Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze45.0ms (0.6%)

Memory

1.5MiB live, 53.2MiB allocated; 24ms collecting garbage

Algorithm

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample4.6s (64%)

Memory

131.5MiB live, 4 392.1MiB allocated; 2.2s collecting garbage

Samples

2.6s	26 581×	0	invalid
648.0ms	5 569×	1	valid
169.0ms	2 687×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.3s

ival-sin: 1.2s (52.7% of total)

ival-fabs: 294.0ms (12.9% of total)

ival-<: 195.0ms (8.6% of total)

adjust: 144.0ms (6.3% of total)

ival-add!: 140.0ms (6.1% of total)

ival-mult!: 137.0ms (6% of total)

ival-sub!: 89.0ms (3.9% of total)

ival-and: 63.0ms (2.8% of total)

ival-assert: 13.0ms (0.6% of total)

Bogosity

preprocess71.0ms (1%)

Memory

-42.0MiB live, 39.0MiB allocated; 63ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	46
1	99	42
2	497	42
3	2750	42

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 12 to 12 computations (0% saved)

series4.0ms (0.1%)

Memory

6.4MiB live, 6.4MiB allocated; 0ms collecting garbage

Counts

6 → 31

Calls

Call 1

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) (* 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 (+ 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 (+ 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) (* 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 (+ 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)))))

Calls

6 calls:

Time	Variable		Point	Expression
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	x	@	0	((- (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))

rewrite137.0ms (1.9%)

Memory

45.5MiB live, 134.7MiB allocated; 20ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	145	512
0	150	496
1	1041	496
0	8334	461

Stop Event

1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

37 → 101

Calls

Call 1

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) (* 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 (+ 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 (+ 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) (* 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 (+ 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 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))))
(.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (neg.f64 (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (*.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x))))))
(/.f64 (neg.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (neg.f64 (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 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 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (*.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
(neg.f64 (-.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(fma.f64 (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))))
(-.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (neg.f64 (sin.f64 x))))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(+.f64 (.f64 (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(+.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x)))) (-.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x))))
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (cos.f64 eps))) (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))))
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (.f64 (.f64 (cos.f64 eps) (neg.f64 (sin.f64 x))) (.f64 (cos.f64 eps) (neg.f64 (sin.f64 x))))) (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (neg.f64 (sin.f64 x)))))
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (cos.f64 eps))) (.f64 (.f64 (cos.f64 x) (neg.f64 (sin.f64 eps))) (.f64 (cos.f64 x) (neg.f64 (sin.f64 eps))))) (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (neg.f64 (sin.f64 eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)) (-.f64 (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x))) (.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x))))))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))))))
(/.f64 (-.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 eps) (neg.f64 (sin.f64 x))) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (.f64 (cos.f64 eps) (neg.f64 (sin.f64 x))) (.f64 (cos.f64 eps) (neg.f64 (sin.f64 x))) (.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (neg.f64 (sin.f64 x)))))))
(/.f64 (-.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) (neg.f64 (sin.f64 eps))) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (cos.f64 eps)) (fma.f64 (.f64 (cos.f64 x) (neg.f64 (sin.f64 eps))) (.f64 (cos.f64 x) (neg.f64 (sin.f64 eps))) (.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (neg.f64 (sin.f64 eps)))))))
(neg.f64 (-.f64 (.f64 (cos.f64 eps) (neg.f64 (sin.f64 x))) (.f64 (sin.f64 eps) (cos.f64 x))))
(neg.f64 (-.f64 (.f64 (cos.f64 x) (neg.f64 (sin.f64 eps))) (.f64 (sin.f64 x) (cos.f64 eps))))
(neg.f64 (sin.f64 (-.f64 (neg.f64 x) eps)))
(sin.f64 (+.f64 eps x))
(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) (neg.f64 (*.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) (neg.f64 (*.f64 (cos.f64 x) (neg.f64 (sin.f64 eps)))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
(-.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (cos.f64 eps)) (sin.f64 x)))
(-.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (neg.f64 (.f64 (cos.f64 eps) (sin.f64 x))))
(-.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (neg.f64 (sin.f64 x))))
(-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps)))
(-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (neg.f64 (.f64 (cos.f64 x) (sin.f64 eps))))
(-.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (neg.f64 (sin.f64 eps))))
(+.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x))))
(+.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (neg.f64 (.f64 (cos.f64 eps) (neg.f64 (sin.f64 x)))))
(+.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x)))
(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps))))
(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (neg.f64 (.f64 (cos.f64 x) (neg.f64 (sin.f64 eps)))))
(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
(.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(.f64 (.f64 (-.f64 eps x) (+.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps (*.f64 x (-.f64 x eps)))))
(.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(/.f64 (neg.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 eps eps (.f64 x (-.f64 x eps)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps))) (neg.f64 (fma.f64 x x (.f64 eps (-.f64 eps x)))))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (*.f64 (-.f64 eps x) (+.f64 eps x)) (-.f64 eps x))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 eps eps (.f64 x (-.f64 x eps))))
(/.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps)) (fma.f64 x x (.f64 eps (-.f64 eps x))))
(neg.f64 (-.f64 (neg.f64 x) eps))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (.f64 (.f64 x x) x) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (/.f64 (.f64 (.f64 eps eps) (neg.f64 eps)) (fma.f64 x x (.f64 eps (-.f64 eps x)))))
(-.f64 (/.f64 (.f64 (.f64 eps eps) eps) (fma.f64 eps eps (.f64 x (-.f64 x eps)))) (/.f64 (.f64 (neg.f64 x) (.f64 x x)) (fma.f64 eps eps (.f64 x (-.f64 x eps)))))
(-.f64 eps (neg.f64 x))
(-.f64 x (neg.f64 eps))
(+.f64 (/.f64 (.f64 (.f64 x x) x) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (/.f64 (.f64 (.f64 eps eps) eps) (fma.f64 x x (.f64 eps (-.f64 eps x)))))
(+.f64 (/.f64 (.f64 (.f64 eps eps) eps) (fma.f64 eps eps (.f64 x (-.f64 x eps)))) (/.f64 (.f64 (.f64 x x) x) (fma.f64 eps eps (.f64 x (-.f64 x eps)))))
(+.f64 eps x)
(+.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 x (-.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 x (-.f64 (fma.f64 x (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))) (cos.f64 eps)) #s(literal 1 binary64)) (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 eps) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 x (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 x (fma.f64 (.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (.f64 (sin.f64 eps) #s(literal -1/2 binary64))) (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) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (fma.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 (fma.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)) (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) (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) (fma.f64 (/.f64 eps x) x 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 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 x) eps (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 eps (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps (sin.f64 x)))
#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) (fma.f64 (/.f64 x eps) eps eps))

eval13.0ms (0.2%)

Memory: -29.4MiB live, 15.9MiB allocated; 6ms collecting garbage
Compiler: Compiled 1 102 to 384 computations (65.2% saved)

prune7.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated; 0ms collecting garbage

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	81	10	91
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	11	92

Accuracy

99.9%

Counts

92 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.1%	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
	61.4%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
✓	61.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	60.2%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶	60.0%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
	61.2%	(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
▶	99.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
▶	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 282 to 268 computations (5% saved)

series40.0ms (0.6%)

