literal 1/24 binary64) |
#s(literal 1/2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps)) |
(+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps) |
(*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) |
(fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) |
(*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) |
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) |
#s(literal -1/720 binary64) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) |
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) |
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (* -1/6 (pow eps 3))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3)))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (pow eps 3)))))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (+ (* 1/12 (* (pow eps 2) x)) (* 1/12 (pow eps 3))))))))))) |
#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 x #s(hole binary64 x)) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1/6 (pow eps 3)))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 3) x))))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* 1/12 (pow eps 3))))))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* -1/6 (pow eps 2)))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps)))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2))))) |
#s(approx (* (cos x) eps) #s(hole binary64 eps)) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2)))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))))) |
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 1)) |
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2))))) |
#s(approx (* x x) #s(hole binary64 (pow x 2))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 x))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)))) |
#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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 eps)) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))))) |
#s(approx (* (* (* x x) eps) -1/2) #s(hole binary64 (* -1/2 (* eps (pow x 2))))) |
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2)))) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 1)) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2))))) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))) |
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 -1/2)) |
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 (- (* 1/24 (pow x 2)) 1/2))) |
#s(approx (* 1/24 (* x x)) #s(hole binary64 (* 1/24 (pow x 2)))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 eps)) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2)))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* -1/2 (* eps (pow x 2))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) #s(hole binary64 (* 1/24 (* eps x)))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) #s(hole binary64 (* x (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) #s(hole binary64 (* 1/24 eps))) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) #s(hole binary64 (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))) |
#s(approx (+ (* (* x x) -1/720) 1/24) #s(hole binary64 1/24)) |
#s(approx (+ (* (* x x) -1/720) 1/24) #s(hole binary64 (+ 1/24 (* -1/720 (pow x 2))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))))) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 x)) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2)))))) |
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 1)) |
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x)))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ (* eps (cos x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
#s(approx (cos x) #s(hole binary64 (cos x))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x)))) |
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* -1/2 (pow x 2)))) |
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 (sin x)))) |
#s(approx (sin x) #s(hole binary64 (sin x))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x)))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2))))))) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* 1/24 (pow x 4)))) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))) |
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 (* 1/24 (pow x 2)))) |
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* -1/720 (* eps (pow x 6))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6)))))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* -1/720 (* eps (pow x 6))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (* -1/720 (* eps (pow x 4))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) #s(hole binary64 (* -1/720 (* eps (pow x 3))))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) #s(hole binary64 (* (pow x 3) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) #s(hole binary64 (* -1/720 (* eps (pow x 2))))) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (+ (* (* x x) -1/720) 1/24) #s(hole binary64 (* -1/720 (pow x 2)))) |
#s(approx (+ (* (* x x) -1/720) 1/24) #s(hole binary64 (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x)))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x)))) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* -1/6 (pow x 3)))) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))) |
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 (* -1/6 (pow x 2)))) |
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/6)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x)))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps))))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1/24 (/ eps (pow x 2))) (* 1/720 eps)))))) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* eps (cos x)))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))) |
#s(approx eps #s(hole binary64 eps)) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* -1/2 (* eps (sin x))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x)))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x)))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2)))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* eps (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) #s(hole binary64 (* eps (* x (+ 1/24 (* -1/720 (pow x 2))))))) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) #s(hole binary64 (* eps (+ 1/24 (* -1/720 (pow x 2)))))) |
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 (* eps (cos x))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x)))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x)))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))) 1))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* -1 (* eps (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | eps | @ | -inf | ((- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (cos x) x eps (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 -1/6 (* -1/2 (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* (* (* x x) eps) -1/2) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* (* (+ (* (* x x) -1/720) 1/24) eps) x) (* (+ (* (* x x) -1/720) 1/24) eps) (+ (* (* x x) -1/720) 1/24) -1/720 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1)) |
| 5.0ms | eps | @ | inf | ((- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (cos x) x eps (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 -1/6 (* -1/2 (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* (* (* x x) eps) -1/2) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* (* (+ (* (* x x) -1/720) 1/24) eps) x) (* (+ (* (* x x) -1/720) 1/24) eps) (+ (* (* x x) -1/720) 1/24) -1/720 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1)) |
