Metrics for 2sin (example 3.3)

start0.0ms (0%)

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

analyze39.0ms (0.6%)

Memory

-13.8MiB live, 30.4MiB allocated; 11ms 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)

sample4.3s (62.8%)

Memory

153.2MiB live, 4 385.5MiB allocated; 1.7s collecting garbage

Samples

1.7s	26 113×	0	invalid
778.0ms	5 577×	1	valid
200.0ms	2 679×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.7s

ival-sin: 651.0ms (38.5% of total)

ival-fabs: 269.0ms (15.9% of total)

ival-add!: 196.0ms (11.6% of total)

ival-<: 140.0ms (8.3% of total)

ival-mult!: 135.0ms (8% of total)

adjust: 134.0ms (7.9% of total)

ival-sub!: 90.0ms (5.3% of total)

ival-and: 63.0ms (3.7% of total)

ival-assert: 13.0ms (0.8% of total)

Bogosity

preprocess83.0ms (1.2%)

Memory

-29.3MiB live, 16.4MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	25	50
2	32	50
3	40	50
4	53	50
5	81	50
6	140	50
7	385	50
8	1451	50
9	5230	50

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 12 to 12 computations (0% saved)

series5.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated; 0ms collecting garbage

Counts

6 → 36

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)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))

rewrite192.0ms (2.8%)

Memory

22.6MiB live, 167.7MiB allocated; 48ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	538
0	155	526
1	931	520
0	8567	489

Stop Event

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

Counts

42 → 105

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)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Outputs
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (neg.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))))))
(fma.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))))
(fma.f64 (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(-.f64 (/.f64 (-.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) (sin.f64 (+.f64 eps x)))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))))))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x) (sin.f64 x)))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps))))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x))) (.f64 (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))) (fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x))) (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 x) (sin.f64 eps))))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x)))) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 eps) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps))))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x)) (-.f64 (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 x) (sin.f64 eps))))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x))) (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 eps) (sin.f64 x))))))
(sin.f64 (+.f64 eps x))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
(-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps)))
(-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))
(-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (neg.f64 (cos.f64 eps)) (sin.f64 x)))
(-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)))
(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps))))
(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 x) (sin.f64 eps)))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x))))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 eps) (sin.f64 x)))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (*.f64 (-.f64 eps x) (+.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 eps (-.f64 eps x) (.f64 x 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 (*.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 (-.f64 eps x) (.f64 x x)))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 eps eps (.f64 x (-.f64 x eps))))
(-.f64 (/.f64 (.f64 (.f64 x x) x) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (/.f64 (.f64 (.f64 eps eps) (neg.f64 eps)) (fma.f64 eps (-.f64 eps x) (.f64 x 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 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 eps (neg.f64 x))
(-.f64 x (neg.f64 eps))
(+.f64 (/.f64 (.f64 (.f64 x x) x) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (/.f64 (.f64 (.f64 eps eps) eps) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(+.f64 (/.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 (*.f64 (neg.f64 x) #s(literal -1 binary64)))
(+.f64 eps x)
(+.f64 x (*.f64 (neg.f64 eps) #s(literal -1 binary64)))
(+.f64 x eps)
x
eps
(sin.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 x (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 x (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))) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (sin.f64 eps)))
#s(approx (sin (+ x eps)) (sin.f64 eps))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 eps) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 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) x)
#s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) 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) x)
#s(approx (+ x eps) (fma.f64 (/.f64 eps x) x x))
#s(approx (sin x) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 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)) (sin.f64 x))
#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)
#s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval13.0ms (0.2%)

Memory: -23.6MiB live, 20.1MiB allocated; 6ms collecting garbage
Compiler: Compiled 1 107 to 385 computations (65.2% saved)

prune7.0ms (0.1%)

Memory

13.3MiB live, 13.3MiB allocated; 0ms collecting garbage

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	88	10	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	11	99

Accuracy

99.9%

Counts

99 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	64.0%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	7.2%	(/.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 x) (sin.f64 (+.f64 eps x))))
▶	99.7%	(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
✓	63.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	62.3%	(-.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)))
▶	63.8%	(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 x (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (sin.f64 eps)))
	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))
▶	99.4%	#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))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	97.2%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 262 to 252 computations (3.8% saved)

series40.0ms (0.6%)

Memory

29.5MiB live, 72.3MiB allocated; 5ms collecting garbage

Counts

38 → 198

Calls

Call 1

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

Outputs
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (sin eps)))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (+ (sin eps) (* -1 (* x (+ 1 (* -1 (cos eps))))))))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) (+ 1 (* -1 (cos eps))))))))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* x (- 1/6 (* 1/6 (cos eps)))))) (+ 1 (* -1 (cos eps))))))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (sin eps)))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (* x (+ 1 (* -1 (cos eps))))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (* x (+ 1 (+ (* -1 (cos eps)) (* (pow x 2) (- (* 1/6 (cos eps)) 1/6)))))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (* x (+ 1 (+ (* -1 (cos eps)) (* (pow x 2) (- (+ (* 1/6 (cos eps)) (* (pow x 2) (+ 1/120 (* -1/120 (cos eps))))) 1/6)))))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (* x (+ 1 (+ (* -1 (cos eps)) (* (pow x 2) (- (+ (* 1/6 (cos eps)) (* (pow x 2) (+ 1/120 (+ (* -1/120 (cos eps)) (* (pow x 2) (- (* 1/5040 (cos eps)) 1/5040)))))) 1/6)))))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 x)))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* 1/6 (pow x 2)) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 1))
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* 2 (sin (* 1/2 eps)))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (/ (- x (- x eps)) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (- x (- x eps)) #s(hole binary64 eps))
#s(approx (- x eps) #s(hole binary64 (* -1 eps)))
#s(approx (- x eps) #s(hole binary64 (- x eps)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 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) 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) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (+ eps x) x) 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))
#s(approx (+ eps x) #s(hole binary64 (+ eps 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) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (* (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 (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (- (* (cos x) (sin eps)) (+ (sin x) (* -1 (* (cos eps) (sin x)))))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (* (cos x) (sin eps))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (+ (sin x) (* -1 (* (cos eps) (sin x))))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (* 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 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (- x eps) #s(hole binary64 x))
#s(approx (- x eps) #s(hole binary64 (* x (+ 1 (* -1 (/ eps x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 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))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps 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) -1/2) #s(hole binary64 (* -1/2 (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 (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (- x eps) #s(hole binary64 (* -1 (* x (- (/ eps x) 1)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 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 (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (* -1 (+ (sin x) (* -1 (sin x))))))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (- (* eps (cos x)) (+ (sin x) (* -1 (sin x))))))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (- (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (+ (sin x) (* -1 (sin x))))))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (- (* eps (+ (cos x) (* eps (- (* -1/6 (* eps (cos x))) (* 1/2 (sin x)))))) (+ (sin x) (* -1 (sin x))))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (* eps (cos x))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (+ (sin x) (* -1 (sin x)))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (+ (sin x) (+ (* -1 (sin x)) (* 1/2 (* (pow eps 2) (sin x)))))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (+ (sin x) (+ (* -1 (sin x)) (* (pow eps 2) (+ (* -1/24 (* (pow eps 2) (sin x))) (* 1/2 (sin x))))))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (+ (sin x) (+ (* -1 (sin x)) (* (pow eps 2) (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/24 (sin x)) (* 1/720 (* (pow eps 2) (sin x)))))))))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (- x eps) #s(hole binary64 (+ x (* -1 eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (cos x)))
#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 (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- x eps) #s(hole binary64 (* eps (- (/ x eps) 1))))
#s(approx (/ (+ (+ eps x) x) 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 (* (+ (* 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 (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 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (- x eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ x eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 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 (* (+ (* 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
11.0ms	x	@	-inf	((- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) (* (cos x) (sin eps)) (cos x) x (sin eps) eps (+ (* (neg (sin x)) (cos eps)) (sin x)) (neg (sin x)) (sin x) (cos eps) (- (sin (+ x eps)) (sin x)) (- (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) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) 2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps 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) (* (sin x) -1/2) -1/2)
7.0ms	x	@	0	((- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) (* (cos x) (sin eps)) (cos x) x (sin eps) eps (+ (* (neg (sin x)) (cos eps)) (sin x)) (neg (sin x)) (sin x) (cos eps) (- (sin (+ x eps)) (sin x)) (- (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) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) 2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps 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) (* (sin x) -1/2) -1/2)
6.0ms	x	@	inf	((- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) (* (cos x) (sin eps)) (cos x) x (sin eps) eps (+ (* (neg (sin x)) (cos eps)) (sin x)) (neg (sin x)) (sin x) (cos eps) (- (sin (+ x eps)) (sin x)) (- (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) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) 2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps 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) (* (sin x) -1/2) -1/2)
5.0ms	eps	@	-inf	((- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) (* (cos x) (sin eps)) (cos x) x (sin eps) eps (+ (* (neg (sin x)) (cos eps)) (sin x)) (neg (sin x)) (sin x) (cos eps) (- (sin (+ x eps)) (sin x)) (- (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) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) 2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps 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) (* (sin x) -1/2) -1/2)
4.0ms	eps	@	0	((- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) (* (cos x) (sin eps)) (cos x) x (sin eps) eps (+ (* (neg (sin x)) (cos eps)) (sin x)) (neg (sin x)) (sin x) (cos eps) (- (sin (+ x eps)) (sin x)) (- (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) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) 2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps 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) (* (sin x) -1/2) -1/2)