Memory

-11.2MiB live, 45.0MiB allocated; 13ms collecting garbage

Counts

33 → 136

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
(.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps)
(fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x))
eps
(fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
#s(literal 1/24 binary64)
(*.f64 (cos.f64 x) #s(literal -1/6 binary64))
(cos.f64 x)
#s(literal -1/6 binary64)
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 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))
(*.f64 x x)
#s(literal 1 binary64)
#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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
(.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps)
(fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x))
(fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(*.f64 (cos.f64 x) eps)

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 (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/12 (pow eps 2)) (* eps (* x (+ 1/12 (* -1/144 (pow eps 2)))))) 1/2))))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/12 eps) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) 1/2)))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 -1/6))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (- (* 1/24 (* eps x)) 1/6)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* 1/12 x))) 1/6)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* x (+ 1/12 (* -1/144 (* eps x)))))) 1/6)))
#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 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 (* (cos x) -1/6) #s(hole binary64 (- (* 1/12 (pow x 2)) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* -1/144 (pow x 2)))) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/4320 (pow x 2)) 1/144)))) 1/6)))
#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 (* (sin x) -1/2) #s(hole binary64 (* -1/2 x)))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))
#s(approx (* (sin x) -1/2) #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 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 x) -1/6) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#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 (* -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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #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 (* -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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (* -1/6 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps 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) -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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #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 (- (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 (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 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)) #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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (sin x)))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (sin x)))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* 1/24 (* (pow eps 2) (sin x)))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (* 1/24 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (* eps (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x 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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (* -1 (* eps (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#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)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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) (* (sin x) -1/2)) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))

Calls

6 calls:

Time	Variable		Point	Expression
16.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (* (sin x) eps) (sin x) x 1/24 (* (cos x) -1/6) (cos x) -1/6 (* (sin x) -1/2) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) 1 (- (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 (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) eps))
6.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (* (sin x) eps) (sin x) x 1/24 (* (cos x) -1/6) (cos x) -1/6 (* (sin x) -1/2) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) 1 (- (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 (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) eps))
5.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (* (sin x) eps) (sin x) x 1/24 (* (cos x) -1/6) (cos x) -1/6 (* (sin x) -1/2) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) 1 (- (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 (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) eps))
4.0ms	x	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (* (sin x) eps) (sin x) x 1/24 (* (cos x) -1/6) (cos x) -1/6 (* (sin x) -1/2) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) 1 (- (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 (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) eps))
4.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (* (sin x) eps) (sin x) x 1/24 (* (cos x) -1/6) (cos x) -1/6 (* (sin x) -1/2) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) 1 (- (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 (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) eps))

rewrite174.0ms (2.4%)

Memory

35.3MiB live, 166.6MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	615	3784
0	667	3716
1	4256	3716
0	8327	3536

Stop Event

1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

169 → 380

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
(.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps)
(fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x))
eps
(fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
#s(literal 1/24 binary64)
(*.f64 (cos.f64 x) #s(literal -1/6 binary64))
(cos.f64 x)
#s(literal -1/6 binary64)
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 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))
(*.f64 x x)
#s(literal 1 binary64)
#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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
(.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps)
(fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x))
(fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(*.f64 (cos.f64 x) eps)
#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 (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/12 (pow eps 2)) (* eps (* x (+ 1/12 (* -1/144 (pow eps 2)))))) 1/2))))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/12 eps) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) 1/2)))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 -1/6))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (- (* 1/24 (* eps x)) 1/6)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* 1/12 x))) 1/6)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* x (+ 1/12 (* -1/144 (* eps x)))))) 1/6)))
#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 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 (* (cos x) -1/6) #s(hole binary64 (- (* 1/12 (pow x 2)) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* -1/144 (pow x 2)))) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/4320 (pow x 2)) 1/144)))) 1/6)))
#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 (* (sin x) -1/2) #s(hole binary64 (* -1/2 x)))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))
#s(approx (* (sin x) -1/2) #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 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 x) -1/6) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#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 (* -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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #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 (* -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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (* -1/6 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps 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) -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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #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 (- (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 (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 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)) #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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (sin x)))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (sin x)))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* 1/24 (* (pow eps 2) (sin x)))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (* 1/24 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (* eps (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x 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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (* -1 (* eps (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#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)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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) (* (sin x) -1/2)) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
(.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps)
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
(fma.f64 (cos.f64 x) eps (.f64 eps (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))
(fma.f64 (cos.f64 x) eps (.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps))
(fma.f64 eps (cos.f64 x) (.f64 eps (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))
(fma.f64 eps (cos.f64 x) (.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 eps (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (neg.f64 (-.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (cos.f64 x))))
(/.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (pow.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 (cos.f64 x) (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 2 binary64)) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (cos.f64 x))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 3 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 (pow.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps))))))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (-.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (cos.f64 x)))
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (pow.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 2 binary64))) (-.f64 (cos.f64 x) (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 2 binary64)) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (cos.f64 x)))))
(/.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 (pow.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))))
(fma.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x))
(-.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (neg.f64 (cos.f64 x)))
(-.f64 (cos.f64 x) (.f64 (neg.f64 eps) (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))))
(-.f64 (cos.f64 x) (neg.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))
(+.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (cos.f64 x))
(+.f64 (cos.f64 x) (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps))
eps
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#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (cos x) -1/6) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
#s(approx (cos x) (cos.f64 x))
#s(approx (* (sin x) -1/2) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (* (+ (* (* x x) -1/6) 1) x) (.f64 (.f64 (*.f64 x x) x) #s(literal -1/6 binary64)))
#s(approx (* (+ (* (* x x) -1/6) 1) x) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 (.f64 x x) x)))
#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 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x 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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))))
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) 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 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (* (+ (* (* x x) -1/6) 1) x) (.f64 (.f64 (neg.f64 x) (.f64 x x)) (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))))
#s(approx (sin eps) (.f64 (fma.f64 (fma.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 (fma.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)) (fma.f64 (cos.f64 x) eps (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 eps (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps (sin.f64 x)))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (.f64 (.f64 (.f64 eps eps) (*.f64 eps eps)) (sin.f64 x)) #s(literal 1/24 binary64)))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal 1/24 binary64))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal 1/24 binary64)))) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (.f64 (.f64 eps eps) eps))))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (.f64 (.f64 (.f64 (.f64 eps eps) eps) (sin.f64 x)) #s(literal 1/24 binary64)))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (.f64 (.f64 (.f64 eps eps) eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal 1/24 binary64)))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (.f64 (.f64 (.f64 eps eps) eps) (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal 1/24 binary64))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (.f64 (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (.f64 (.f64 eps eps) eps))))) (.f64 (.f64 eps eps) eps)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal 1/24 binary64))) (*.f64 eps eps)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (.f64 (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal 1/24 binary64)))) (.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal 1/24 binary64))) eps))
#s(approx (+ x eps) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 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 (+ (* (* (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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (.f64 (.f64 (cos.f64 x) (.f64 (.f64 eps eps) eps)) #s(literal -1/6 binary64)))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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))) (.f64 (.f64 eps eps) eps)))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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)))) (.f64 (.f64 eps eps) eps)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (.f64 (.f64 (*.f64 eps eps) (cos.f64 x)) #s(literal -1/6 binary64)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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) (* (sin x) -1/2)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (.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)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 (cos.f64 x) #s(literal 1/6 binary64))) eps))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (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))) eps))) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (neg.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64))) (.f64 (.f64 eps eps) eps))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (neg.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps))) (.f64 (.f64 eps eps) eps))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (.f64 (.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.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))) eps)))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 (cos.f64 x) #s(literal 1/6 binary64))) eps))) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (.f64 (neg.f64 eps) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64)))))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 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)))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (neg.f64 (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 (cos.f64 x) #s(literal 1/6 binary64))) (.f64 (.f64 eps eps) eps))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (neg.f64 (.f64 (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))) (.f64 (*.f64 eps eps) eps))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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) (* (sin x) -1/2)) (.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)))))

eval60.0ms (0.8%)