| 5.0ms | x | @ | inf | ((- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (cos x) x eps (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 -1/6 (* -1/2 (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* (* (* x x) eps) -1/2) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* (* (+ (* (* x x) -1/720) 1/24) eps) x) (* (+ (* (* x x) -1/720) 1/24) eps) (+ (* (* x x) -1/720) 1/24) -1/720 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1)) |
| 5.0ms | eps | @ | 0 | ((- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (cos x) x eps (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 -1/6 (* -1/2 (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* (* (* x x) eps) -1/2) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* (* (+ (* (* x x) -1/720) 1/24) eps) x) (* (+ (* (* x x) -1/720) 1/24) eps) (+ (* (* x x) -1/720) 1/24) -1/720 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1)) |
| 5.0ms | x | @ | -inf | ((- (sin (+ x eps)) (sin x)) (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (cos x) x eps (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 -1/6 (* -1/2 (sin x)) (sin x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* (* (* x x) eps) -1/2) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* (* (+ (* (* x x) -1/720) 1/24) eps) x) (* (+ (* (* x x) -1/720) 1/24) eps) (+ (* (* x x) -1/720) 1/24) -1/720 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 617 | 4681 |
| 0 | 671 | 4538 |
| 1 | 3414 | 4535 |
| 0 | 8207 | 4310 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))) |
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)) |
(cos.f64 x) |
x |
eps |
(*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps) |
(*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) |
(fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) |
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(*.f64 x x) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
#s(literal -1/6 binary64) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(sin.f64 x) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) |
(*.f64 (*.f64 x x) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
(*.f64 #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))) eps) |
#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))) |
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/24 binary64) (*.f64 x x)) |
#s(literal 1/24 binary64) |
#s(literal 1/2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps)) |
(+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps) |
(*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) |
(fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) |
(*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) |
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) |
#s(literal -1/720 binary64) |
(*.f64 #s(literal -1/2 binary64) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) |
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x) |
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (* -1/6 (pow eps 3))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3)))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (pow eps 3)))))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ eps (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (+ (* 1/12 (* (pow eps 2) x)) (* 1/12 (pow eps 3))))))))))) |
#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 x #s(hole binary64 x)) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1/6 (pow eps 3)))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* -1/6 (pow eps 3))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 3) x))))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (+ (* -1/6 (pow eps 3)) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* 1/12 (pow eps 3))))))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* -1/6 (pow eps 2)))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps)))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2))))) |
#s(approx (* (cos x) eps) #s(hole binary64 eps)) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2)))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))))) |
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 1)) |
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2))))) |
#s(approx (* x x) #s(hole binary64 (pow x 2))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 x))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)))) |
#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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 eps)) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))))) |
#s(approx (* (* (* x x) eps) -1/2) #s(hole binary64 (* -1/2 (* eps (pow x 2))))) |
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2)))) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 1)) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2))))) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))) |
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 -1/2)) |
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 (- (* 1/24 (pow x 2)) 1/2))) |
#s(approx (* 1/24 (* x x)) #s(hole binary64 (* 1/24 (pow x 2)))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 eps)) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2)))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* -1/2 (* eps (pow x 2))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) #s(hole binary64 (* 1/24 (* eps x)))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) #s(hole binary64 (* x (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) #s(hole binary64 (* 1/24 eps))) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) #s(hole binary64 (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))) |
#s(approx (+ (* (* x x) -1/720) 1/24) #s(hole binary64 1/24)) |
#s(approx (+ (* (* x x) -1/720) 1/24) #s(hole binary64 (+ 1/24 (* -1/720 (pow x 2))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2))))))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps))))))))) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 x)) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2)))))) |
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 1)) |
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x)))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (+ (* eps (cos x)) (* (pow eps 2) (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
#s(approx (cos x) #s(hole binary64 (cos x))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) |
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x)))) |
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* -1/2 (pow x 2)))) |
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2)))) |
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 (sin x)))) |
#s(approx (sin x) #s(hole binary64 (sin x))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x)))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2))))))) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* 1/24 (pow x 4)))) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))) |
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 (* 1/24 (pow x 2)))) |
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* -1/720 (* eps (pow x 6))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6)))))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* -1/720 (* eps (pow x 6))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (* -1/720 (* eps (pow x 4))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 4) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) #s(hole binary64 (* -1/720 (* eps (pow x 3))))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) #s(hole binary64 (* (pow x 3) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) #s(hole binary64 (* -1/720 (* eps (pow x 2))))) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))) |
#s(approx (+ (* (* x x) -1/720) 1/24) #s(hole binary64 (* -1/720 (pow x 2)))) |
#s(approx (+ (* (* x x) -1/720) 1/24) #s(hole binary64 (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x)))))) |
