Metrics for 2sin (example 3.3)

start0.0ms (0%)

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

analyze29.0ms (0.5%)

Memory

19.4MiB live, 19.4MiB allocated; 0ms 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)

sample3.8s (60.3%)

Memory

90.0MiB live, 2 645.1MiB allocated; 649ms collecting garbage

Samples

1.9s	26 282×	0	invalid
703.0ms	5 600×	1	valid
155.0ms	2 656×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-sin: 619.0ms (38.9% of total)

ival-fabs: 225.0ms (14.1% of total)

ival-sub!: 161.0ms (10.1% of total)

adjust: 138.0ms (8.7% of total)

ival-mult!: 128.0ms (8% of total)

ival-add!: 126.0ms (7.9% of total)

ival-<: 119.0ms (7.5% of total)

ival-and: 62.0ms (3.9% of total)

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

Bogosity

preprocess88.0ms (1.4%)

Memory

-18.3MiB live, 28.1MiB 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
▶	63.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 12 to 12 computations (0% saved)

series5.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB 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	eps	@	inf	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms	x	@	0	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))

rewrite151.0ms (2.4%)

Memory

-18.2MiB live, 122.8MiB allocated; 21ms 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))))

eval10.0ms (0.2%)

Memory: 18.5MiB live, 18.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 106 to 384 computations (65.3% saved)

prune9.0ms (0.1%)

Memory

16.3MiB live, 16.3MiB allocated; 0ms collecting garbage

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	84	13	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	14	98

Accuracy

99.9%

Counts

98 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.5%	(/.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))))
	63.4%	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	99.7%	(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
✓	63.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	62.7%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
▶	62.8%	(-.f64 (sin.f64 (+.f64 x eps)) #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)))
	62.7%	(-.f64 (sin.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))) (sin.f64 x))
▶	63.4%	(.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))))
	98.8%	#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)))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 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))
▶	99.9%	#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))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 376 to 360 computations (4.3% saved)

series68.0ms (1.1%)