Memory: -23.7MiB live, 77.6MiB allocated; 21ms collecting garbage
Compiler: Compiled 5 702 to 2 004 computations (64.9% saved)

prune25.0ms (0.4%)

Memory

-10.5MiB live, 35.6MiB allocated; 5ms collecting garbage

Pruning

24 alts after pruning (21 fresh and 3 done)

	Pruned	Kept	Total
New	373	16	389
Fresh	0	5	5
Picked	3	2	5
Done	0	1	1
Total	376	24	400

Accuracy

99.9%

Counts

400 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.1%	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
	61.4%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
✓	61.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	60.2%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶	61.2%	(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) (.f64 (fma.f64 (fma.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))
	98.7%	#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))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	98.2%	#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))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (fma.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))) eps))
	47.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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))) eps))
	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
▶	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)))
▶	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
	98.2%	#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)))
	26.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (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))) eps))) (.f64 (.f64 eps eps) (.f64 eps eps)))))

Compiler

Compiled 978 to 901 computations (7.9% saved)

series52.0ms (0.7%)

Memory

21.7MiB live, 66.2MiB allocated; 7ms collecting garbage

Counts

46 → 198

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
(.f64 (fma.f64 eps (fma.f64 (.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps)
(fma.f64 eps (fma.f64 (.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))
eps
(fma.f64 (.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps)
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))
x
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
#s(literal -1/6 binary64)
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(sin.f64 x)
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps))
(fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps)
(.f64 (.f64 eps eps) x)
(*.f64 eps eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.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)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)
(fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (*.f64 #s(literal -1/2 binary64) eps))
#s(literal 1/12 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
(.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps)
(fma.f64 eps #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)))
(fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))
(*.f64 #s(literal -1/6 binary64) eps)
(cos.f64 x)
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))))
(sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))
(*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))
(-.f64 (+.f64 eps x) x)
(+.f64 eps x)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))
(*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))
(+.f64 (+.f64 eps x) 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 (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (* eps (+ (sin (* 1/2 (PI))) (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI)))))))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (+ (* eps (* x (+ (cos (* 1/2 (PI))) (* eps (- (* -1/6 (* eps (cos (* 1/2 (PI))))) 1/2))))) (* eps (+ (sin (* 1/2 (PI))) (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI))))))))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (+ (* eps (+ (sin (* 1/2 (PI))) (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI))))))) (* x (+ (* eps (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/12 (* (pow eps 2) (sin (* 1/2 (PI)))))))) (* eps (+ (cos (* 1/2 (PI))) (* eps (- (* -1/6 (* eps (cos (* 1/2 (PI))))) 1/2)))))))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (+ (* eps (+ (sin (* 1/2 (PI))) (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI))))))) (* x (+ (* eps (+ (cos (* 1/2 (PI))) (* eps (- (* -1/6 (* eps (cos (* 1/2 (PI))))) 1/2)))) (* x (+ (* eps (* x (+ (* -1/6 (cos (* 1/2 (PI)))) (* eps (+ 1/12 (* 1/36 (* eps (cos (* 1/2 (PI)))))))))) (* eps (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/12 (* (pow eps 2) (sin (* 1/2 (PI))))))))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (+ (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI))))) (* x (+ (cos (* 1/2 (PI))) (* eps (- (* -1/6 (* eps (cos (* 1/2 (PI))))) 1/2))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (+ (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI))))) (* x (+ (cos (* 1/2 (PI))) (+ (* eps (- (* -1/6 (* eps (cos (* 1/2 (PI))))) 1/2)) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/12 (* (pow eps 2) (sin (* 1/2 (PI))))))))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (+ (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI))))) (* x (+ (cos (* 1/2 (PI))) (+ (* eps (- (* -1/6 (* eps (cos (* 1/2 (PI))))) 1/2)) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (+ (* 1/12 (* (pow eps 2) (sin (* 1/2 (PI))))) (* x (+ (* -1/6 (cos (* 1/2 (PI)))) (* eps (+ 1/12 (* 1/36 (* eps (cos (* 1/2 (PI)))))))))))))))))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 (* eps (sin (* 1/2 (PI)))))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 (* eps (sin (* 1/2 (PI))))) (* x (- (* -1/6 (* eps (cos (* 1/2 (PI))))) 1/2)))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 (* eps (sin (* 1/2 (PI))))) (* x (- (+ (* -1/6 (* eps (cos (* 1/2 (PI))))) (* 1/12 (* eps (* x (sin (* 1/2 (PI))))))) 1/2)))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 (* eps (sin (* 1/2 (PI))))) (* x (- (+ (* -1/6 (* eps (cos (* 1/2 (PI))))) (* x (+ (* 1/12 (* eps (sin (* 1/2 (PI))))) (* x (+ 1/12 (* 1/36 (* eps (cos (* 1/2 (PI)))))))))) 1/2)))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (* 1/2 (PI))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* eps (* x (cos (* 1/2 (PI))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))) (* eps (cos (* 1/2 (PI)))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* eps (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* -1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* -1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx x #s(hole binary64 x))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* -1/2 x)))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))
#s(approx (* (sin x) -1/2) #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 (+ 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 (* (* eps eps) x) #s(hole binary64 (* (pow eps 2) x)))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
#s(approx (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
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#s(approx (* (- (+ eps x) x) 1/2) #s(hole binary64 (* 1/2 eps)))
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#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
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#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
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#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (- (* 1/2 (PI)) (* -1 x))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
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#s(approx (+ (* (* (* eps eps) x) -1/2) eps) #s(hole binary64 (* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))))
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#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/12 (pow eps 2))))))
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#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* -1 (* x (+ 1/2 (* 1/6 (/ eps x)))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps 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) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
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#s(approx (+ (* (* (* eps eps) x) -1/2) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (* eps x))))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
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#s(approx (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/12 (* eps x)) 1/2))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
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#s(approx (sin (* (- (+ eps x) x) 1/2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
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#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
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#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (sin (+ x (* 1/2 (PI)))))))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (sin (+ x (* 1/2 (PI))))) (/ (sin (+ x (* 1/2 (PI)))) (pow eps 2)))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (* -1/6 (* (pow eps 2) (sin (+ x (* 1/2 (PI))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (sin (+ x (* 1/2 (PI)))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (sin (+ x (* 1/2 (PI))))) (/ (sin (+ x (* 1/2 (PI)))) (pow eps 2)))))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 (* eps (sin (+ x (* 1/2 (PI))))))))
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#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 (+ (* (* (* eps eps) x) -1/2) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/2))))
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#s(approx (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
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#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
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#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* eps (- (* -1/2 (/ x eps)) 1/6))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
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#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (sin (+ x (* 1/2 (PI)))) eps)) eps)) (* 1/6 (sin (+ x (* 1/2 (PI))))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (sin (+ x (* 1/2 (PI)))) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (sin (+ x (* 1/2 (PI)))))))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (sin (+ x (* 1/2 (PI))))) (* 1/2 (/ (sin x) eps)))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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) (* (sin x) -1/2)) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* -1 (* eps (+ 1/6 (* 1/2 (/ x eps)))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) x (/ (PI) 2) (PI) 2 -1/6 (* (sin x) -1/2) (sin x) -1/2 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (* eps eps) x) -1/2) eps) (* (* eps eps) x) (* eps eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) 1/12 (* -1/2 eps) (* (* eps eps) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (+ (* -1/2 x) (* -1/6 eps)) (* -1/6 eps) (cos x) (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) (sin (* (- (+ eps x) x) 1/2)) (* (- (+ eps x) x) 1/2) (- (+ eps x) x) (+ eps x) 1/2 (cos (* (+ (+ eps x) x) 1/2)) (* (+ (+ eps x) x) 1/2) (+ (+ eps x) x))
11.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) x (/ (PI) 2) (PI) 2 -1/6 (* (sin x) -1/2) (sin x) -1/2 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (* eps eps) x) -1/2) eps) (* (* eps eps) x) (* eps eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) 1/12 (* -1/2 eps) (* (* eps eps) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (+ (* -1/2 x) (* -1/6 eps)) (* -1/6 eps) (cos x) (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) (sin (* (- (+ eps x) x) 1/2)) (* (- (+ eps x) x) 1/2) (- (+ eps x) x) (+ eps x) 1/2 (cos (* (+ (+ eps x) x) 1/2)) (* (+ (+ eps x) x) 1/2) (+ (+ eps x) x))
7.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) x (/ (PI) 2) (PI) 2 -1/6 (* (sin x) -1/2) (sin x) -1/2 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (* eps eps) x) -1/2) eps) (* (* eps eps) x) (* eps eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) 1/12 (* -1/2 eps) (* (* eps eps) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (+ (* -1/2 x) (* -1/6 eps)) (* -1/6 eps) (cos x) (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) (sin (* (- (+ eps x) x) 1/2)) (* (- (+ eps x) x) 1/2) (- (+ eps x) x) (+ eps x) 1/2 (cos (* (+ (+ eps x) x) 1/2)) (* (+ (+ eps x) x) 1/2) (+ (+ eps x) x))
7.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) x (/ (PI) 2) (PI) 2 -1/6 (* (sin x) -1/2) (sin x) -1/2 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (* eps eps) x) -1/2) eps) (* (* eps eps) x) (* eps eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) 1/12 (* -1/2 eps) (* (* eps eps) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (+ (* -1/2 x) (* -1/6 eps)) (* -1/6 eps) (cos x) (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) (sin (* (- (+ eps x) x) 1/2)) (* (- (+ eps x) x) 1/2) (- (+ eps x) x) (+ eps x) 1/2 (cos (* (+ (+ eps x) x) 1/2)) (* (+ (+ eps x) x) 1/2) (+ (+ eps x) x))
6.0ms	x	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) x (/ (PI) 2) (PI) 2 -1/6 (* (sin x) -1/2) (sin x) -1/2 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (* eps eps) x) -1/2) eps) (* (* eps eps) x) (* eps eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) 1/12 (* -1/2 eps) (* (* eps eps) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (+ (* -1/2 x) (* -1/6 eps)) (* -1/6 eps) (cos x) (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) (sin (* (- (+ eps x) x) 1/2)) (* (- (+ eps x) x) 1/2) (- (+ eps x) x) (+ eps x) 1/2 (cos (* (+ (+ eps x) x) 1/2)) (* (+ (+ eps x) x) 1/2) (+ (+ eps x) x))