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x)))) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* -1/6 (pow x 3)))) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))) |
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 (* -1/6 (pow x 2)))) |
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/6)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x)))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps))))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1/24 (/ eps (pow x 2))) (* 1/720 eps)))))) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* eps (cos x)))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))) |
#s(approx eps #s(hole binary64 eps)) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* -1/2 (* eps (sin x))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x)))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x)))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2)))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* eps (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) #s(hole binary64 (* eps (* x (+ 1/24 (* -1/720 (pow x 2))))))) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) #s(hole binary64 (* eps (+ 1/24 (* -1/720 (pow x 2)))))) |
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x))))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 (* eps (cos x))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x)))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x))))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x)))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x)))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))) 1))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) #s(hole binary64 (* -1 (* eps (* (pow x 2) (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))))))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1 (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))))))))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 eps (+.f64 (cos.f64 x) (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))) |
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (*.f64 (cos.f64 x) eps) (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps))))) |
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps))))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)) #s(literal 2 binary64))) (-.f64 (*.f64 (cos.f64 x) eps) (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))) |
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))))) |
(fma.f64 (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps (*.f64 (cos.f64 x) eps)) |
(fma.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps) (*.f64 (cos.f64 x) eps)) |
(fma.f64 (cos.f64 x) eps (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps))) |
(fma.f64 eps (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (*.f64 (cos.f64 x) eps)) |
(fma.f64 eps (cos.f64 x) (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 x) eps) (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))) (/.f64 (pow.f64 (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 x) eps) (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps))))) |
(-.f64 (*.f64 (cos.f64 x) eps) (*.f64 (neg.f64 (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)) eps)) |
(+.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))))) (/.f64 (pow.f64 (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps))))))) |
(+.f64 (*.f64 (cos.f64 x) eps) (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps))) |
(+.f64 (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)) (*.f64 (cos.f64 x) eps)) |
(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))))) |
(sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))) |
(sin.f64 (+.f64 x (/.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))))) |
x |
eps |
(*.f64 (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps) |
(*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)) |
(*.f64 eps (*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)) |
(*.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) |
(*.f64 eps (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/6 binary64) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
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#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) x) (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (fma.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps (+.f64 eps x))) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) |
#s(approx (* (cos x) eps) eps) |
#s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps)) |
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) |
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/720 binary64) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) |
#s(approx (+ (* (* x x) -1/2) 1) #s(literal 1 binary64)) |
#s(approx (+ (* (* x x) -1/2) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
#s(approx (* x x) (*.f64 x x)) |
#s(approx (* -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) x)) |
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) |
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x)) |
#s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/10080 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x)) |
#s(approx (sin 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 (*.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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64)) x eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 eps eps) x) (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) eps) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (fma.f64 (*.f64 (*.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64)) x eps)) |
#s(approx (* (* (* x x) eps) -1/2) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))) |
#s(approx (* (* x x) eps) (*.f64 (*.f64 x x) eps)) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64)) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
#s(approx (- (* 1/24 (* x x)) 1/2) #s(literal -1/2 binary64)) |
#s(approx (- (* 1/24 (* x x)) 1/2) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) |
#s(approx (* 1/24 (* x x)) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) eps) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps)) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/720 binary64) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/720 binary64) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) eps))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (fma.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/720 binary64) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) (*.f64 (*.f64 #s(literal 1/24 binary64) eps) x)) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/720 binary64) (*.f64 #s(literal 1/24 binary64) eps)) x)) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) (*.f64 #s(literal 1/24 binary64) eps)) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/720 binary64) (*.f64 #s(literal 1/24 binary64) eps))) |
#s(approx (+ (* (* x x) -1/720) 1/24) #s(literal 1/24 binary64)) |
#s(approx (+ (* (* x x) -1/720) 1/24) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) |
#s(approx (* (sin x) eps) (*.f64 eps x)) |
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)) |
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x)) |
#s(approx (* (sin x) eps) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/120 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x)) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) x) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) |
#s(approx (+ (* (* x x) -1/6) 1) #s(literal 1 binary64)) |
#s(approx (+ (* (* x x) -1/6) 1) (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64))) |