Memory

7.9MiB live, 98.7MiB allocated; 12ms collecting garbage

Counts

57 → 320

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
(.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps)
(fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x))
eps
(fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
#s(literal 1/24 binary64)
(*.f64 (cos.f64 x) #s(literal -1/6 binary64))
(cos.f64 x)
#s(literal -1/6 binary64)
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 (-.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)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
#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))
(.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)
(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))
(.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)
(-.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))
(.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x)
(.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) x)
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))
#s(literal -1/5040 binary64)
(*.f64 x x)
#s(literal 1/120 binary64)
#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)
(/.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 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))))
#s(literal 1/2 binary64)
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(*.f64 #s(literal 2 binary64) (+.f64 eps x))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))
(cos.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(sin.f64 (+.f64 eps x))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/12 (pow eps 2)) (* eps (* x (+ 1/12 (* -1/144 (pow eps 2)))))) 1/2))))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/12 eps) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) 1/2)))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 -1/6))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (- (* 1/24 (* eps x)) 1/6)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* 1/12 x))) 1/6)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* x (+ 1/12 (* -1/144 (* eps x)))))) 1/6)))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx x #s(hole binary64 x))
#s(approx (* (cos x) -1/6) #s(hole binary64 -1/6))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* 1/12 (pow x 2)) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* -1/144 (pow x 2)))) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/4320 (pow x 2)) 1/144)))) 1/6)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* -1/2 x)))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#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 (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 1))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* -1/6 x)))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* x (- (* 1/120 (pow x 2)) 1/6))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 -1/6))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* 1/120 (pow x 2))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* 1/120 x)))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* x (+ 1/120 (* -1/5040 (pow x 2))))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 1/120))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (+ 1/120 (* -1/5040 (pow x 2)))))
#s(approx (* 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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (/ (- 1/2 (* 1/2 (cos (* 2 eps)))) (sin eps))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (- (+ (* x (- (/ (sin (* 2 eps)) (sin eps)) (/ (* (+ 1 (cos eps)) (- 1/2 (* 1/2 (cos (* 2 eps))))) (pow (sin eps) 2)))) (* 1/2 (/ 1 (sin eps)))) (* 1/2 (/ (cos (* 2 eps)) (sin eps))))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (- (+ (* x (- (+ (* x (- (* -1 (/ (+ 1 (* -1 (cos (* 2 eps)))) (sin eps))) (+ (* -1/2 (/ (- 1/2 (* 1/2 (cos (* 2 eps)))) (sin eps))) (/ (* (+ 1 (cos eps)) (- (/ (sin (* 2 eps)) (sin eps)) (/ (* (+ 1 (cos eps)) (- 1/2 (* 1/2 (cos (* 2 eps))))) (pow (sin eps) 2)))) (sin eps))))) (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- 1/2 (* 1/2 (cos (* 2 eps))))) (pow (sin eps) 2)))) (* 1/2 (/ 1 (sin eps)))) (* 1/2 (/ (cos (* 2 eps)) (sin eps))))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (- (+ (* x (- (+ (* x (- (+ (* -1 (/ (+ 1 (* -1 (cos (* 2 eps)))) (sin eps))) (* x (- (* -2/3 (/ (sin (* 2 eps)) (sin eps))) (+ (* -1/2 (- (/ (sin (* 2 eps)) (sin eps)) (/ (* (+ 1 (cos eps)) (- 1/2 (* 1/2 (cos (* 2 eps))))) (pow (sin eps) 2)))) (+ (/ (* (+ 1 (cos eps)) (- (* -1 (/ (+ 1 (* -1 (cos (* 2 eps)))) (sin eps))) (+ (* -1/2 (/ (- 1/2 (* 1/2 (cos (* 2 eps)))) (sin eps))) (/ (* (+ 1 (cos eps)) (- (/ (sin (* 2 eps)) (sin eps)) (/ (* (+ 1 (cos eps)) (- 1/2 (* 1/2 (cos (* 2 eps))))) (pow (sin eps) 2)))) (sin eps))))) (sin eps)) (/ (* (- 1/2 (* 1/2 (cos (* 2 eps)))) (- (* -1/6 (cos eps)) 1/6)) (pow (sin eps) 2))))))) (+ (* -1/2 (/ (- 1/2 (* 1/2 (cos (* 2 eps)))) (sin eps))) (/ (* (+ 1 (cos eps)) (- (/ (sin (* 2 eps)) (sin eps)) (/ (* (+ 1 (cos eps)) (- 1/2 (* 1/2 (cos (* 2 eps))))) (pow (sin eps) 2)))) (sin eps))))) (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- 1/2 (* 1/2 (cos (* 2 eps))))) (pow (sin eps) 2)))) (* 1/2 (/ 1 (sin eps)))) (* 1/2 (/ (cos (* 2 eps)) (sin eps))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 eps))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (- (+ 1/2 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (- (+ 1/2 (* x (- (* -1 (* x (+ 1 (* -1 (cos (* 2 eps)))))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (- (+ 1/2 (* x (- (* x (- (* -2/3 (* x (sin (* 2 eps)))) (+ 1 (* -1 (cos (* 2 eps)))))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 eps))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- (+ 1/2 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- (+ 1/2 (* x (- (* x (cos (* 2 eps))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- (+ 1/2 (* x (- (* x (- (* -2/3 (* x (sin (* 2 eps)))) (* -1 (cos (* 2 eps))))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (* 1/2 (cos (* 2 eps)))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* -1 (* x (cos (* 2 eps)))))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 2 eps)))))))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (cos (* 2 eps))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (+ (cos (* 2 eps)) (* -2 (* x (sin (* 2 eps)))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (+ (cos (* 2 eps)) (* x (- (* -2 (* x (cos (* 2 eps)))) (* 2 (sin (* 2 eps))))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (+ (cos (* 2 eps)) (* x (- (* x (+ (* -2 (cos (* 2 eps))) (* 4/3 (* x (sin (* 2 eps)))))) (* 2 (sin (* 2 eps))))))))
#s(approx (* 2 (+ eps x)) #s(hole binary64 (* 2 eps)))