rewrite200.0ms (2.8%)

Memory

-24.1MiB live, 160.2MiB allocated; 35ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	928	6418
0	985	5847
1	6256	5600
0	8476	5299

Stop Event

1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

244 → 452

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
(.f64 (fma.f64 eps (fma.f64 (.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps)
(fma.f64 eps (fma.f64 (.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))
eps
(fma.f64 (.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps)
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))
x
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
#s(literal -1/6 binary64)
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(sin.f64 x)
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps))
(fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps)
(.f64 (.f64 eps eps) x)
(*.f64 eps eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.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)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)
(fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (*.f64 #s(literal -1/2 binary64) eps))
#s(literal 1/12 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
(.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps)
(fma.f64 eps #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)))
(fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))
(*.f64 #s(literal -1/6 binary64) eps)
(cos.f64 x)
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))))
(sin.f64 (*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))
(*.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))
(-.f64 (+.f64 eps x) x)
(+.f64 eps x)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))
(*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))
(+.f64 (+.f64 eps x) 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 (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (* eps (+ (sin (* 1/2 (PI))) (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI)))))))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (+ (* eps (* x (+ (cos (* 1/2 (PI))) (* eps (- (* -1/6 (* eps (cos (* 1/2 (PI))))) 1/2))))) (* eps (+ (sin (* 1/2 (PI))) (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI))))))))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (+ (* eps (+ (sin (* 1/2 (PI))) (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI))))))) (* x (+ (* eps (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/12 (* (pow eps 2) (sin (* 1/2 (PI)))))))) (* eps (+ (cos (* 1/2 (PI))) (* eps (- (* -1/6 (* eps (cos (* 1/2 (PI))))) 1/2)))))))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (+ (* eps (+ (sin (* 1/2 (PI))) (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI))))))) (* x (+ (* eps (+ (cos (* 1/2 (PI))) (* eps (- (* -1/6 (* eps (cos (* 1/2 (PI))))) 1/2)))) (* x (+ (* eps (* x (+ (* -1/6 (cos (* 1/2 (PI)))) (* eps (+ 1/12 (* 1/36 (* eps (cos (* 1/2 (PI)))))))))) (* eps (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/12 (* (pow eps 2) (sin (* 1/2 (PI))))))))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (+ (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI))))) (* x (+ (cos (* 1/2 (PI))) (* eps (- (* -1/6 (* eps (cos (* 1/2 (PI))))) 1/2))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (+ (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI))))) (* x (+ (cos (* 1/2 (PI))) (+ (* eps (- (* -1/6 (* eps (cos (* 1/2 (PI))))) 1/2)) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/12 (* (pow eps 2) (sin (* 1/2 (PI))))))))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (+ (* -1/6 (* (pow eps 2) (sin (* 1/2 (PI))))) (* x (+ (cos (* 1/2 (PI))) (+ (* eps (- (* -1/6 (* eps (cos (* 1/2 (PI))))) 1/2)) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (+ (* 1/12 (* (pow eps 2) (sin (* 1/2 (PI))))) (* x (+ (* -1/6 (cos (* 1/2 (PI)))) (* eps (+ 1/12 (* 1/36 (* eps (cos (* 1/2 (PI)))))))))))))))))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 (* eps (sin (* 1/2 (PI)))))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 (* eps (sin (* 1/2 (PI))))) (* x (- (* -1/6 (* eps (cos (* 1/2 (PI))))) 1/2)))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 (* eps (sin (* 1/2 (PI))))) (* x (- (+ (* -1/6 (* eps (cos (* 1/2 (PI))))) (* 1/12 (* eps (* x (sin (* 1/2 (PI))))))) 1/2)))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 (* eps (sin (* 1/2 (PI))))) (* x (- (+ (* -1/6 (* eps (cos (* 1/2 (PI))))) (* x (+ (* 1/12 (* eps (sin (* 1/2 (PI))))) (* x (+ 1/12 (* 1/36 (* eps (cos (* 1/2 (PI)))))))))) 1/2)))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (* 1/2 (PI))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* eps (* x (cos (* 1/2 (PI))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))) (* eps (cos (* 1/2 (PI)))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* eps (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* -1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* -1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx x #s(hole binary64 x))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* -1/2 x)))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))
#s(approx (* (sin x) -1/2) #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 (+ 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 (* (* eps eps) x) #s(hole binary64 (* (pow eps 2) x)))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
#s(approx (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (* (- (+ eps x) x) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (sin (+ x (* 1/2 (PI))))))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (sin (+ x (* 1/2 (PI)))))))))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (sin (+ x (* 1/2 (PI)))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (+ x (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (PI) x))))))
#s(approx (* (sin x) -1/2) #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 (+ (* (* (* eps eps) x) -1/2) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (+ (* (* (* eps eps) x) -1/2) eps) #s(hole binary64 (* x (+ (* -1/2 (pow eps 2)) (/ eps x)))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* 1/12 (* (pow eps 2) (pow x 3)))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* (pow x 3) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* (pow x 3) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ eps (pow x 3))))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* 1/12 (* (pow eps 2) (pow x 2)))))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow x 2) (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow x 2) (+ (* -1/2 (/ eps x)) (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))))))
#s(approx (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) #s(hole binary64 (* 1/12 (* (pow eps 2) x))))
#s(approx (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) #s(hole binary64 (* x (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* x (- (* -1/6 (/ eps x)) 1/2))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (* eps (+ (sin (- (* 1/2 (PI)) (* -1 x))) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (sin (- (* 1/2 (PI)) (* -1 x)))))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (sin (- (* 1/2 (PI)) (* -1 x))) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (sin (- (* 1/2 (PI)) (* -1 x))))))))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (sin (- (* 1/2 (PI)) (* -1 x))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (- (* 1/2 (PI)) (* -1 x))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (PI) x)) 1)))))
#s(approx (+ (* (* (* eps eps) x) -1/2) eps) #s(hole binary64 (* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x)))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))) x)) (* -1/12 (pow eps 2)))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)) x)) (* -1/12 (pow eps 2)))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/12 (pow eps 2))))))
#s(approx (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) #s(hole binary64 (* -1 (* x (+ (* -1/12 (pow eps 2)) (* 1/2 (/ eps x)))))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* -1 (* x (+ 1/2 (* 1/6 (/ eps x)))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps 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) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (* eps (+ (sin (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (+ (sin (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (* (* eps eps) x) -1/2) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (* eps x))))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2))))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2))))))