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (cos x) (cos.f64 x)) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps)) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) |
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps)) |
#s(approx (+ (* (* x x) -1/2) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) |
#s(approx (+ (* (* x x) -1/2) 1) (*.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)) (*.f64 x x))) |
#s(approx (* -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
#s(approx (sin x) (sin.f64 x)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps (/.f64 (*.f64 eps eps) x))) (*.f64 x x))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 eps (/.f64 (*.f64 eps eps) x)) (/.f64 eps (*.f64 x x))) (*.f64 x x))) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64))) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (*.f64 (-.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) (pow.f64 x #s(literal 4 binary64)))) |
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (*.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/24 binary64)) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) (pow.f64 x #s(literal 4 binary64)))) |
#s(approx (- (* 1/24 (* x x)) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))) |
#s(approx (- (* 1/24 (* x x)) 1/2) (*.f64 (-.f64 #s(literal 1/24 binary64) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) (*.f64 x x))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) (*.f64 (*.f64 #s(literal -1/720 binary64) eps) (pow.f64 x #s(literal 6 binary64)))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) (*.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) eps)))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) (*.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) eps))))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) (*.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/720 binary64) eps (fma.f64 (/.f64 #s(literal 1/24 binary64) x) (/.f64 eps x) (/.f64 eps (pow.f64 x #s(literal 6 binary64)))))))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) (*.f64 (*.f64 #s(literal -1/720 binary64) eps) (pow.f64 x #s(literal 6 binary64)))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) (*.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) eps)))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) (*.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) eps))))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) eps) #s(literal -1/720 binary64))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) eps)) (pow.f64 x #s(literal 4 binary64)))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) eps))) (pow.f64 x #s(literal 4 binary64)))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) eps) #s(literal -1/720 binary64))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) eps)))) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/720 binary64))) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/720 binary64) eps)) (*.f64 x x))) |
#s(approx (+ (* (* x x) -1/720) 1/24) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))) |
#s(approx (+ (* (* x x) -1/720) 1/24) (*.f64 (-.f64 (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/24 binary64)) #s(literal 1/720 binary64)) (*.f64 x x))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))) |
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps)) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64))) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) (*.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))) |
#s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) |
#s(approx (+ (* (* x x) -1/6) 1) (*.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/6 binary64)) (*.f64 x x))) |
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 (/.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/2 binary64) (/.f64 (neg.f64 eps) x)) x))) (*.f64 x x))) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) (*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (/.f64 eps (*.f64 x x)) (*.f64 #s(literal 1/720 binary64) eps)))) |
#s(approx (* (+ (* (* x x) -1/6) 1) x) (*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal -2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (cos.f64 x) eps)) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx eps eps) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (cos.f64 x) eps)) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 x x)) #s(literal 1 binary64)) eps)) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps)) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) (*.f64 (*.f64 (*.f64 x x) eps) (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) eps)) |
#s(approx (* (* (+ (* (* x x) -1/720) 1/24) eps) x) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) x) eps)) |
#s(approx (* (+ (* (* x x) -1/720) 1/24) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps)) |
#s(approx (* -1/2 eps) (*.f64 #s(literal -1/2 binary64) eps)) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (cos.f64 x)) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)) (cos.f64 x))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 3 binary64)))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (/.f64 (cos.f64 x) (*.f64 eps eps)))) (pow.f64 eps #s(literal 3 binary64)))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)) (cos.f64 x))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 3 binary64)))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) (cos.f64 x))) |
#s(approx (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) (*.f64 eps eps))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps)) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x))) |
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (*.f64 eps eps))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) (*.f64 eps eps))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x))))) |
#s(approx (+ (* (cos x) eps) (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal 1/6 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))))) |
#s(approx (* (* (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) eps) eps) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x))))) |
#s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (cos.f64 x))))) |
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) eps))) (*.f64 eps eps))) |
#s(approx (+ (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) eps) (*.f64 (neg.f64 eps) (-.f64 (*.f64 (fma.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal 1 binary64)))) |
#s(approx (* (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (* x x)) (*.f64 (neg.f64 eps) (*.f64 (fma.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x)))) |
#s(approx (+ (* (* (* (+ (* (* x x) -1/720) 1/24) eps) x) x) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) |
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps))))) |
Compiled 22 502 to 3 069 computations (86.4% saved)
20 alts after pruning (12 fresh and 8 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 572 | 3 | 575 |
| Fresh | 3 | 9 | 12 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 4 | 4 |
| Total | 576 | 20 | 596 |
| Status | Accuracy | Program |
|---|---|---|
| 99.9% | #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/10080 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) | |
| 99.9% | #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) | |
| ✓ | 99.9% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| 99.8% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| ✓ | 99.8% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) | |
| ✓ | 99.8% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) | |