#s(approx (* 2 (+ eps x)) #s(hole binary64 (+ (* 2 eps) (* 2 x))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (pow x 2)))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 1/2))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* -1 (pow x 2)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos (* 2 x)) #s(hole binary64 1))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (sin eps)))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin eps) (* x (+ 1 (cos eps))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6))))))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (* -1/6 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* -1/5040 (pow x 7))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 (* -1/5040 (pow x 6))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* -1/5040 (pow x 5))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* -1/5040 (pow x 3))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* -1/5040 (pow x 2))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (* 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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (/ (- (* 1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (- (* 1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 (+ eps x)))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (* 1/2 (cos (* 2 (+ eps x))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (cos (* 2 (+ eps x)))))
#s(approx (* 2 (+ eps x)) #s(hole binary64 (* 2 x)))
#s(approx (* 2 (+ eps x)) #s(hole binary64 (* x (+ 2 (* 2 (/ eps x))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (* 1/2 (cos (* 2 x)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (cos (* 2 x))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin x) (sin (+ eps x)))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (+ eps 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 (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* -1 (* (pow x 5) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (/ (- (* 1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x)))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (- (* 1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- eps (* -1 x))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (* 1/2 (cos (* 2 (- eps (* -1 x)))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (cos (* 2 (- eps (* -1 x))))))
#s(approx (* 2 (+ eps x)) #s(hole binary64 (* -1 (* x (- (* -2 (/ eps x)) 2)))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin x) (sin (- eps (* -1 x))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (- eps (* -1 x)))))
#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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (* -1/6 (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 (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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* 1/2 (/ (* eps (sin (* 2 x))) (sin x)))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* eps (+ (* 1/2 (/ (sin (* 2 x)) (sin x))) (* eps (- (* 1/2 (/ (cos (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2)))))))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* eps (+ (* 1/2 (/ (sin (* 2 x)) (sin x))) (* eps (- (+ (* 1/2 (/ (cos (* 2 x)) (sin x))) (* eps (- (* -1/3 (/ (sin (* 2 x)) (sin x))) (+ (* -1/8 (/ (sin (* 2 x)) (sin x))) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (cos (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2))))) (sin x))))))) (* 1/4 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2)))))))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* eps (+ (* 1/2 (/ (sin (* 2 x)) (sin x))) (* eps (- (+ (* 1/2 (/ (cos (* 2 x)) (sin x))) (* eps (- (+ (* -1/3 (/ (sin (* 2 x)) (sin x))) (* eps (- (* -1/6 (/ (cos (* 2 x)) (sin x))) (+ (* -1/4 (- (* 1/2 (/ (cos (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2))))) (+ (* -1/24 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2))) (* 1/2 (/ (* (cos x) (- (* -1/3 (/ (sin (* 2 x)) (sin x))) (+ (* -1/8 (/ (sin (* 2 x)) (sin x))) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (cos (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2))))) (sin x)))))) (sin x)))))))) (+ (* -1/8 (/ (sin (* 2 x)) (sin x))) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (cos (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2))))) (sin x))))))) (* 1/4 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2)))))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (* eps (sin (* 2 x)))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (* eps (- (* eps (cos (* 2 x))) (* -1 (sin (* 2 x)))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (* eps (- (* eps (- (* -2/3 (* eps (sin (* 2 x)))) (* -1 (cos (* 2 x))))) (* -1 (sin (* 2 x)))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (* eps (- (* eps (- (* eps (- (* -1/3 (* eps (cos (* 2 x)))) (* 2/3 (sin (* 2 x))))) (* -1 (cos (* 2 x))))) (* -1 (sin (* 2 x)))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- (+ 1/2 (* eps (sin (* 2 x)))) (* 1/2 (cos (* 2 x))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- (+ 1/2 (* eps (- (* eps (cos (* 2 x))) (* -1 (sin (* 2 x)))))) (* 1/2 (cos (* 2 x))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- (+ 1/2 (* eps (- (* eps (- (* -2/3 (* eps (sin (* 2 x)))) (* -1 (cos (* 2 x))))) (* -1 (sin (* 2 x)))))) (* 1/2 (cos (* 2 x))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (* 1/2 (cos (* 2 x)))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (+ (* -1 (* eps (sin (* 2 x)))) (* 1/2 (cos (* 2 x))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x)))))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x)))))))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (cos (* 2 x))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (+ (cos (* 2 x)) (* -2 (* eps (sin (* 2 x)))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (+ (cos (* 2 x)) (* eps (- (* -2 (* eps (cos (* 2 x)))) (* 2 (sin (* 2 x))))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (+ (cos (* 2 x)) (* eps (- (* eps (+ (* -2 (cos (* 2 x))) (* 4/3 (* eps (sin (* 2 x)))))) (* 2 (sin (* 2 x))))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (* 2 (sin x))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (* 2 (sin x)) (* eps (cos x)))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin x)))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (sin x)))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (sin x)))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* 1/24 (* (pow eps 2) (sin x)))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (* 1/24 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (* eps (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (sin eps) #s(hole binary64 (sin 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 (* 2 (+ eps x)) #s(hole binary64 (* eps (+ 2 (* 2 (/ x eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (* -1 (* eps (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (* 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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (/ (- (* 1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps)))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (- (* 1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (* 1/2 (cos (* 2 (- x (* -1 eps)))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (cos (* 2 (- x (* -1 eps))))))
#s(approx (* 2 (+ eps x)) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 2)))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin x) (sin (- x (* -1 eps))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (- x (* -1 eps)))))