#s(approx (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/12 (* eps x)) 1/2))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (sin (+ x (* 1/2 (PI))))))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (sin (+ x (* 1/2 (PI)))))))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (sin (+ x (* 1/2 (PI))))) (/ (sin (+ x (* 1/2 (PI)))) (pow eps 2)))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (* -1/6 (* (pow eps 2) (sin (+ x (* 1/2 (PI))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (sin (+ x (* 1/2 (PI)))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (sin (+ x (* 1/2 (PI))))) (/ (sin (+ x (* 1/2 (PI)))) (pow eps 2)))))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 (* eps (sin (+ x (* 1/2 (PI))))))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (sin (+ x (* 1/2 (PI)))))))))
#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 (+ (* (* (* eps eps) x) -1/2) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* (pow eps 2) (* x (- (* 1/12 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))))
#s(approx (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* eps (- (* -1/2 (/ x eps)) 1/6))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (sin (+ x (* 1/2 (PI))))) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (sin (+ x (* 1/2 (PI)))) eps)) eps)) (* 1/6 (sin (+ x (* 1/2 (PI))))))))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (sin (+ x (* 1/2 (PI)))) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (sin (+ x (* 1/2 (PI)))))))))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (sin (+ x (* 1/2 (PI))))) (* 1/2 (/ (sin x) eps)))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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 (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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) (* (sin x) -1/2)) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (+ (* -1/2 x) (* -1/6 eps)) #s(hole binary64 (* -1 (* eps (+ 1/6 (* 1/2 (/ x eps)))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
(.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps)
(.f64 eps (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
(fma.f64 (cos.f64 x) eps (.f64 eps (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))
(fma.f64 (cos.f64 x) eps (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps))
(fma.f64 eps (cos.f64 x) (.f64 eps (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))
(fma.f64 eps (cos.f64 x) (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 eps (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps))
(/.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (cos.f64 x)))
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps))) (-.f64 (cos.f64 x) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) 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 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)) (.f64 (cos.f64 x) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))))
(fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x))
(-.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (neg.f64 (cos.f64 x)))
(-.f64 (cos.f64 x) (.f64 (neg.f64 eps) (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))))
(-.f64 (cos.f64 x) (neg.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))
(+.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (cos.f64 x))
(+.f64 (cos.f64 x) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps))
eps
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)))) (-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))))
(/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (-.f64 (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))))))
(/.f64 (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) #s(literal -1/216 binary64) (.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(literal -1/8 binary64))) (fma.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)) (-.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
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#s(approx x x)
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#s(approx (* (- (+ eps x) x) 1/2) (*.f64 #s(literal 1/2 binary64) eps))
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#s(approx (* (sin x) -1/2) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
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#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (.f64 (.f64 (*.f64 eps eps) (cos.f64 x)) #s(literal -1/6 binary64)))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (.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 (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (.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 (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)))
#s(approx (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (.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 (+ (* -1/2 x) (* -1/6 eps)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) eps))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (* (+ (+ eps x) x) 1/2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (+ eps x) x) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) (neg.f64 (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) (cos.f64 x))) (.f64 (.f64 eps eps) eps))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) (neg.f64 (.f64 (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))) (.f64 (*.f64 eps eps) eps))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (.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 (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (.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 (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (.f64 eps eps)))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) (neg.f64 (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) (cos.f64 x))) (.f64 (.f64 eps eps) eps))))
#s(approx (* (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) eps) (neg.f64 (.f64 (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))) (.f64 (*.f64 eps eps) eps))))
#s(approx (+ (* eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (.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 (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (.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 x) (* -1/6 eps)) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) #s(literal 1/6 binary64))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) (.f64 (cos.f64 (.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))))
#s(approx (* (+ (+ eps x) x) 1/2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (+ eps x) x) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -2 binary64) #s(literal -1 binary64))))

eval73.0ms (1%)

Memory: 40.6MiB live, 95.3MiB allocated; 52ms collecting garbage
Compiler: Compiled 6 261 to 2 396 computations (61.7% saved)

prune36.0ms (0.5%)

Memory

-2.6MiB live, 42.6MiB allocated; 24ms collecting garbage

Pruning

27 alts after pruning (25 fresh and 2 done)

	Pruned	Kept	Total
New	382	17	399
Fresh	8	8	16
Picked	5	0	5
Done	1	2	3
Total	396	27	423

Accuracy

99.9%

Counts

423 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	61.4%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
✓	61.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	60.2%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶	99.8%	(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
	99.8%	(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
	99.7%	(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
	98.7%	#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))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (.f64 (.f64 #s(literal 1 binary64) eps) #s(literal -1/6 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
▶	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	98.2%	#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))
	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #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))) eps))
▶	98.2%	#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)))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x))) x eps)))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x eps)))
	50.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (.f64 eps eps)))))
	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))))
	5.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
▶	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
	26.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (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))) eps))) (.f64 (.f64 eps eps) (.f64 eps eps)))))