rewrite181.0ms (2.7%)

Memory

-13.0MiB live, 228.6MiB allocated; 31ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	813	4256
0	866	4081
1	4777	4061
0	8201	3871

Stop Event

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

Counts

236 → 393

Calls

Call 1

Inputs
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
(*.f64 (cos.f64 x) (sin.f64 eps))
(cos.f64 x)
x
(sin.f64 eps)
eps
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x))
(neg.f64 (sin.f64 x))
(sin.f64 x)
(cos.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (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 -1/6 binary64)
#s(literal 1 binary64)
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))))
#s(literal 2 binary64)
(sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))
(/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))
(-.f64 x (-.f64 x eps))
(-.f64 x eps)
(cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(+.f64 (+.f64 eps x) x)
(+.f64 eps 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)
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (sin eps)))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (+ (sin eps) (* -1 (* x (+ 1 (* -1 (cos eps))))))))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) (+ 1 (* -1 (cos eps))))))))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* x (- 1/6 (* 1/6 (cos eps)))))) (+ 1 (* -1 (cos eps))))))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (sin eps)))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (* x (+ 1 (* -1 (cos eps))))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (* x (+ 1 (+ (* -1 (cos eps)) (* (pow x 2) (- (* 1/6 (cos eps)) 1/6)))))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (* x (+ 1 (+ (* -1 (cos eps)) (* (pow x 2) (- (+ (* 1/6 (cos eps)) (* (pow x 2) (+ 1/120 (* -1/120 (cos eps))))) 1/6)))))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (* x (+ 1 (+ (* -1 (cos eps)) (* (pow x 2) (- (+ (* 1/6 (cos eps)) (* (pow x 2) (+ 1/120 (+ (* -1/120 (cos eps)) (* (pow x 2) (- (* 1/5040 (cos eps)) 1/5040)))))) 1/6)))))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 x)))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* 1/6 (pow x 2)) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* -1/120 (pow x 2)))) 1))))
#s(approx (neg (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/6 (* (pow x 2) (- (* 1/5040 (pow x 2)) 1/120)))) 1))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 1))
#s(approx (+ (* (* x x) -1/6) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* 2 (sin (* 1/2 eps)))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (/ (- x (- x eps)) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (- x (- x eps)) #s(hole binary64 eps))
#s(approx (- x eps) #s(hole binary64 (* -1 eps)))
#s(approx (- x eps) #s(hole binary64 (- x eps)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 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) 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) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (+ eps x) x) 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))
#s(approx (+ eps x) #s(hole binary64 (+ eps 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) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (* (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 (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (- (* (cos x) (sin eps)) (+ (sin x) (* -1 (* (cos eps) (sin x)))))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (* (cos x) (sin eps))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (+ (sin x) (* -1 (* (cos eps) (sin x))))))
#s(approx (neg (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (* 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 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (- x eps) #s(hole binary64 x))
#s(approx (- x eps) #s(hole binary64 (* x (+ 1 (* -1 (/ eps x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 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))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps 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) -1/2) #s(hole binary64 (* -1/2 (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 (* (+ (* (* x x) -1/6) 1) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (- x eps) #s(hole binary64 (* -1 (* x (- (/ eps x) 1)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 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 (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (* -1 (+ (sin x) (* -1 (sin x))))))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (- (* eps (cos x)) (+ (sin x) (* -1 (sin x))))))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (- (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (+ (sin x) (* -1 (sin x))))))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) #s(hole binary64 (- (* eps (+ (cos x) (* eps (- (* -1/6 (* eps (cos x))) (* 1/2 (sin x)))))) (+ (sin x) (* -1 (sin x))))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (* eps (cos x))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))))
#s(approx (* (cos x) (sin eps)) #s(hole binary64 (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (+ (sin x) (* -1 (sin x)))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (+ (sin x) (+ (* -1 (sin x)) (* 1/2 (* (pow eps 2) (sin x)))))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (+ (sin x) (+ (* -1 (sin x)) (* (pow eps 2) (+ (* -1/24 (* (pow eps 2) (sin x))) (* 1/2 (sin x))))))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) #s(hole binary64 (+ (sin x) (+ (* -1 (sin x)) (* (pow eps 2) (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/24 (sin x)) (* 1/720 (* (pow eps 2) (sin x)))))))))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- x (- x eps)) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (- x eps) #s(hole binary64 (+ x (* -1 eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (cos x)))
#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 (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- x eps) #s(hole binary64 (* eps (- (/ x eps) 1))))
#s(approx (/ (+ (+ eps x) x) 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 (* (+ (* 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 (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 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (- x eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ x eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 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 (* (+ (* 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
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (-.f64 eps (neg.f64 x)) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (-.f64 eps (neg.f64 x)) x) #s(literal 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 (neg.f64 x)))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64))) (fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (-.f64 eps (neg.f64 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 (neg.f64 x)))))) (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))))
(/.f64 (-.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x))))))
(-.f64 (-.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)))
(-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x))
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
(*.f64 (sin.f64 eps) (cos.f64 x))
(*.f64 (cos.f64 x) (sin.f64 eps))
(/.f64 (+.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 (+.f64 eps (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 eps (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 eps (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) eps)) (cos.f64 (+.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) eps))) #s(literal 2 binary64))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
x
(sin.f64 eps)
eps
(/.f64 (-.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (sin.f64 x)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) #s(literal 2 binary64))) (-.f64 (sin.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps))))
(/.f64 (+.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) #s(literal 2 binary64)) (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (sin.f64 x)))))
(/.f64 (+.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) #s(literal 3 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) #s(literal 2 binary64)) (.f64 (sin.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps))))))
(fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x))
(fma.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal -1 binary64) (sin.f64 x))
(fma.f64 (neg.f64 (cos.f64 eps)) (sin.f64 x) (sin.f64 x))
(fma.f64 #s(literal -1 binary64) (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(fma.f64 (cos.f64 eps) (neg.f64 (sin.f64 x)) (sin.f64 x))
(-.f64 (sin.f64 x) (.f64 #s(literal 1 binary64) (.f64 (cos.f64 eps) (sin.f64 x))))
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (sin.f64 x))
(+.f64 (sin.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)))
(*.f64 #s(literal -1 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal -1 binary64))
(neg.f64 (sin.f64 x))
(sin.f64 (+.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (neg.f64 x))
(sin.f64 (+.f64 x (PI.f64)))
(fma.f64 (sin.f64 x) (cos.f64 (PI.f64)) (*.f64 (cos.f64 x) (sin.f64 (PI.f64))))
(-.f64 (.f64 (cos.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (.f64 (sin.f64 x) (cos.f64 (PI.f64))) (.f64 (cos.f64 x) (sin.f64 (PI.f64))))
(sin.f64 x)
(sin.f64 (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))))
(fma.f64 (sin.f64 eps) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 eps) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (neg.f64 eps)))
(cos.f64 (neg.f64 eps))
(cos.f64 eps)
(+.f64 (.f64 (sin.f64 eps) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 eps) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 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(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))) (+.f64 (sin.f64 (+.f64 eps x)) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))))) (fma.f64 #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) (.f64 (sin.f64 (+.f64 eps x)) #s(approx (sin x) (.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))))
(-.f64 (sin.f64 (+.f64 eps x)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(sin.f64 (+.f64 eps x))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (sin.f64 eps) (cos.f64 x)))