Calls

6 calls:

Time	Variable		Point	Expression
17.0ms	x	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (* (sin x) eps) (sin x) x 1/24 (* (cos x) -1/6) (cos x) -1/6 (* (sin x) -1/2) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 (* x x) 1/120 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) (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) 1/2 (* 1/2 (cos (* 2 (+ eps x)))) (cos (* 2 (+ eps x))) (* 2 (+ eps x)) (- 1/2 (* 1/2 (cos (* 2 x)))) (* 1/2 (cos (* 2 x))) (cos (* 2 x)) (* 2 x) (+ (sin x) (sin (+ eps x))) (sin (+ eps x)))
12.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (* (sin x) eps) (sin x) x 1/24 (* (cos x) -1/6) (cos x) -1/6 (* (sin x) -1/2) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 (* x x) 1/120 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) (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) 1/2 (* 1/2 (cos (* 2 (+ eps x)))) (cos (* 2 (+ eps x))) (* 2 (+ eps x)) (- 1/2 (* 1/2 (cos (* 2 x)))) (* 1/2 (cos (* 2 x))) (cos (* 2 x)) (* 2 x) (+ (sin x) (sin (+ eps x))) (sin (+ eps x)))
10.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (* (sin x) eps) (sin x) x 1/24 (* (cos x) -1/6) (cos x) -1/6 (* (sin x) -1/2) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 (* x x) 1/120 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) (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) 1/2 (* 1/2 (cos (* 2 (+ eps x)))) (cos (* 2 (+ eps x))) (* 2 (+ eps x)) (- 1/2 (* 1/2 (cos (* 2 x)))) (* 1/2 (cos (* 2 x))) (cos (* 2 x)) (* 2 x) (+ (sin x) (sin (+ eps x))) (sin (+ eps x)))
10.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (* (sin x) eps) (sin x) x 1/24 (* (cos x) -1/6) (cos x) -1/6 (* (sin x) -1/2) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 (* x x) 1/120 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) (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) 1/2 (* 1/2 (cos (* 2 (+ eps x)))) (cos (* 2 (+ eps x))) (* 2 (+ eps x)) (- 1/2 (* 1/2 (cos (* 2 x)))) (* 1/2 (cos (* 2 x))) (cos (* 2 x)) (* 2 x) (+ (sin x) (sin (+ eps x))) (sin (+ eps x)))
8.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (* (sin x) eps) (sin x) x 1/24 (* (cos x) -1/6) (cos x) -1/6 (* (sin x) -1/2) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 (* x x) 1/120 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) (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) 1/2 (* 1/2 (cos (* 2 (+ eps x)))) (cos (* 2 (+ eps x))) (* 2 (+ eps x)) (- 1/2 (* 1/2 (cos (* 2 x)))) (* 1/2 (cos (* 2 x))) (cos (* 2 x)) (* 2 x) (+ (sin x) (sin (+ eps x))) (sin (+ eps x)))

rewrite299.0ms (4.7%)