| 99.6% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) #s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) | |
| ✓ | 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) | |
| 99.3% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) | |
| ✓ | 99.2% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) | |
| ✓ | 5.0% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
| ✓ | 98.2% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
| 99.2% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) | |
| 99.3% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) | |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) | |
| ✓ | 99.3% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
Compiled 1 821 to 702 computations (61.4% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) #s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/10080 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))) |
3 calls:
| 13.0ms | eps |
| 8.0ms | x |
| 8.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 100.0% | 1 | x |
| 100.0% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) #s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/10080 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
3 calls:
| 10.0ms | x |
| 7.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 7.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 100.0% | 1 | x |
| 100.0% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) #s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/10080 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
3 calls:
| 9.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 7.0ms | eps |
| 7.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 100.0% | 1 | x |
| 100.0% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) #s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/10080 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/10080 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
3 calls:
| 7.0ms | x |
| 7.0ms | eps |
| 7.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) #s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
3 calls:
| 8.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 6.0ms | x |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) #s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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(literal -1/2 binary64) (cos.f64 x)) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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(literal -1/2 binary64) (cos.f64 x)) eps)) |
3 calls:
| 6.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 6.0ms | x |
| 6.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) #s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
3 calls:
| 6.0ms | x |
| 6.0ms | eps |
| 6.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) #s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
3 calls:
| 6.0ms | x |
| 6.0ms | eps |
| 6.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.8% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.8% | 1 | x |
| 99.8% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) #s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) |
3 calls:
| 27.0ms | eps |
| 6.0ms | x |
| 6.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.6% | 1 | x |
| 99.6% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) #s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
3 calls:
| 5.0ms | x |
| 5.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 5.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.6% | 1 | x |
| 99.6% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
3 calls:
| 5.0ms | x |
| 5.0ms | eps |
| 5.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.5% | 1 | x |
| 99.5% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
3 calls:
| 6.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 4.0ms | eps |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.5% | 1 | x |
| 99.5% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
3 calls:
| 4.0ms | eps |
| 4.0ms | x |
| 4.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.3% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.3% | 1 | x |
| 99.3% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
3 calls:
| 3.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.3% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.3% | 1 | x |
| 99.3% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
3 calls:
| 6.0ms | x |
| 3.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.3% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.3% | 1 | x |
| 99.3% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
3 calls:
| 3.0ms | eps |
| 3.0ms | x |
| 3.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.2% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.2% | 1 | x |
| 99.2% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
3 calls:
| 3.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.2% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.2% | 1 | x |
| 99.2% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
3 calls:
| 5.0ms | x |
| 3.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.2% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.2% | 1 | x |
| 99.2% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 eps eps))) x eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
3 calls:
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2.0ms | eps |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.0% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.0% | 1 | x |
| 99.0% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
3 calls:
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2.0ms | x |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.0% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 99.0% | 1 | x |
| 99.0% | 1 | eps |
Compiled 9 to 10 computations (-11.1% saved)
Total -59.7b remaining (-5220.4%)
Threshold costs -59.7b (-5220.4%)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (*.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
3 calls:
| 1.0ms | eps |
| 1.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.2% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 98.2% | 1 | eps |
| 98.2% | 1 | x |
Compiled 9 to 10 computations (-11.1% saved)
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 180 | 740 |
| 1 | 245 | 734 |
| 2 | 408 | 734 |
| 3 | 1029 | 730 |
| 4 | 2904 | 730 |
| 5 | 5925 | 730 |
| 1× | node limit |
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/10080 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(approx (* (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/10080 binary64) (*.f64 x x)) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/6 binary64) #s(approx (* -1/2 (sin x)) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/240 binary64) (*.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))) eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (+ (* (* (cos x) eps) -1/6) (* -1/2 (sin x))) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #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)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 (neg.f64 eps) (fma.f64 (-.f64 (*.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) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(approx (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (*.f64 #s(literal 1/24 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #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))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(approx (+ (* (+ (* -1/720 (* (* x x) eps)) (* 1/24 eps)) (* x x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)) |
| 1× | fuel |
Compiled 740 to 184 computations (75.1% saved)
Compiled 1 494 to 380 computations (74.6% saved)
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