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(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) (sin.f64 eps))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) (fma.f64 (neg.f64 x) (+.f64 (neg.f64 (cos.f64 eps)) #s(literal 1 binary64)) (sin.f64 eps)))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) (fma.f64 x (-.f64 (-.f64 (.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (neg.f64 (cos.f64 eps))) (sin.f64 eps)))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) (fma.f64 x (-.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x) #s(literal 1 binary64)) (neg.f64 (cos.f64 eps))) (sin.f64 eps)))
#s(approx (* (cos x) (sin eps)) (sin.f64 eps))
#s(approx (* (cos x) (sin eps)) (fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) (sin.f64 eps) (sin.f64 eps)))
#s(approx (* (cos x) (sin eps)) (fma.f64 (fma.f64 (.f64 (.f64 x x) (sin.f64 eps)) #s(literal 1/24 binary64) (.f64 (sin.f64 eps) #s(literal -1/2 binary64))) (.f64 x x) (sin.f64 eps)))
#s(approx (* (cos x) (sin eps)) (fma.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 eps) (.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) (sin.f64 eps))) (.f64 x x))) (.f64 x x) (sin.f64 eps)))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx x x)
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) (*.f64 (+.f64 (neg.f64 (cos.f64 eps)) #s(literal 1 binary64)) x))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) (.f64 (+.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (cos.f64 eps)) #s(literal 1/6 binary64)) (*.f64 x x) (neg.f64 (cos.f64 eps))) #s(literal 1 binary64)) x))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) (.f64 x (+.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal 1/6 binary64) (-.f64 (.f64 (fma.f64 (cos.f64 eps) #s(literal -1/120 binary64) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 (cos.f64 eps))) #s(literal 1 binary64))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) (.f64 (+.f64 (fma.f64 (-.f64 (fma.f64 (+.f64 (fma.f64 (cos.f64 eps) #s(literal -1/120 binary64) #s(literal 1/120 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/5040 binary64) (cos.f64 eps)) #s(literal 1/5040 binary64)) (.f64 x x))) (.f64 x x) (.f64 #s(literal 1/6 binary64) (cos.f64 eps))) #s(literal 1/6 binary64)) (*.f64 x x) (neg.f64 (cos.f64 eps))) #s(literal 1 binary64)) x))
#s(approx (neg (sin x)) (neg.f64 x))
#s(approx (neg (sin x)) (.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x))
#s(approx (neg (sin x)) (.f64 (-.f64 (.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 (neg (sin x)) (.f64 (-.f64 (.f64 (fma.f64 (-.f64 (.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) x)
#s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (- (sin (+ x eps)) (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)) (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 (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (* (+ (* (* x x) -1/6) 1) x) x)
#s(approx (* (+ (* (* x x) -1/6) 1) x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (+ (* (* x x) -1/6) 1) #s(literal 1 binary64))
#s(approx (+ (* (* x x) -1/6) 1) (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (sin.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (fma.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) x) #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (fma.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64) (neg.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))) x (sin.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) (neg.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) x (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))) x (sin.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
#s(approx (sin (/ (- x (- x eps)) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (/ (- x (- x eps)) 2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (- x (- x eps)) eps)
#s(approx (- x eps) (neg.f64 eps))
#s(approx (- x eps) (-.f64 x eps))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (neg.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 x (-.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) #s(literal -1/2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 x (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) x) #s(literal 1/6 binary64) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (+ eps x) x) eps)
#s(approx (+ (+ eps x) x) (fma.f64 #s(literal 2 binary64) x eps))
#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps (.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) x)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (.f64 eps x) #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 eps x (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) 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 (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (* (cos x) eps) eps)
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/720 binary64) (.f64 #s(literal 1/24 binary64) eps)) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (* (sin x) -1/2) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
#s(approx (* (sin x) -1/2) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) x))
#s(approx (* (sin x) -1/2) (.f64 (-.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/10080 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) x))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
#s(approx (* (cos x) (sin eps)) (*.f64 (sin.f64 eps) (cos.f64 x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
#s(approx (neg (sin x)) (neg.f64 (sin.f64 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 (+ eps x) x)
#s(approx (+ eps x) (*.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 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- x eps) x)
#s(approx (- x eps) (*.f64 (+.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)) x))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) x)
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (+ (+ eps x) x) (+.f64 x x))
#s(approx (+ (+ eps x) x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) 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) -1/2) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (-.f64 eps (neg.f64 x))))
#s(approx (+ eps x) (*.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 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 eps x) #s(literal 1 binary64))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (+ eps x) x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 2 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) (neg.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x))))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) (-.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal 0 binary64) (sin.f64 x))))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 #s(literal 0 binary64) (sin.f64 x))))
#s(approx (- (* (cos x) (sin eps)) (+ (* (neg (sin x)) (cos eps)) (sin x))) (-.f64 (.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 #s(literal 0 binary64) (sin.f64 x))))
#s(approx (* (cos x) (sin eps)) (*.f64 (cos.f64 x) eps))
#s(approx (* (cos x) (sin eps)) (.f64 (fma.f64 (.f64 (*.f64 eps eps) (cos.f64 x)) #s(literal -1/6 binary64) (cos.f64 x)) eps))
#s(approx (* (cos x) (sin eps)) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/120 binary64)) (cos.f64 x) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 eps eps) (cos.f64 x)) eps))
#s(approx (* (cos x) (sin eps)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal -1/5040 binary64)) (cos.f64 x) (.f64 #s(literal 1/120 binary64) (cos.f64 x))) (.f64 eps eps) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 eps eps) (cos.f64 x)) eps))
#s(approx (sin eps) eps)
#s(approx (sin eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 eps eps)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx eps eps)
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) (fma.f64 #s(literal 0 binary64) (sin.f64 x) (.f64 (.f64 #s(literal 1/2 binary64) (*.f64 eps eps)) (sin.f64 x))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) (fma.f64 #s(literal 0 binary64) (sin.f64 x) (.f64 (fma.f64 (.f64 (.f64 eps eps) (sin.f64 x)) #s(literal -1/24 binary64) (.f64 (sin.f64 x) #s(literal 1/2 binary64))) (*.f64 eps eps))))
#s(approx (+ (* (neg (sin x)) (cos eps)) (sin x)) (fma.f64 #s(literal 0 binary64) (sin.f64 x) (.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (.f64 (.f64 #s(literal 1/720 binary64) (.f64 eps eps)) (sin.f64 x))) (.f64 eps eps))) (*.f64 eps eps))))
#s(approx (cos eps) #s(literal 1 binary64))
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 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)) (sin.f64 x))
#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 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (*.f64 (cos.f64 x) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (fma.f64 eps (fma.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) eps) #s(literal 2 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) #s(literal 2 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 (* 2 (sin (/ (- x (- x eps)) 2))) eps)
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (sin (/ (- x (- x eps)) 2)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (sin (/ (- x (- x eps)) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (- x (- x eps)) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (- x (- x eps)) 2)) (.f64 (fma.f64 (-.f64 (.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 (- x eps) (+.f64 (neg.f64 eps) x))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 x))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 eps (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
#s(approx (cos (/ (+ (+ eps x) x) 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)))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (*.f64 (cos.f64 x) 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) (cos.f64 x)) eps))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (cos.f64 x))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
#s(approx (sin eps) (sin.f64 eps))
#s(approx (cos eps) (cos.f64 eps))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (- x eps) (*.f64 (-.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (/ (+ (+ eps x) x) 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 (* (+ (* 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 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (-.f64 x (neg.f64 eps))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (- x eps) (*.f64 (neg.f64 eps) (+.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 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) (-.f64 (.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 (* (+ (* 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 #s(literal 1/6 binary64) (cos.f64 x))) (.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 #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 (+ (* (* (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 #s(literal 1/6 binary64) (cos.f64 x)))))