Compiler

Compiled 1 341 to 1 247 computations (7% saved)

series36.0ms (0.5%)

Memory

-7.2MiB live, 38.1MiB allocated; 21ms collecting garbage

Counts

41 → 153

Calls

Call 1

Inputs
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#s(literal 2 binary64)
(.f64 #s(approx (sin ( (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64))
#s(literal -1/645120 binary64)
(*.f64 eps eps)
eps
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))
(*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))
(+.f64 (+.f64 eps x) x)
(+.f64 eps x)
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)))
#s(literal -1/2 binary64)
(fma.f64 eps x (*.f64 eps eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (sin x) (.f64 (fma.f64 (fma.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 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))
#s(literal 1/120 binary64)
(*.f64 x x)
#s(literal -1/6 binary64)
#s(literal 1 binary64)

Outputs
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ (+ eps x) x) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 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) -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))) #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 (* (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 (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 (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (+ (* (+ (* 1/120 (* 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 (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (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 (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (sin x) #s(hole binary64 (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 (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#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 (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 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 (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* -1/48 (pow eps 2)))))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) #s(hole binary64 -1/48))
#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) #s(hole binary64 (- (* 1/3840 (pow eps 2)) 1/48)))
#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) #s(hole binary64 (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))
#s(approx (+ (* -1/645120 (* eps eps)) 1/3840) #s(hole binary64 1/3840))
#s(approx (+ (* -1/645120 (* eps eps)) 1/3840) #s(hole binary64 (+ 1/3840 (* -1/645120 (pow eps 2)))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (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 (+ (* (* -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 (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 (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1/645120 (pow eps 7))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 (* -1/645120 (pow eps 6))))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))))
#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) #s(hole binary64 (* -1/645120 (pow eps 4))))
#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) #s(hole binary64 (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))))
#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) #s(hole binary64 (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))))
#s(approx (+ (* -1/645120 (* eps eps)) 1/3840) #s(hole binary64 (* -1/645120 (pow eps 2))))
#s(approx (+ (* -1/645120 (* eps eps)) 1/3840) #s(hole binary64 (* (pow eps 2) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x 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 (+ (* (* -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 (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#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 (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))

Calls

6 calls:

Time	Variable		Point	Expression
15.0ms	x	@	inf	((* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) (sin (* (- (+ eps x) x) 1/2)) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (+ (* -1/645120 (* eps eps)) 1/3840) -1/645120 (* eps eps) eps 1/3840 -1/48 1/2 (cos (* (+ (+ eps x) x) 1/2)) (* (+ (+ eps x) x) 1/2) (+ (+ eps x) x) (+ eps x) 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))) -1/2 (+ (* eps x) (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ 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) -1/6 1)
4.0ms	eps	@	-inf	((* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) (sin (* (- (+ eps x) x) 1/2)) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (+ (* -1/645120 (* eps eps)) 1/3840) -1/645120 (* eps eps) eps 1/3840 -1/48 1/2 (cos (* (+ (+ eps x) x) 1/2)) (* (+ (+ eps x) x) 1/2) (+ (+ eps x) x) (+ eps x) 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))) -1/2 (+ (* eps x) (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ 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) -1/6 1)
4.0ms	eps	@	inf	((* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) (sin (* (- (+ eps x) x) 1/2)) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (+ (* -1/645120 (* eps eps)) 1/3840) -1/645120 (* eps eps) eps 1/3840 -1/48 1/2 (cos (* (+ (+ eps x) x) 1/2)) (* (+ (+ eps x) x) 1/2) (+ (+ eps x) x) (+ eps x) 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))) -1/2 (+ (* eps x) (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ 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) -1/6 1)
4.0ms	x	@	-inf	((* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) (sin (* (- (+ eps x) x) 1/2)) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (+ (* -1/645120 (* eps eps)) 1/3840) -1/645120 (* eps eps) eps 1/3840 -1/48 1/2 (cos (* (+ (+ eps x) x) 1/2)) (* (+ (+ eps x) x) 1/2) (+ (+ eps x) x) (+ eps x) 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))) -1/2 (+ (* eps x) (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ 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) -1/6 1)
3.0ms	eps	@	0	((* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) (sin (* (- (+ eps x) x) 1/2)) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (+ (* -1/645120 (* eps eps)) 1/3840) -1/645120 (* eps eps) eps 1/3840 -1/48 1/2 (cos (* (+ (+ eps x) x) 1/2)) (* (+ (+ eps x) x) 1/2) (+ (+ eps x) x) (+ eps x) 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))) -1/2 (+ (* eps x) (* eps eps)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ 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) -1/6 1)

rewrite210.0ms (2.9%)

Memory

-5.6MiB live, 178.6MiB allocated; 41ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	647	3941
0	692	3767
1	4014	3747
0	8286	3563

Stop Event

1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

194 → 478

Calls

Call 1

Inputs
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#s(literal 2 binary64)
(.f64 #s(approx (sin ( (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64))
#s(literal -1/645120 binary64)
(*.f64 eps eps)
eps
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
(cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))
(*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))
(+.f64 (+.f64 eps x) x)
(+.f64 eps x)
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)))
#s(literal -1/2 binary64)
(fma.f64 eps x (*.f64 eps eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (sin x) (.f64 (fma.f64 (fma.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 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))
#s(literal 1/120 binary64)
(*.f64 x x)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ (+ eps x) x) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 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) -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))) #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 (* (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 (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 (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (+ (* (+ (* 1/120 (* 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 (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (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 (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (sin x) #s(hole binary64 (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 (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#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 (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 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 (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* -1/48 (pow eps 2)))))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))
#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) #s(hole binary64 -1/48))
#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) #s(hole binary64 (- (* 1/3840 (pow eps 2)) 1/48)))
#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) #s(hole binary64 (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))
#s(approx (+ (* -1/645120 (* eps eps)) 1/3840) #s(hole binary64 1/3840))
#s(approx (+ (* -1/645120 (* eps eps)) 1/3840) #s(hole binary64 (+ 1/3840 (* -1/645120 (pow eps 2)))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (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 (+ (* (* -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 (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 (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1/645120 (pow eps 7))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 (* -1/645120 (pow eps 6))))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))))
#s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))))
#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) #s(hole binary64 (* -1/645120 (pow eps 4))))
#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) #s(hole binary64 (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))))
#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) #s(hole binary64 (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))))
#s(approx (+ (* -1/645120 (* eps eps)) 1/3840) #s(hole binary64 (* -1/645120 (pow eps 2))))
#s(approx (+ (* -1/645120 (* eps eps)) 1/3840) #s(hole binary64 (* (pow eps 2) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x 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 (+ (* (* -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 (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (+ eps x) x) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#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 (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))