Memory

-2.6MiB live, 216.8MiB allocated; 87ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1247	8766
0	1331	8149
1	7075	8129
0	8011	7838

Stop Event

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

Counts

377 → 585

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
(.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps)
(fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x))
eps
(fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
#s(literal 1/24 binary64)
(*.f64 (cos.f64 x) #s(literal -1/6 binary64))
(cos.f64 x)
#s(literal -1/6 binary64)
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 (-.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)))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
#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))
(.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)
(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))
(.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)
(-.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))
(.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x)
(.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) x)
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))
#s(literal -1/5040 binary64)
(*.f64 x x)
#s(literal 1/120 binary64)
#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)
(/.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 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x)))))
#s(literal 1/2 binary64)
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x)))
(*.f64 #s(literal 2 binary64) (+.f64 eps x))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))
(cos.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(sin.f64 (+.f64 eps 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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/12 (pow eps 2)) (* eps (* x (+ 1/12 (* -1/144 (pow eps 2)))))) 1/2))))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/12 eps) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) 1/2)))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 -1/6))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (- (* 1/24 (* eps x)) 1/6)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* 1/12 x))) 1/6)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* x (+ 1/12 (* -1/144 (* eps x)))))) 1/6)))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx x #s(hole binary64 x))
#s(approx (* (cos x) -1/6) #s(hole binary64 -1/6))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* 1/12 (pow x 2)) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* -1/144 (pow x 2)))) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/4320 (pow x 2)) 1/144)))) 1/6)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* -1/2 x)))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#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 (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 1))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* -1/6 x)))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* x (- (* 1/120 (pow x 2)) 1/6))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 -1/6))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* 1/120 (pow x 2))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* 1/120 x)))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* x (+ 1/120 (* -1/5040 (pow x 2))))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 1/120))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (+ 1/120 (* -1/5040 (pow x 2)))))
#s(approx (* 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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (/ (- 1/2 (* 1/2 (cos (* 2 eps)))) (sin eps))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (- (+ (* x (- (/ (sin (* 2 eps)) (sin eps)) (/ (* (+ 1 (cos eps)) (- 1/2 (* 1/2 (cos (* 2 eps))))) (pow (sin eps) 2)))) (* 1/2 (/ 1 (sin eps)))) (* 1/2 (/ (cos (* 2 eps)) (sin eps))))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (- (+ (* x (- (+ (* x (- (* -1 (/ (+ 1 (* -1 (cos (* 2 eps)))) (sin eps))) (+ (* -1/2 (/ (- 1/2 (* 1/2 (cos (* 2 eps)))) (sin eps))) (/ (* (+ 1 (cos eps)) (- (/ (sin (* 2 eps)) (sin eps)) (/ (* (+ 1 (cos eps)) (- 1/2 (* 1/2 (cos (* 2 eps))))) (pow (sin eps) 2)))) (sin eps))))) (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- 1/2 (* 1/2 (cos (* 2 eps))))) (pow (sin eps) 2)))) (* 1/2 (/ 1 (sin eps)))) (* 1/2 (/ (cos (* 2 eps)) (sin eps))))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (- (+ (* x (- (+ (* x (- (+ (* -1 (/ (+ 1 (* -1 (cos (* 2 eps)))) (sin eps))) (* x (- (* -2/3 (/ (sin (* 2 eps)) (sin eps))) (+ (* -1/2 (- (/ (sin (* 2 eps)) (sin eps)) (/ (* (+ 1 (cos eps)) (- 1/2 (* 1/2 (cos (* 2 eps))))) (pow (sin eps) 2)))) (+ (/ (* (+ 1 (cos eps)) (- (* -1 (/ (+ 1 (* -1 (cos (* 2 eps)))) (sin eps))) (+ (* -1/2 (/ (- 1/2 (* 1/2 (cos (* 2 eps)))) (sin eps))) (/ (* (+ 1 (cos eps)) (- (/ (sin (* 2 eps)) (sin eps)) (/ (* (+ 1 (cos eps)) (- 1/2 (* 1/2 (cos (* 2 eps))))) (pow (sin eps) 2)))) (sin eps))))) (sin eps)) (/ (* (- 1/2 (* 1/2 (cos (* 2 eps)))) (- (* -1/6 (cos eps)) 1/6)) (pow (sin eps) 2))))))) (+ (* -1/2 (/ (- 1/2 (* 1/2 (cos (* 2 eps)))) (sin eps))) (/ (* (+ 1 (cos eps)) (- (/ (sin (* 2 eps)) (sin eps)) (/ (* (+ 1 (cos eps)) (- 1/2 (* 1/2 (cos (* 2 eps))))) (pow (sin eps) 2)))) (sin eps))))) (/ (sin (* 2 eps)) (sin eps))) (/ (* (+ 1 (cos eps)) (- 1/2 (* 1/2 (cos (* 2 eps))))) (pow (sin eps) 2)))) (* 1/2 (/ 1 (sin eps)))) (* 1/2 (/ (cos (* 2 eps)) (sin eps))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 eps))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (- (+ 1/2 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (- (+ 1/2 (* x (- (* -1 (* x (+ 1 (* -1 (cos (* 2 eps)))))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (- (+ 1/2 (* x (- (* x (- (* -2/3 (* x (sin (* 2 eps)))) (+ 1 (* -1 (cos (* 2 eps)))))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 eps))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- (+ 1/2 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- (+ 1/2 (* x (- (* x (cos (* 2 eps))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- (+ 1/2 (* x (- (* x (- (* -2/3 (* x (sin (* 2 eps)))) (* -1 (cos (* 2 eps))))) (* -1 (sin (* 2 eps)))))) (* 1/2 (cos (* 2 eps))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (* 1/2 (cos (* 2 eps)))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* -1 (* x (cos (* 2 eps)))))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 2 eps)))))))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (cos (* 2 eps))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (+ (cos (* 2 eps)) (* -2 (* x (sin (* 2 eps)))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (+ (cos (* 2 eps)) (* x (- (* -2 (* x (cos (* 2 eps)))) (* 2 (sin (* 2 eps))))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (+ (cos (* 2 eps)) (* x (- (* x (+ (* -2 (cos (* 2 eps))) (* 4/3 (* x (sin (* 2 eps)))))) (* 2 (sin (* 2 eps))))))))
#s(approx (* 2 (+ eps x)) #s(hole binary64 (* 2 eps)))
#s(approx (* 2 (+ eps x)) #s(hole binary64 (+ (* 2 eps) (* 2 x))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (pow x 2)))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 1/2))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* -1 (pow x 2)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos (* 2 x)) #s(hole binary64 1))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (sin eps)))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin eps) (* x (+ 1 (cos eps))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin eps) (* x (+ 1 (+ (cos eps) (* -1/2 (* x (sin eps)))))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin eps) (* x (+ 1 (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (- (* -1/6 (cos eps)) 1/6))))))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (* -1/6 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* -1/5040 (pow x 7))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 (* -1/5040 (pow x 6))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 (* (pow x 6) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(hole binary64 (* (pow x 6) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* -1/5040 (pow x 5))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* (pow x 5) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* -1/5040 (pow x 4))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) #s(hole binary64 (* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* -1/5040 (pow x 3))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* -1/5040 (pow x 2))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(hole binary64 (* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))))