eval70.0ms (1%)

Memory: 16.8MiB live, 61.8MiB allocated; 4ms collecting garbage
Compiler: Compiled 4 424 to 1 934 computations (56.3% saved)

prune25.0ms (0.4%)

Memory

-14.8MiB live, 30.8MiB allocated; 4ms collecting garbage

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	386	12	398
Fresh	2	3	5
Picked	4	1	5
Done	0	1	1
Total	392	17	409

Accuracy

100.0%

Counts

409 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	64.0%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	99.8%	(-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(approx (+ ( (neg (sin x)) (cos eps)) (sin x)) (fma.f64 #s(literal 0 binary64) (sin.f64 x) (.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (.f64 (.f64 #s(literal 1/720 binary64) (.f64 eps eps)) (sin.f64 x))) (.f64 eps eps))) (*.f64 eps eps)))))
	99.5%	(-.f64 (.f64 (cos.f64 x) #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
✓	63.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.8%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
	99.6%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
▶	99.2%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 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))
✓	99.4%	#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))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (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)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	97.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
▶	97.9%	#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 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	97.2%	#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 (.f64 eps x) #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
▶	97.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
▶	99.9%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))

Compiler

Compiled 623 to 586 computations (5.9% saved)

series38.0ms (0.6%)

Memory

24.3MiB live, 68.1MiB allocated; 5ms collecting garbage

Counts

41 → 222

Calls

Call 1

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

Outputs
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #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 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #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 (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 eps)))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 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 (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 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 (* (+ (* 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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* 2 (sin (* 1/2 eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 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) 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) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (+ eps x) x) 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))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin 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) #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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (+ eps (* 2 x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 x))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* x (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 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))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (- eps (* -2 x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* 1/6 (/ (pow eps 2) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 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 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #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 (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos x))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* -1 (* eps (sin x))) (* 2 (cos x)))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos x)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 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 #s(hole binary64 eps))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (cos x)))
#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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (- (* 1/12 (pow eps 2)) 1/2)))
#s(approx (* 1/12 (* eps eps)) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (* eps eps) -1/6) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 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) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin eps) #s(hole binary64 (sin 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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) 1/6))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* 1/12 (* (pow eps 2) x))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (/ (+ (+ eps x) x) 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 (+ (* (* (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 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 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) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	x	@	-inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) 2 (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* -1/2 eps) -1/2 (* (* eps eps) -1/6) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (cos x))
5.0ms	eps	@	-inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) 2 (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* -1/2 eps) -1/2 (* (* eps eps) -1/6) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (cos x))
5.0ms	eps	@	inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) 2 (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* -1/2 eps) -1/2 (* (* eps eps) -1/6) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (cos x))
5.0ms	x	@	inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) 2 (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* -1/2 eps) -1/2 (* (* eps eps) -1/6) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (cos x))
4.0ms	eps	@	0	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) 2 (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* -1/2 eps) -1/2 (* (* eps eps) -1/6) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) (cos x))

rewrite265.0ms (3.9%)

Memory

-8.2MiB live, 238.9MiB allocated; 59ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	810	5755
0	856	5592
1	4532	5552
0	8277	5301

Stop Event

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

Counts

263 → 417

Calls

Call 1

Inputs
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
#s(literal 2 binary64)
(cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
x
eps
#s(literal 1/2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (sin eps) 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 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps)
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
(+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/12 binary64) (.f64 eps eps))
#s(literal 1/12 binary64)
(*.f64 eps eps)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) eps)
(cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(+.f64 (+.f64 eps x) x)
(+.f64 eps x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
(cos.f64 x)
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #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 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #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 (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 eps)))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 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 (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 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 (* (+ (* 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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* 2 (sin (* 1/2 eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 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) 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) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (+ eps x) x) 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))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin 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) #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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (+ eps (* 2 x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 x))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* x (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 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))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (- eps (* -2 x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1 (/ (+ (* 1/6 (/ (pow eps 2) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 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 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #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 (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos x))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* -1 (* eps (sin x))) (* 2 (cos x)))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos x)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 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 #s(hole binary64 eps))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (cos x)))
#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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (- (* 1/12 (pow eps 2)) 1/2)))
#s(approx (* 1/12 (* eps eps)) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (* eps eps) -1/6) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 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) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin eps) #s(hole binary64 (sin 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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) 1/6))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* 1/12 (* (pow eps 2) x))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (/ (+ (+ eps x) x) 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 (+ (* (* (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 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 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) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))