Outputs
(.f64 (.f64 #s(literal 2 binary64) #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64)) eps))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
(.f64 (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(approx (sin ( (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(approx (sin ( (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64)) eps))))
(fma.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(approx (sin ( (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64)) eps)) (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64)) eps))))
(fma.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64)) eps)) (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(approx (sin ( (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64)) eps))))
(+.f64 (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64)) eps))) (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64)) eps))))
#s(literal 2 binary64)
(.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64)) eps)))
(.f64 #s(approx (sin ( (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
#s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64)) eps)
(.f64 eps (fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 eps (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) eps)))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) eps) eps))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 eps (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) eps)))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) eps) eps))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 eps (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps)))
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(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 (neg.f64 (neg.f64 x)))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x)))
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(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 (neg.f64 (neg.f64 eps)))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
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(neg.f64 (-.f64 (neg.f64 x) eps))
(neg.f64 (-.f64 (neg.f64 eps) x))
(-.f64 x (neg.f64 eps))
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(fma.f64 #s(literal 1 binary64) x (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) x))
(fma.f64 x #s(literal 1 binary64) (.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)))
(+.f64 (.f64 x #s(literal 1 binary64)) (.f64 x (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) x))
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(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(-.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (.f64 (neg.f64 (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))))
(-.f64 #s(literal 1 binary64) (neg.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x)))
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#s(literal 1/120 binary64)
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(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
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(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
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#s(literal -1/6 binary64)
#s(literal 1 binary64)
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#s(approx (sin (* (- (+ eps x) x) 1/2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
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#s(approx (* (+ (+ eps x) x) 1/2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (* (+ (+ eps x) x) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (+ eps x) x) eps)
#s(approx (+ (+ eps x) x) (fma.f64 x #s(literal 2 binary64) eps))
#s(approx (+ eps x) (+.f64 x eps))
#s(approx x 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)))
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#s(approx (sin (+ x eps)) (sin.f64 (+.f64 x eps)))
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#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 x) eps (sin.f64 x)))
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#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal -1/645120 binary64)))
#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/645120 binary64))))
#s(approx (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/645120 binary64)) (/.f64 #s(literal 1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (+ (* -1/645120 (* eps eps)) 1/3840) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))
#s(approx (+ (* -1/645120 (* eps eps)) 1/3840) (.f64 (-.f64 (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/645120 binary64)) (*.f64 eps eps)))
#s(approx (* (+ (+ eps x) x) 1/2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (+ eps x) x) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 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 (fma.f64 (/.f64 (.f64 x x) eps) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) eps))) (*.f64 eps eps)))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (.f64 (fma.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 (* 2 (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2)))) (.f64 (.f64 (cos.f64 (.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)))
#s(approx (* (sin (* (- (+ eps x) x) 1/2)) (cos (* (+ (+ eps x) x) 1/2))) (.f64 (cos.f64 (.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (neg.f64 (.f64 (-.f64 #s(literal 1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 7 binary64)))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (neg.f64 (.f64 (+.f64 #s(literal 1/645120 binary64) (-.f64 (/.f64 #s(literal 1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)))) (pow.f64 eps #s(literal 7 binary64)))))
#s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (neg.f64 (.f64 (-.f64 (+.f64 #s(literal 1/645120 binary64) (-.f64 (/.f64 #s(literal 1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) eps)))) (pow.f64 eps #s(literal 7 binary64)))))
#s(approx (cos (* (+ (+ eps x) x) 1/2)) (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))))
#s(approx (* (+ (+ eps x) x) 1/2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (+ eps x) x) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -2 binary64) #s(literal -1 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps eps)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 x eps)))

eval78.0ms (1.1%)

Memory: 22.2MiB live, 68.0MiB allocated; 4ms collecting garbage
Compiler: Compiled 5 866 to 2 550 computations (56.5% saved)

prune66.0ms (0.9%)

Memory

-11.3MiB live, 52.0MiB allocated; 7ms collecting garbage

Pruning

34 alts after pruning (29 fresh and 5 done)

	Pruned	Kept	Total
New	419	17	436
Fresh	8	12	20
Picked	2	3	5
Done	0	2	2
Total	429	34	463

Accuracy

100.0%

Counts

463 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
	61.4%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
✓	61.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	60.2%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
	100.0%	(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)))))))
	99.8%	(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))))))
	99.8%	(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 #s(approx (* (+ (+ eps x) x) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
	99.7%	(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(approx (cos (* (+ (+ eps x) x) 1/2)) (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/48 binary64) (.f64 #s(literal -1/8 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))))
	99.8%	(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
	99.7%	(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
	99.3%	(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
	18.0%	(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) #s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (neg.f64 (.f64 (-.f64 (+.f64 #s(literal 1/645120 binary64) (-.f64 (/.f64 #s(literal 1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) eps)))) (pow.f64 eps #s(literal 7 binary64)))))) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
	98.7%	#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))
✓	99.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
✓	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	98.2%	#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))
	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #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))) eps))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.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))
	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
	98.0%	#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))
	98.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 x eps) eps) #s(literal -1/2 binary64)) x eps)))
	98.1%	#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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
	5.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
	50.2%	#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 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps 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)))))
✓	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
	26.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (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))) eps))) (.f64 (.f64 eps eps) (.f64 eps eps)))))

Compiler

Compiled 1 669 to 1 218 computations (27% saved)

regimes80.0ms (1.1%)

Memory

-34.9MiB live, 54.7MiB allocated; 9ms collecting garbage

Counts

61 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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 x eps) 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 (fma.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) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) 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 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (.f64 (.f64 #s(literal 1 binary64) eps) #s(literal -1/6 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) (.f64 (fma.f64 (fma.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 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 #s(approx (* (+ (+ eps x) x) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#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 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) #s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (neg.f64 (.f64 (-.f64 (+.f64 #s(literal 1/645120 binary64) (-.f64 (/.f64 #s(literal 1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) eps)))) (pow.f64 eps #s(literal 7 binary64)))))) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (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))) eps))) (.f64 (.f64 eps eps) (.f64 eps eps)))))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(approx (cos (* (+ (+ eps x) x) 1/2)) (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/48 binary64) (.f64 #s(literal -1/8 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)))))))

Outputs
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)))))))

Outputs

(*.f64 #s(literal 2 binary64) (*.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))))))

Calls

3 calls:

40.0ms	eps
13.0ms	x
13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

Accuracy	Segments	Branch
100.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
100.0%	1	`x`
100.0%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes46.0ms (0.6%)

Memory

38.6MiB live, 82.3MiB allocated; 6ms collecting garbage

Counts

60 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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 x eps) 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 (fma.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) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) 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 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (.f64 (.f64 #s(literal 1 binary64) eps) #s(literal -1/6 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) (.f64 (fma.f64 (fma.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 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 #s(approx (* (+ (+ eps x) x) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#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 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 (-.f64 (+.f64 eps x) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) #s(approx (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (neg.f64 (.f64 (-.f64 (+.f64 #s(literal 1/645120 binary64) (-.f64 (/.f64 #s(literal 1/48 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal 1/3840 binary64) (.f64 eps eps)))) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 eps eps) eps)))) (pow.f64 eps #s(literal 7 binary64)))))) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (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))) eps))) (.f64 (.f64 eps eps) (.f64 eps eps)))))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(approx (cos (* (+ (+ eps x) x) 1/2)) (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/48 binary64) (.f64 #s(literal -1/8 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))))

Outputs
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 #s(approx (* (+ (+ eps x) x) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))

Outputs

(*.f64 #s(literal 2 binary64) (*.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 #s(approx (* (+ (+ eps x) x) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))))

Calls

3 calls:

17.0ms	x
13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
13.0ms	eps

Results

Accuracy	Segments	Branch
99.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.8%	1	`x`
99.8%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes55.0ms (0.8%)

Memory

-13.0MiB live, 41.4MiB allocated; 7ms collecting garbage

Counts

46 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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 x eps) 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 (fma.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) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) 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 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (.f64 (.f64 #s(literal 1 binary64) eps) #s(literal -1/6 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) (.f64 (fma.f64 (fma.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 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Outputs

(*.f64 #s(literal 2 binary64) (*.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))

Calls

3 calls:

33.0ms	x
10.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms	eps

Results

Accuracy	Segments	Branch
99.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.8%	1	`x`
99.8%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes45.0ms (0.6%)

Memory

3.4MiB live, 49.1MiB allocated; 3ms collecting garbage

Counts

43 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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 x eps) 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 (fma.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) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) 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 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (.f64 (.f64 #s(literal 1 binary64) eps) #s(literal -1/6 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) (.f64 (fma.f64 (fma.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

(*.f64 #s(literal 2 binary64) (*.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))

Calls

3 calls:

24.0ms	x
10.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	eps

Results

Accuracy	Segments	Branch
99.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.7%	1	`x`
99.7%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes32.0ms (0.4%)

Memory

-3.2MiB live, 40.4MiB allocated; 6ms collecting garbage

Counts

38 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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 x eps) 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 (fma.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) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) 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 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(.f64 #s(literal 2 binary64) (.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (.f64 (.f64 #s(literal 1 binary64) eps) #s(literal -1/6 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))

Outputs

(*.f64 #s(literal 2 binary64) (*.f64 #s(approx (sin (* (- (+ eps x) x) 1/2)) (*.f64 #s(approx (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) #s(literal 1/2 binary64)) eps)) (cos.f64 (*.f64 (+.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)))))

Calls

3 calls:

13.0ms	x
9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	eps

Results

Accuracy	Segments	Branch
99.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.3%	1	`x`
99.3%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes28.0ms (0.4%)

Memory

2.8MiB live, 45.6MiB allocated; 5ms collecting garbage

Counts

34 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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 x eps) 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 (fma.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) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) 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 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))

Outputs

#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 eps #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) (cos.f64 x)) eps))

Calls

3 calls:

11.0ms	x
8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	eps

Results

Accuracy	Segments	Branch
98.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.8%	1	`x`
98.8%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes65.0ms (0.9%)

Memory

-30.1MiB live, 31.0MiB allocated; 15ms collecting garbage

Counts

32 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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 x eps) 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 (fma.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) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) 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))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))

Calls

3 calls:

49.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	x
7.0ms	eps

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes21.0ms (0.3%)

Memory

29.6MiB live, 29.6MiB allocated; 0ms collecting garbage

Counts

29 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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 x eps) 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 (fma.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) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))

Calls

3 calls:

7.0ms	eps
7.0ms	x
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes47.0ms (0.7%)

Memory

-26.4MiB live, 20.7MiB allocated; 2ms collecting garbage

Counts

28 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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 x eps) 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 (fma.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) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))

Calls

3 calls:

33.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	x
6.0ms	eps

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes20.0ms (0.3%)

Memory

24.3MiB live, 24.3MiB allocated; 0ms collecting garbage

Counts

27 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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 x eps) 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 (fma.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) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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 (cos.f64 x) eps))

Calls

3 calls:

6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	x
6.0ms	eps

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes34.0ms (0.5%)

Memory

-23.4MiB live, 21.0MiB allocated; 4ms collecting garbage

Counts

25 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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 x eps) 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 (fma.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) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.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)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (fma.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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (+.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #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))) eps))

Outputs

#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 eps #s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))

Calls

3 calls:

6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
98.6%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.6%	1	`x`
98.6%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes16.0ms (0.2%)

Memory

30.9MiB live, 30.9MiB allocated; 0ms collecting garbage

Counts

21 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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 x eps) 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 (fma.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) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (.f64 eps eps)))))

Outputs

#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.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))

Calls

3 calls:

5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	x
5.0ms	eps

Results

Accuracy	Segments	Branch
98.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.4%	1	`x`
98.4%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes18.0ms (0.3%)

Memory

-8.9MiB live, 32.8MiB allocated; 7ms collecting garbage

Counts

18 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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 x eps) 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 (fma.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) #s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)) eps))) (*.f64 eps eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps))) #s(approx (sin (+ x (/ (PI) 2))) (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 x x))) x eps)))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))

Calls

3 calls:

8.0ms	x
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	eps

Results

Accuracy	Segments	Branch
98.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.3%	1	`x`
98.3%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes11.0ms (0.2%)

Memory

19.8MiB live, 19.8MiB allocated; 0ms collecting garbage

Counts

13 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 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 x eps) 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 x eps) eps) #s(literal -1/2 binary64)) x eps)))

Calls

3 calls:

3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps
3.0ms	x

Results

Accuracy	Segments	Branch
98.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.2%	1	`x`
98.2%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes13.0ms (0.2%)

Memory

-40.0MiB live, 16.8MiB allocated; 6ms collecting garbage

Counts

10 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (.f64 (.f64 eps x) #s(literal -1/2 binary64))) x 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) #s(approx (+ ( eps x) (* eps eps)) (*.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #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)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (sin (+ x (/ (PI) 2))) eps) -1/6) (* (sin x) -1/2))) (sin (+ x (/ (PI) 2)))) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))

Outputs

#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))) x eps)))

Calls

3 calls:

6.0ms	x
3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps

Results

Accuracy	Segments	Branch
98.1%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.1%	1	`x`
98.1%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes5.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (.f64 (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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) 1/12) (* -1/2 eps)) x) (* (* eps eps) -1/2)) x) eps) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))))

Calls

3 calls:

2.0ms	x
2.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	eps

Results

Accuracy	Segments	Branch
98.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.0%	1	`x`
98.0%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes5.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB allocated; 0ms collecting garbage

Accuracy

Total -58.8b remaining (-2936.9%)

Threshold costs -58.8b (-2936.9%)

Counts

3 → 1

Calls

Call 1

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 (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) -1/2) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x))))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))

Calls

3 calls:

1.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms	x
1.0ms	eps

Results

Accuracy	Segments	Branch
96.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
96.9%	1	`x`
96.9%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

derivations560.0ms (7.8%)

Memory

-6.7MiB live, 409.8MiB allocated; 66ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 247 to 167 computations (32.4% saved)

preprocess156.0ms (2.2%)

Memory: -3.9MiB live, 283.1MiB allocated; 46ms collecting garbage
Compiler: Compiled 290 to 206 computations (29% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze45.0ms (0.6%)

sample4.6s (64%)

preprocess71.0ms (1%)

series4.0ms (0.1%)

rewrite137.0ms (1.9%)

eval13.0ms (0.2%)

prune7.0ms (0.1%)

series40.0ms (0.6%)

rewrite174.0ms (2.4%)

eval60.0ms (0.8%)

prune25.0ms (0.4%)

series52.0ms (0.7%)

rewrite200.0ms (2.8%)

eval73.0ms (1%)

prune36.0ms (0.5%)

series36.0ms (0.5%)

rewrite210.0ms (2.9%)

eval78.0ms (1.1%)

prune66.0ms (0.9%)

regimes80.0ms (1.1%)

regimes46.0ms (0.6%)

regimes55.0ms (0.8%)

regimes45.0ms (0.6%)

regimes32.0ms (0.4%)

regimes28.0ms (0.4%)

regimes65.0ms (0.9%)

regimes21.0ms (0.3%)

regimes47.0ms (0.7%)

regimes20.0ms (0.3%)

regimes34.0ms (0.5%)

regimes16.0ms (0.2%)

regimes18.0ms (0.3%)

regimes11.0ms (0.2%)

regimes13.0ms (0.2%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

derivations560.0ms (7.8%)

preprocess156.0ms (2.2%)

end0.0ms (0%)

Profiling