#s(approx (* (* 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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (/ (- (* 1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x))))) (+ (sin x) (sin (+ eps x))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (- (* 1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (+ eps x)))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 (+ eps x)))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (* 1/2 (cos (* 2 (+ eps x))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (cos (* 2 (+ eps x)))))
#s(approx (* 2 (+ eps x)) #s(hole binary64 (* 2 x)))
#s(approx (* 2 (+ eps x)) #s(hole binary64 (* x (+ 2 (* 2 (/ eps x))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (* 1/2 (cos (* 2 x)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (cos (* 2 x))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin x) (sin (+ eps x)))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (+ eps 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 (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* -1 (* (pow x 5) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) #s(hole binary64 (* -1 (* (pow x 5) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (/ (- (* 1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- eps (* -1 x)))))) (+ (sin x) (sin (- eps (* -1 x)))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (- (* 1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- eps (* -1 x))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (* 1/2 (cos (* 2 (- eps (* -1 x)))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (cos (* 2 (- eps (* -1 x))))))
#s(approx (* 2 (+ eps x)) #s(hole binary64 (* -1 (* x (- (* -2 (/ eps x)) 2)))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin x) (sin (- eps (* -1 x))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (- eps (* -1 x)))))
#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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (* -1/6 (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 (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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* 1/2 (/ (* eps (sin (* 2 x))) (sin x)))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* eps (+ (* 1/2 (/ (sin (* 2 x)) (sin x))) (* eps (- (* 1/2 (/ (cos (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2)))))))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* eps (+ (* 1/2 (/ (sin (* 2 x)) (sin x))) (* eps (- (+ (* 1/2 (/ (cos (* 2 x)) (sin x))) (* eps (- (* -1/3 (/ (sin (* 2 x)) (sin x))) (+ (* -1/8 (/ (sin (* 2 x)) (sin x))) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (cos (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2))))) (sin x))))))) (* 1/4 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2)))))))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (* eps (+ (* 1/2 (/ (sin (* 2 x)) (sin x))) (* eps (- (+ (* 1/2 (/ (cos (* 2 x)) (sin x))) (* eps (- (+ (* -1/3 (/ (sin (* 2 x)) (sin x))) (* eps (- (* -1/6 (/ (cos (* 2 x)) (sin x))) (+ (* -1/4 (- (* 1/2 (/ (cos (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2))))) (+ (* -1/24 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2))) (* 1/2 (/ (* (cos x) (- (* -1/3 (/ (sin (* 2 x)) (sin x))) (+ (* -1/8 (/ (sin (* 2 x)) (sin x))) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (cos (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2))))) (sin x)))))) (sin x)))))))) (+ (* -1/8 (/ (sin (* 2 x)) (sin x))) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (cos (* 2 x)) (sin x))) (* 1/4 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2))))) (sin x))))))) (* 1/4 (/ (* (cos x) (sin (* 2 x))) (pow (sin x) 2)))))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (* eps (sin (* 2 x)))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (* eps (- (* eps (cos (* 2 x))) (* -1 (sin (* 2 x)))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (* eps (- (* eps (- (* -2/3 (* eps (sin (* 2 x)))) (* -1 (cos (* 2 x))))) (* -1 (sin (* 2 x)))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (* eps (- (* eps (- (* eps (- (* -1/3 (* eps (cos (* 2 x)))) (* 2/3 (sin (* 2 x))))) (* -1 (cos (* 2 x))))) (* -1 (sin (* 2 x)))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- (+ 1/2 (* eps (sin (* 2 x)))) (* 1/2 (cos (* 2 x))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- (+ 1/2 (* eps (- (* eps (cos (* 2 x))) (* -1 (sin (* 2 x)))))) (* 1/2 (cos (* 2 x))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- (+ 1/2 (* eps (- (* eps (- (* -2/3 (* eps (sin (* 2 x)))) (* -1 (cos (* 2 x))))) (* -1 (sin (* 2 x)))))) (* 1/2 (cos (* 2 x))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (* 1/2 (cos (* 2 x)))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (+ (* -1 (* eps (sin (* 2 x)))) (* 1/2 (cos (* 2 x))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x)))))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x)))))))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (cos (* 2 x))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (+ (cos (* 2 x)) (* -2 (* eps (sin (* 2 x)))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (+ (cos (* 2 x)) (* eps (- (* -2 (* eps (cos (* 2 x)))) (* 2 (sin (* 2 x))))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (+ (cos (* 2 x)) (* eps (- (* eps (+ (* -2 (cos (* 2 x))) (* 4/3 (* eps (sin (* 2 x)))))) (* 2 (sin (* 2 x))))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (* 2 (sin x))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (* 2 (sin x)) (* eps (cos x)))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (* 2 (sin x)) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (* 2 (sin x)) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin x)))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (sin x)))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (sin x)))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* 1/24 (* (pow eps 2) (sin x)))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (* 1/24 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (* eps (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (sin eps) #s(hole binary64 (sin 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 (* 2 (+ eps x)) #s(hole binary64 (* eps (+ 2 (* 2 (/ x eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(hole binary64 (* -1 (* eps (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (* 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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) #s(hole binary64 (/ (- (* 1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps)))))) (+ (sin x) (sin (- x (* -1 eps)))))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (- (* 1/2 (cos (* 2 x))) (* 1/2 (cos (* 2 (- x (* -1 eps))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) #s(hole binary64 (- 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) #s(hole binary64 (* 1/2 (cos (* 2 (- x (* -1 eps)))))))
#s(approx (cos (* 2 (+ eps x))) #s(hole binary64 (cos (* 2 (- x (* -1 eps))))))
#s(approx (* 2 (+ eps x)) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 2)))))
#s(approx (+ (sin x) (sin (+ eps x))) #s(hole binary64 (+ (sin x) (sin (- x (* -1 eps))))))
#s(approx (sin (+ eps x)) #s(hole binary64 (sin (- x (* -1 eps)))))