Outputs
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
(+.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
#s(literal 2 binary64)
(sin.f64 (+.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(-.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)))))
(-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)))))
(cos.f64 (neg.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(cos.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))) (+.f64 eps (*.f64 #s(literal -2 binary64) x)))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (+.f64 x x) (+.f64 x x))) (-.f64 eps (+.f64 x x)))
(/.f64 (-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x x)) (-.f64 (+.f64 eps x) x))
(/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps eps)) (-.f64 (+.f64 x x) eps))
(/.f64 (-.f64 (.f64 (.f64 eps eps) eps) (.f64 #s(literal -8 binary64) (.f64 (.f64 x x) x))) (fma.f64 eps eps (fma.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x) (.f64 eps (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x))) (fma.f64 eps eps (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps (+.f64 x x)))))
(/.f64 (fma.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (+.f64 eps x) (.f64 (.f64 x x) x)) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (*.f64 (+.f64 eps x) x))))
(/.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) (fma.f64 (+.f64 x x) (+.f64 x x) (-.f64 (.f64 eps eps) (.f64 (+.f64 x x) eps))))
(fma.f64 x #s(literal 2 binary64) eps)
(fma.f64 #s(literal 2 binary64) x eps)
(-.f64 eps (*.f64 #s(literal -2 binary64) x))
(+.f64 (+.f64 x x) eps)
(+.f64 (+.f64 eps x) x)
(+.f64 eps (+.f64 x x))
(+.f64 x (+.f64 eps x))
x
eps
#s(literal 1/2 binary64)
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(exp.f64 (.f64 (log.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (sin eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
(.f64 eps #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 (fma.f64 (fma.f64 (-.f64 (.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 2 binary64)) #s(literal 1 binary64)) (-.f64 (fma.f64 (fma.f64 (-.f64 (.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)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (fma.f64 (-.f64 (.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 2 binary64))) (-.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (-.f64 (.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)))))
(/.f64 (+.f64 (pow.f64 (fma.f64 (fma.f64 (-.f64 (.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 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (fma.f64 (fma.f64 (-.f64 (.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 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 (fma.f64 (-.f64 (.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)))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (fma.f64 (-.f64 (.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 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (fma.f64 (fma.f64 (-.f64 (.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 2 binary64)) (.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (-.f64 (.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)))))))
(fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(+.f64 (fma.f64 (fma.f64 (-.f64 (.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))
(+.f64 (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(+.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x))
(+.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (-.f64 (.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))))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (-.f64 (.f64 (fma.f64 (-.f64 (.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))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (pow.f64 (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 (fma.f64 (-.f64 (.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 (pow.f64 (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x) #s(literal 3 binary64)) (.f64 (.f64 (.f64 eps eps) eps) (.f64 #s(literal -1/216 binary64) (.f64 (.f64 eps eps) eps)))) (+.f64 (pow.f64 (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 (.f64 (fma.f64 (-.f64 (.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))))))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) eps) (.f64 #s(literal -1/216 binary64) (.f64 (.f64 eps eps) eps)) (pow.f64 (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x)))))
(fma.f64 (fma.f64 (-.f64 (.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)))
(fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x))
(fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x))
(fma.f64 eps (.f64 #s(literal -1/6 binary64) eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x))
(fma.f64 x (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
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#s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (* 2 x) eps) eps)
#s(approx (+ (* 2 x) eps) (fma.f64 x #s(literal 2 binary64) eps))
#s(approx x x)
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#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps))
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#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (neg.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
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#s(approx (/ (+ (+ eps x) x) 2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (* 2 x) eps) eps)
#s(approx (+ (* 2 x) eps) (fma.f64 x #s(literal 2 binary64) eps))
#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) #s(literal -1/2 binary64)) x eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps))) x eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64)))
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#s(approx (* (sin x) eps) (*.f64 eps x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/120 binary64) eps)) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (sin x) x)
#s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
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#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
#s(approx (* (+ (* 2 x) eps) 1/2) x)
#s(approx (* (+ (* 2 x) eps) 1/2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (+ (* 2 x) eps) (+.f64 x x))
#s(approx (+ (* 2 x) eps) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
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#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal -1/6 binary64) (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))) #s(literal 1/2 binary64)) (.f64 x x)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (.f64 x x)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 x x)))) #s(literal 1/2 binary64)) (.f64 x x)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
#s(approx (/ (+ (+ eps x) x) 2) x)
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (+ (* 2 x) eps) (+.f64 x x))
#s(approx (+ (* 2 x) eps) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (sin x) (sin.f64 x))
#s(approx (cos x) (cos.f64 x))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
#s(approx (* (+ (* 2 x) eps) 1/2) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* 2 x) eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
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#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (neg.f64 (/.f64 (fma.f64 (/.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 #s(literal 1/2 binary64) eps)) x))) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) (neg.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
#s(approx (/ (+ (+ eps x) x) 2) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* 2 x) eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 2 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (*.f64 (cos.f64 x) eps))
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eval47.0ms (0.7%)

Memory: -2.9MiB live, 87.4MiB allocated; 8ms collecting garbage
Compiler: Compiled 5 201 to 2 242 computations (56.9% saved)

prune40.0ms (0.6%)

Memory

0.2MiB live, 46.6MiB allocated; 2ms collecting garbage

Pruning

33 alts after pruning (28 fresh and 5 done)

	Pruned	Kept	Total
New	368	20	388
Fresh	2	8	10
Picked	2	3	5
Done	0	2	2
Total	372	33	405

Accuracy

100.0%

Counts

405 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	64.0%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	99.8%	(-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(approx (+ ( (neg (sin x)) (cos eps)) (sin x)) (fma.f64 #s(literal 0 binary64) (sin.f64 x) (.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (.f64 (.f64 #s(literal 1/720 binary64) (.f64 eps eps)) (sin.f64 x))) (.f64 eps eps))) (*.f64 eps eps)))))
	99.5%	(-.f64 (.f64 (cos.f64 x) #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
✓	63.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.8%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
	99.6%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
	99.2%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
	99.2%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))))
✓	99.2%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
	99.2%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
	99.2%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))))
▶	98.8%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) x)))
✓	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))
✓	99.4%	#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))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	97.8%	#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))
	97.2%	#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) eps) x #s(literal 1 binary64))) eps))
	97.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	97.2%	#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 (.f64 eps x) #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	97.9%	#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 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (.f64 x x))) #s(literal 1 binary64))) eps))
▶	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
▶	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
	5.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (.f64 eps eps)))) eps))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (.f64 x x)))) eps))
	97.8%	#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)))
✓	97.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
▶	100.0%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (-.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)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
	99.9%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (+.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
	91.4%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (exp.f64 (.f64 (log.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))))
▶	99.6%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
	99.9%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))

Compiler

Compiled 1 546 to 1 465 computations (5.2% saved)

series52.0ms (0.8%)

Memory

-0.2MiB live, 109.4MiB allocated; 23ms collecting garbage

Counts

49 → 238

Calls

Call 1

Inputs
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (-.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)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 #s(literal 2 binary64) (-.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)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 #s(literal 2 binary64) (-.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))))))
#s(literal 2 binary64)
(-.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)))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (+.f64 x x) #s(literal 1/2 binary64))
(+.f64 x x)
x
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps)
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))))
(.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(*.f64 eps eps)
#s(literal 1/12 binary64)
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) x)))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) eps)
(cos.f64 #s(approx (/ (+ (+ eps x) x) 2) x))
#s(approx (/ (+ (+ eps x) x) 2) x)
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
(cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
#s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)

Outputs
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (* (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) #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 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) #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 (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) #s(hole binary64 (* 2 (cos (* 1/2 eps)))))
#s(approx (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) #s(hole binary64 (+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))))
#s(approx (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) #s(hole binary64 (+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))))
#s(approx (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) #s(hole binary64 (+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
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#s(approx (cos (* (+ x x) 1/2)) #s(hole binary64 1))
#s(approx (cos (* (+ x x) 1/2)) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos (* (+ x x) 1/2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos (* (+ x x) 1/2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (+ x x) 1/2) #s(hole binary64 x))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) #s(hole binary64 (* x (sin (* 1/2 eps)))))
#s(approx (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) #s(hole binary64 (* x (+ (sin (* 1/2 eps)) (* -1/6 (* (pow x 2) (sin (* 1/2 eps))))))))
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#s(approx (sin (* (+ x x) 1/2)) #s(hole binary64 x))
#s(approx (sin (* (+ x x) 1/2)) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin (* (+ x x) 1/2)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin (* (+ x x) 1/2)) #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)))
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#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
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#s(approx (* x x) #s(hole binary64 (pow x 2)))
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#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
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#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #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 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #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))))))))))
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#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))))
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#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 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 (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))))
#s(approx (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) #s(hole binary64 (* 2 (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))))
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#s(approx (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) #s(hole binary64 (* (cos x) (cos (* 1/2 eps)))))
#s(approx (cos (* (+ x x) 1/2)) #s(hole binary64 (cos x)))
#s(approx (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) #s(hole binary64 (* (sin x) (sin (* 1/2 eps)))))
#s(approx (sin (* (+ x x) 1/2)) #s(hole binary64 (sin x)))
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#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))))
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#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))) 1/2))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (+ eps (* 2 x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 x))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
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#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (- eps (* -2 x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
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#s(approx (cos (* 1/2 eps)) #s(hole binary64 1))
#s(approx (cos (* 1/2 eps)) #s(hole binary64 (+ 1 (* -1/8 (pow eps 2)))))
#s(approx (cos (* 1/2 eps)) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8)))))
#s(approx (cos (* 1/2 eps)) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8)))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) #s(hole binary64 (* 1/2 (* eps (sin x)))))
#s(approx (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) #s(hole binary64 (* eps (+ (* -1/48 (* (pow eps 2) (sin x))) (* 1/2 (sin x))))))
#s(approx (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* 1/3840 (* (pow eps 2) (sin x)))))))))
#s(approx (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (sin x))) (* 1/3840 (sin x))))))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (cos x)))
#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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
#s(approx (* (* x x) (- (* (* eps eps) 1/12) 1/2)) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (* (* x x) (- (* (* eps eps) 1/12) 1/2)) #s(hole binary64 (+ (* -1/2 (pow x 2)) (* 1/12 (* (pow eps 2) (pow x 2))))))
#s(approx (- (* (* eps eps) 1/12) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* eps eps) 1/12) 1/2) #s(hole binary64 (- (* 1/12 (pow eps 2)) 1/2)))
#s(approx (* (* eps eps) 1/12) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #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 (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos x))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* -1 (* eps (sin x))) (* 2 (cos x)))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos x)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* -1/48 (pow eps 2)))))
#s(approx (cos (* 1/2 eps)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) 1/6))))
#s(approx (* (* x x) (- (* (* eps eps) 1/12) 1/2)) #s(hole binary64 (* 1/12 (* (pow eps 2) (pow x 2)))))
#s(approx (* (* x x) (- (* (* eps eps) 1/12) 1/2)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2))))))
#s(approx (- (* (* eps eps) 1/12) 1/2) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/12) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* -1/48 (pow eps 3))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (* -1/48 (pow eps 2))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))))

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (cos (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (+ x x) 1/2)) (* (+ x x) 1/2) (+ x x) x (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) (sin (* 1/2 eps)) (sin (* (+ x x) 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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (* (* x x) (- (* (* eps eps) 1/12) 1/2)) (- (* (* eps eps) 1/12) 1/2) (* (* eps eps) 1/12) (* eps eps) 1/12 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)
6.0ms	x	@	inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (cos (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (+ x x) 1/2)) (* (+ x x) 1/2) (+ x x) x (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) (sin (* 1/2 eps)) (sin (* (+ x x) 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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (* (* x x) (- (* (* eps eps) 1/12) 1/2)) (- (* (* eps eps) 1/12) 1/2) (* (* eps eps) 1/12) (* eps eps) 1/12 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)
6.0ms	x	@	-inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (cos (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (+ x x) 1/2)) (* (+ x x) 1/2) (+ x x) x (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) (sin (* 1/2 eps)) (sin (* (+ x x) 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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (* (* x x) (- (* (* eps eps) 1/12) 1/2)) (- (* (* eps eps) 1/12) 1/2) (* (* eps eps) 1/12) (* eps eps) 1/12 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)
6.0ms	eps	@	-inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (cos (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (+ x x) 1/2)) (* (+ x x) 1/2) (+ x x) x (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) (sin (* 1/2 eps)) (sin (* (+ x x) 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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (* (* x x) (- (* (* eps eps) 1/12) 1/2)) (- (* (* eps eps) 1/12) 1/2) (* (* eps eps) 1/12) (* eps eps) 1/12 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)
4.0ms	x	@	0	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (cos (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (+ x x) 1/2)) (* (+ x x) 1/2) (+ x x) x (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) (sin (* 1/2 eps)) (sin (* (+ x x) 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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (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)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (* (* x x) (- (* (* eps eps) 1/12) 1/2)) (- (* (* eps eps) 1/12) 1/2) (* (* eps eps) 1/12) (* eps eps) 1/12 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)

rewrite235.0ms (3.4%)

Memory

34.6MiB live, 253.2MiB allocated; 50ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	859	7473
0	913	6794
1	4765	6734
0	8027	6358