Outputs
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
(.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps)
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
(fma.f64 (cos.f64 x) eps (.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps))
(fma.f64 (cos.f64 x) eps (.f64 eps (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))
(fma.f64 eps (cos.f64 x) (.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps))
(fma.f64 eps (cos.f64 x) (.f64 eps (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 eps (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))
(/.f64 (-.f64 (.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)) (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) (-.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (cos.f64 x)))
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps))) (-.f64 (cos.f64 x) (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (cos.f64 x)))))
(/.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (-.f64 (.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)) (.f64 (cos.f64 x) (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps)))))
(fma.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x))
(-.f64 (cos.f64 x) (.f64 (neg.f64 eps) (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))))
(+.f64 (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) (cos.f64 x))
(+.f64 (cos.f64 x) (.f64 (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps))
eps
(/.f64 (-.f64 (.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps) (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps)) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (-.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps) (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps))) (-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps)))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps) (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps) (-.f64 (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (-.f64 (.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps) (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps)) (.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps)))))
(fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps))
(fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps))
(fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)))))
(-.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps) (.f64 (neg.f64 (sin.f64 x)) #s(literal -1/2 binary64)))
(+.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps))
(+.f64 (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)))) (-.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (cos.f64 x) #s(literal -1/6 binary64)))) (-.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (-.f64 (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (-.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))))))
(fma.f64 (.f64 #s(literal 1/24 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)))
(fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)))
(fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(fma.f64 (sin.f64 x) (.f64 #s(literal 1/24 binary64) eps) (.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(-.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (*.f64 (neg.f64 (cos.f64 x)) #s(literal -1/6 binary64)))
(-.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 #s(literal -1/24 binary64) (*.f64 (sin.f64 x) eps)))
(+.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(+.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)))
(*.f64 (sin.f64 x) eps)
(*.f64 eps (sin.f64 x))
(sin.f64 x)
x
#s(literal 1/24 binary64)
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#s(literal 1/2 binary64)
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(fma.f64 eps #s(literal 2 binary64) (+.f64 x x))
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#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (fma.f64 (-.f64 (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x (.f64 #s(literal 1/12 binary64) eps)) x (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) #s(literal -1/6 binary64))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (-.f64 (.f64 (.f64 eps x) #s(literal 1/24 binary64)) #s(literal 1/6 binary64)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) x) #s(literal 1/6 binary64)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps x) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/24 binary64) eps)) x) #s(literal 1/6 binary64)))
#s(approx (* (sin x) eps) (*.f64 eps x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/120 binary64) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/5040 binary64) (.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 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x))
#s(approx x x)
#s(approx (* (cos x) -1/6) #s(literal -1/6 binary64))
#s(approx (* (cos x) -1/6) (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)))
#s(approx (* (cos x) -1/6) (-.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)))
#s(approx (* (cos x) -1/6) (-.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/4320 binary64) (.f64 x x)) #s(literal 1/144 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #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 (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (* (sin x) -1/2) (.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/12 binary64)) #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 (sin (+ eps x)) (sin.f64 eps))
#s(approx (sin (+ eps x)) (fma.f64 (cos.f64 eps) x (sin.f64 eps)))
#s(approx (sin (+ eps x)) (fma.f64 x (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) (sin.f64 eps)))
#s(approx (sin (+ eps x)) (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 (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) x)
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)) x))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) #s(literal 1 binary64))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) (fma.f64 (.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x) x #s(literal 1 binary64)))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) (*.f64 #s(literal -1/6 binary64) x))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) (.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) x))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) (.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) #s(literal -1/6 binary64))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (-.f64 (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (.f64 (.f64 x x) #s(literal 1/120 binary64)))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x) x))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) (*.f64 #s(literal 1/120 binary64) x))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x))
#s(approx (+ (* -1/5040 (* x x)) 1/120) #s(literal 1/120 binary64))
#s(approx (+ (* -1/5040 (* x x)) 1/120) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