Stop Event

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

Counts

287 → 456

Calls

Call 1

Inputs
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(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (+.f64 x x) #s(literal 1/2 binary64))))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
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x
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#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
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#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
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#s(approx (sin (* (+ x x) 1/2)) #s(hole binary64 (sin x)))
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#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 x))
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#s(approx (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) #s(hole binary64 (* 2 (cos x))))
#s(approx (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) #s(hole binary64 (+ (* -1 (* eps (sin x))) (* 2 (cos x)))))
#s(approx (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) #s(hole binary64 (+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))))
#s(approx (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) #s(hole binary64 (+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) #s(hole binary64 (cos x)))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ 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 (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) #s(hole binary64 (cos x)))
#s(approx (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) #s(hole binary64 (+ (cos x) (* -1/8 (* (pow eps 2) (cos x))))))
#s(approx (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) #s(hole binary64 (+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* 1/384 (* (pow eps 2) (cos x))))))))
#s(approx (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) #s(hole binary64 (+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos x))) (* 1/384 (cos x)))))))))
#s(approx (cos (* 1/2 eps)) #s(hole binary64 1))
#s(approx (cos (* 1/2 eps)) #s(hole binary64 (+ 1 (* -1/8 (pow eps 2)))))
#s(approx (cos (* 1/2 eps)) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8)))))
#s(approx (cos (* 1/2 eps)) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8)))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) #s(hole binary64 (* 1/2 (* eps (sin x)))))
#s(approx (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) #s(hole binary64 (* eps (+ (* -1/48 (* (pow eps 2) (sin x))) (* 1/2 (sin x))))))
#s(approx (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* 1/3840 (* (pow eps 2) (sin x)))))))))
#s(approx (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))) #s(hole binary64 (* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (sin x))) (* 1/3840 (sin x))))))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (cos x)))
#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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
#s(approx (* (* x x) (- (* (* eps eps) 1/12) 1/2)) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (* (* x x) (- (* (* eps eps) 1/12) 1/2)) #s(hole binary64 (+ (* -1/2 (pow x 2)) (* 1/12 (* (pow eps 2) (pow x 2))))))
#s(approx (- (* (* eps eps) 1/12) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* eps eps) 1/12) 1/2) #s(hole binary64 (- (* 1/12 (pow eps 2)) 1/2)))
#s(approx (* (* eps eps) 1/12) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #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 (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos x))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* -1 (* eps (sin x))) (* 2 (cos x)))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos x)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* -1/48 (pow eps 2)))))
#s(approx (cos (* 1/2 eps)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) 1/6))))
#s(approx (* (* x x) (- (* (* eps eps) 1/12) 1/2)) #s(hole binary64 (* 1/12 (* (pow eps 2) (pow x 2)))))
#s(approx (* (* x x) (- (* (* eps eps) 1/12) 1/2)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2))))))
#s(approx (- (* (* eps eps) 1/12) 1/2) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/12) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* -1/48 (pow eps 3))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (* -1/48 (pow eps 2))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))))

Outputs
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (sin.f64 (.f64 #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))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (cos.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (neg.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (neg.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (neg.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (neg.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
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x
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#s(approx (* (+ x x) 1/2) x)
#s(approx (+ x x) (+.f64 x x))
#s(approx x x)
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#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps (.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 x x))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps (.f64 (*.f64 x x) #s(literal -1/2 binary64))))
#s(approx (* (* x x) (- (* (* eps eps) 1/12) 1/2)) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
#s(approx (* (* x x) (- (* (* eps eps) 1/12) 1/2)) (fma.f64 (.f64 (.f64 eps x) (.f64 eps x)) #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal -1/2 binary64))))
#s(approx (- (* (* eps eps) 1/12) 1/2) #s(literal -1/2 binary64))
#s(approx (- (* (* eps eps) 1/12) 1/2) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))
#s(approx (* (* eps eps) 1/12) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))
#s(approx (* eps eps) (*.f64 eps eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) eps)
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 x))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 eps (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
#s(approx (cos (/ (+ (+ eps x) x) 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)))
#s(approx (* (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) (*.f64 (cos.f64 x) eps))
#s(approx (* (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) (.f64 (fma.f64 eps (fma.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) eps) #s(literal 2 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (* (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) #s(literal 2 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 (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (*.f64 (cos.f64 x) #s(literal 2 binary64)))
#s(approx (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (fma.f64 (neg.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (fma.f64 (cos.f64 x) #s(literal 2 binary64) (.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)))
#s(approx (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (fma.f64 (cos.f64 x) #s(literal 2 binary64) (.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (*.f64 #s(literal -1/4 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) (cos.f64 x))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) (fma.f64 eps (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ 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)))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)))
#s(approx (cos (* 1/2 eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (sin (* 1/2 eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) 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 #s(literal -1/6 binary64) (cos.f64 x))) (.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 #s(literal -1/6 binary64) (cos.f64 x))) (*.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 (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (.f64 eps eps)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (.f64 eps eps)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (/.f64 (.f64 x x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))) #s(literal 1/6 binary64)) (.f64 eps eps)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) (.f64 eps eps)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (.f64 eps eps)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (fma.f64 (/.f64 (.f64 x x) (.f64 eps eps)) #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))) #s(literal 1/6 binary64)) (.f64 eps eps)))
#s(approx (* (* x x) (- (* (* eps eps) 1/12) 1/2)) (.f64 (.f64 (.f64 eps x) (.f64 eps x)) #s(literal 1/12 binary64)))
#s(approx (* (* x x) (- (* (* eps eps) 1/12) 1/2)) (.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 eps eps)) #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (.f64 eps eps)))
#s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))
#s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (*.f64 eps eps)))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (* (+ (* 2 x) eps) 1/2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* 2 x) eps) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal -1/48 binary64)))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 (.f64 eps eps) eps)))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 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 (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#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 #s(literal 1/6 binary64) (cos.f64 x))) (.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 #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 (+ (* (* (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 (sin.f64 x) #s(literal 1/2 binary64) (neg.f64 (/.f64 (cos.f64 x) eps))) eps))) (.f64 eps eps)))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) (neg.f64 (/.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))) eps))) #s(literal 1/6 binary64)) (.f64 eps eps)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) (neg.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x (/.f64 (.f64 x x) eps))) eps))) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (* (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (sin (* 1/2 eps))) (.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 (* 2 (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2))))) (.f64 (cos.f64 (.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (+ x x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (+ x x) 1/2)))) (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))))
#s(approx (* (+ (* 2 x) eps) 1/2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* 2 x) eps) (.f64 (neg.f64 eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)))))

eval82.0ms (1.2%)

Memory: -24.6MiB live, 78.6MiB allocated; 17ms collecting garbage
Compiler: Compiled 6 108 to 2 609 computations (57.3% saved)

prune39.0ms (0.6%)

Memory

-7.9MiB live, 38.1MiB allocated; 6ms collecting garbage

Pruning

33 alts after pruning (26 fresh and 7 done)

	Pruned	Kept	Total
New	413	6	419
Fresh	3	20	23
Picked	3	2	5
Done	0	5	5
Total	419	33	452

Accuracy

100.0%

Counts

452 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	64.0%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	99.5%	(-.f64 (.f64 (cos.f64 x) #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
✓	63.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.8%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
	99.2%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
	99.2%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))))
✓	99.2%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
	99.2%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
	99.2%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))))
✓	98.8%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) x)))
✓	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))
✓	99.4%	#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))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	97.8%	#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))
	97.2%	#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) eps) x #s(literal 1 binary64))) eps))
	97.2%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	97.2%	#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 (.f64 eps x) #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	97.9%	#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 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (.f64 x x))) #s(literal 1 binary64))) eps))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))) eps))
✓	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
	5.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (.f64 eps eps)))) eps))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (.f64 x x)))) eps))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
	97.8%	#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)))
✓	97.2%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
	99.8%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (-.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)))))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
	99.8%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (-.f64 (.f64 #s(approx (cos ( 1/2 eps)) (fma.f64 (-.f64 (.f64 #s(literal 1/384 binary64) (.f64 eps eps)) #s(literal 1/8 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (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)))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
	99.9%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (+.f64 (neg.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
	91.4%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (exp.f64 (.f64 (log.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))))
	99.9%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
	99.6%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))

Compiler

Compiled 1 468 to 1 164 computations (20.7% saved)

regimes45.0ms (0.7%)

Memory

13.2MiB live, 58.8MiB allocated; 6ms collecting garbage

Counts

49 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (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 (+ (* (* (cos x) eps) -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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) 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 (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (.f64 eps x) #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) 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 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) 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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #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 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) x)))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) 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(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (+.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (+.f64 (neg.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (exp.f64 (.f64 (log.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 x (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (sin.f64 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))
(-.f64 (.f64 (cos.f64 x) #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (-.f64 (.f64 #s(approx (cos ( 1/2 eps)) (fma.f64 (-.f64 (.f64 #s(literal 1/384 binary64) (.f64 eps eps)) #s(literal 1/8 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (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)))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (-.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)))))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (-.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)))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(approx (+ ( (neg (sin x)) (cos eps)) (sin x)) (fma.f64 #s(literal 0 binary64) (sin.f64 x) (.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (.f64 (.f64 #s(literal 1/720 binary64) (.f64 eps eps)) (sin.f64 x))) (.f64 eps eps))) (*.f64 eps eps)))))

Outputs

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

Calls

3 calls:

19.0ms	x
12.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
11.0ms	eps

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)

regimes48.0ms (0.7%)

Memory

20.4MiB live, 65.1MiB allocated; 8ms collecting garbage

Counts

47 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (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 (+ (* (* (cos x) eps) -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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) 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 (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (.f64 eps x) #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) 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 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) 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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #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 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) x)))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) 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(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (+.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (+.f64 (neg.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (exp.f64 (.f64 (log.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 x (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (sin.f64 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))
(-.f64 (.f64 (cos.f64 x) #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (-.f64 (.f64 #s(approx (cos ( 1/2 eps)) (fma.f64 (-.f64 (.f64 #s(literal 1/384 binary64) (.f64 eps eps)) #s(literal 1/8 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (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)))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (-.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)))))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.9%	1	`x`
99.9%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes66.0ms (1%)

Memory

-7.1MiB live, 52.2MiB allocated; 28ms collecting garbage

Counts

36 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (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 (+ (* (* (cos x) eps) -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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) 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 (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (.f64 eps x) #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) 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 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) 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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #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 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) x)))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) 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(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))

Outputs

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

Calls

3 calls:

47.0ms	eps
9.0ms	x
9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

Accuracy	Segments	Branch
99.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.9%	1	`x`
99.9%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes32.0ms (0.5%)

Memory

-32.7MiB live, 59.2MiB allocated; 10ms collecting garbage

Counts

32 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (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 (+ (* (* (cos x) eps) -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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64))) 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 (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (.f64 eps x) #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) 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 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) 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 (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) (.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) (.f64 eps eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) x) (* (* eps eps) -1/6)) (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #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 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) x)))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) 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(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 #s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))

Outputs

(*.f64 #s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))

Calls

3 calls:

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

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)

regimes28.0ms (0.4%)

Memory

14.0MiB live, 59.7MiB allocated; 6ms collecting garbage

Counts

29 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

12.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps
7.0ms	x

Results

Accuracy	Segments	Branch
99.6%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.6%	1	`x`
99.6%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes25.0ms (0.4%)

Memory

-3.5MiB live, 50.0MiB allocated; 5ms collecting garbage

Counts

26 → 1

Calls

Call 1

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

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

Calls

3 calls:

10.0ms	x
7.0ms	eps
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

Accuracy	Segments	Branch
99.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.2%	1	`x`
99.2%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes25.0ms (0.4%)

Memory

-6.8MiB live, 38.5MiB allocated; 5ms collecting garbage

Counts

25 → 1

Calls

Call 1

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

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

Calls

3 calls:

11.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
99.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.2%	1	`x`
99.2%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes22.0ms (0.3%)

Memory

1.1MiB live, 46.9MiB allocated; 5ms collecting garbage

Counts

24 → 1

Calls

Call 1

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

Calls

3 calls:

9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
99.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.2%	1	`x`
99.2%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes21.0ms (0.3%)

Memory

4.5MiB live, 50.3MiB allocated; 6ms collecting garbage

Counts

22 → 1

Calls

Call 1

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

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

Calls

3 calls:

9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
99.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.2%	1	`x`
99.2%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes20.0ms (0.3%)

Memory

18.2MiB live, 70.9MiB allocated; 6ms collecting garbage

Counts

21 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	x
5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	eps

Results

Accuracy	Segments	Branch
99.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.2%	1	`x`
99.2%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes18.0ms (0.3%)

Memory

-6.0MiB live, 40.7MiB allocated; 3ms collecting garbage

Counts

19 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	eps
5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	x

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)

regimes18.0ms (0.3%)

Memory

-12.6MiB live, 33.5MiB allocated; 4ms collecting garbage

Counts

17 → 1

Calls

Call 1

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

Outputs

#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 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.9%	1	`eps`
97.9%	1	`x`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes14.0ms (0.2%)

Memory

29.9MiB live, 29.9MiB allocated; 0ms collecting garbage

Counts

16 → 1

Calls

Call 1

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

Outputs

#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 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.9%	1	`x`
97.9%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes13.0ms (0.2%)

Memory

-20.9MiB live, 25.5MiB allocated; 4ms collecting garbage

Counts

10 → 1

Calls

Call 1

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

Outputs
#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))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.8%	1	`x`
97.8%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes6.0ms (0.1%)

Memory

15.1MiB live, 15.1MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.7%	1	`x`
97.7%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes7.0ms (0.1%)

Memory

-40.4MiB live, 11.5MiB allocated; 5ms collecting garbage

Accuracy

Total -59.1b remaining (-3339.8%)

Threshold costs -59.1b (-3339.8%)

Counts

2 → 1

Calls

Call 1

Inputs

#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))

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

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))

Calls

3 calls:

4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms	x
1.0ms	eps

Results

Accuracy	Segments	Branch
97.2%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.2%	1	`x`
97.2%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

derivations547.0ms (8%)

Memory

17.8MiB live, 614.6MiB allocated; 127ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 219 to 153 computations (30.1% saved)

preprocess133.0ms (2%)

Memory: -30.3MiB live, 351.9MiB allocated; 39ms collecting garbage
Compiler: Compiled 262 to 192 computations (26.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze39.0ms (0.6%)

sample4.3s (62.8%)

preprocess83.0ms (1.2%)

series5.0ms (0.1%)

rewrite192.0ms (2.8%)

eval13.0ms (0.2%)

prune7.0ms (0.1%)

series40.0ms (0.6%)

rewrite181.0ms (2.7%)

eval70.0ms (1%)

prune25.0ms (0.4%)

series38.0ms (0.6%)

rewrite265.0ms (3.9%)

eval47.0ms (0.7%)

prune40.0ms (0.6%)

series52.0ms (0.8%)

rewrite235.0ms (3.4%)

eval82.0ms (1.2%)

prune39.0ms (0.6%)

regimes45.0ms (0.7%)

regimes48.0ms (0.7%)

regimes66.0ms (1%)

regimes32.0ms (0.5%)

regimes28.0ms (0.4%)

regimes25.0ms (0.4%)

regimes25.0ms (0.4%)

regimes22.0ms (0.3%)

regimes21.0ms (0.3%)

regimes20.0ms (0.3%)

regimes18.0ms (0.3%)

regimes18.0ms (0.3%)

regimes14.0ms (0.2%)

regimes13.0ms (0.2%)

regimes6.0ms (0.1%)

regimes7.0ms (0.1%)

derivations547.0ms (8%)

preprocess133.0ms (2%)

end0.0ms (0%)

Profiling