#s(approx (* 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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))) (sin.f64 eps)))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (fma.f64 (-.f64 (/.f64 (sin.f64 (+.f64 eps eps)) (sin.f64 eps)) (/.f64 (.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))) x (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))) (sin.f64 eps))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (fma.f64 (fma.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (cos.f64 (+.f64 eps eps))) #s(literal 1 binary64)) (sin.f64 eps))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))) (sin.f64 eps)) (.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (/.f64 (-.f64 (/.f64 (sin.f64 (+.f64 eps eps)) (sin.f64 eps)) (/.f64 (.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))) (sin.f64 eps))))) x (-.f64 (/.f64 (sin.f64 (+.f64 eps eps)) (sin.f64 eps)) (/.f64 (.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64)))))) x (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))) (sin.f64 eps))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (fma.f64 (fma.f64 (-.f64 (fma.f64 (-.f64 (.f64 #s(literal -2/3 binary64) (/.f64 (sin.f64 (+.f64 eps eps)) (sin.f64 eps))) (fma.f64 (-.f64 (/.f64 (sin.f64 (+.f64 eps eps)) (sin.f64 eps)) (/.f64 (.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))) (/.f64 (-.f64 (.f64 (cos.f64 eps) #s(literal -1/6 binary64)) #s(literal 1/6 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64)))) (.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (cos.f64 (+.f64 eps eps))) #s(literal 1 binary64)) (sin.f64 eps))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))) (sin.f64 eps)) (.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (/.f64 (-.f64 (/.f64 (sin.f64 (+.f64 eps eps)) (sin.f64 eps)) (/.f64 (.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))) (sin.f64 eps))))) (sin.f64 eps)))))) x (neg.f64 (/.f64 (+.f64 (neg.f64 (cos.f64 (+.f64 eps eps))) #s(literal 1 binary64)) (sin.f64 eps)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))) (sin.f64 eps)) (.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (/.f64 (-.f64 (/.f64 (sin.f64 (+.f64 eps eps)) (sin.f64 eps)) (/.f64 (.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))) (sin.f64 eps))))) x (-.f64 (/.f64 (sin.f64 (+.f64 eps eps)) (sin.f64 eps)) (/.f64 (.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64)))))) x (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))) (sin.f64 eps))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (-.f64 (fma.f64 (sin.f64 (+.f64 eps eps)) x #s(literal 1/2 binary64)) (*.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (-.f64 (fma.f64 x (-.f64 (.f64 (neg.f64 x) (+.f64 (neg.f64 (cos.f64 (+.f64 eps eps))) #s(literal 1 binary64))) (neg.f64 (sin.f64 (+.f64 eps eps)))) #s(literal 1/2 binary64)) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (-.f64 (fma.f64 (-.f64 (.f64 (-.f64 (-.f64 (.f64 (.f64 (sin.f64 (+.f64 eps eps)) x) #s(literal -2/3 binary64)) #s(literal 1 binary64)) (neg.f64 (cos.f64 (+.f64 eps eps)))) x) (neg.f64 (sin.f64 (+.f64 eps eps)))) x #s(literal 1/2 binary64)) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (-.f64 (fma.f64 (sin.f64 (+.f64 eps eps)) x #s(literal 1/2 binary64)) (*.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (-.f64 (fma.f64 x (-.f64 (.f64 (cos.f64 (+.f64 eps eps)) x) (neg.f64 (sin.f64 (+.f64 eps eps)))) #s(literal 1/2 binary64)) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (-.f64 (fma.f64 x (-.f64 (.f64 (-.f64 (.f64 (.f64 (sin.f64 (+.f64 eps eps)) x) #s(literal -2/3 binary64)) (neg.f64 (cos.f64 (+.f64 eps eps)))) x) (neg.f64 (sin.f64 (+.f64 eps eps)))) #s(literal 1/2 binary64)) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) (*.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) (fma.f64 (neg.f64 x) (sin.f64 (+.f64 eps eps)) (*.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (*.f64 (fma.f64 (neg.f64 x) (cos.f64 (+.f64 eps eps)) (neg.f64 (sin.f64 (+.f64 eps eps)))) x)))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) (fma.f64 x (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) x) (sin.f64 (+.f64 eps eps)) (neg.f64 (cos.f64 (+.f64 eps eps)))) x (neg.f64 (sin.f64 (+.f64 eps eps)))) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64))))
#s(approx (cos (* 2 (+ eps x))) (cos.f64 (+.f64 eps eps)))
#s(approx (cos (* 2 (+ eps x))) (fma.f64 (*.f64 (sin.f64 (+.f64 eps eps)) x) #s(literal -2 binary64) (cos.f64 (+.f64 eps eps))))
#s(approx (cos (* 2 (+ eps x))) (fma.f64 (fma.f64 (.f64 (cos.f64 (+.f64 eps eps)) x) #s(literal -2 binary64) (.f64 #s(literal -2 binary64) (sin.f64 (+.f64 eps eps)))) x (cos.f64 (+.f64 eps eps))))
#s(approx (cos (* 2 (+ eps x))) (fma.f64 (fma.f64 x (fma.f64 (.f64 (sin.f64 (+.f64 eps eps)) x) #s(literal 4/3 binary64) (.f64 (cos.f64 (+.f64 eps eps)) #s(literal -2 binary64))) (*.f64 #s(literal -2 binary64) (sin.f64 (+.f64 eps eps)))) x (cos.f64 (+.f64 eps eps))))
#s(approx (* 2 (+ eps x)) (+.f64 eps eps))
#s(approx (* 2 (+ eps x)) (*.f64 (+.f64 eps x) #s(literal 2 binary64)))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) (*.f64 x x))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 x x) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 x x)) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 x x) #s(literal 2/45 binary64)) (.f64 x x)) #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 x x)))
#s(approx (* 1/2 (cos (* 2 x))) #s(literal 1/2 binary64))
#s(approx (* 1/2 (cos (* 2 x))) (+.f64 (neg.f64 (*.f64 x x)) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (cos (* 2 x))) (fma.f64 (-.f64 (.f64 #s(literal 1/3 binary64) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (cos (* 2 x))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -2/45 binary64) (.f64 x x) #s(literal 1/3 binary64)) (.f64 x x)) #s(literal 1 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
#s(approx (cos (* 2 x)) #s(literal 1 binary64))
#s(approx (cos (* 2 x)) (fma.f64 #s(literal -2 binary64) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos (* 2 x)) (fma.f64 (-.f64 (.f64 #s(literal 2/3 binary64) (.f64 x x)) #s(literal 2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos (* 2 x)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -4/45 binary64) (.f64 x x) #s(literal 2/3 binary64)) (.f64 x x)) #s(literal 2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (* 2 x) (+.f64 x x))
#s(approx (+ (sin x) (sin (+ eps x))) (sin.f64 eps))
#s(approx (+ (sin x) (sin (+ eps x))) (fma.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (+ (sin x) (sin (+ eps 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) (sin (+ eps x))) (fma.f64 (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (cos.f64 eps) #s(literal -1/6 binary64)) #s(literal 1/6 binary64)) x (.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (sin (+ eps x)) (sin.f64 eps))
#s(approx (sin (+ eps x)) (fma.f64 (cos.f64 eps) x (sin.f64 eps)))
#s(approx (sin (+ eps x)) (fma.f64 x (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) (sin.f64 eps)))
#s(approx (sin (+ eps x)) (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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (cos x) -1/6) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
#s(approx (cos x) (cos.f64 x))
#s(approx (* (sin x) -1/2) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
#s(approx (sin (+ eps x)) (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 (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/5040 binary64)))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/5040 binary64)) (pow.f64 x #s(literal 7 binary64))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (.f64 (-.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -6 binary64)) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) #s(literal -1/5040 binary64)))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (-.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 x x))))))
#s(approx (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) (.f64 (-.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -6 binary64)) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/5040 binary64)))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) (.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/5040 binary64))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) (.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (*.f64 x x))))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/5040 binary64)))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64))))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/5040 binary64)) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 x x) (.f64 x x))))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/5040 binary64)))
#s(approx (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (/.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/5040 binary64))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) (.f64 (.f64 (*.f64 x x) x) #s(literal -1/5040 binary64)))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) (.f64 (.f64 (.f64 x x) x) (-.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/5040 binary64))))
#s(approx (+ (* -1/5040 (* x x)) 1/120) (.f64 (.f64 x x) #s(literal -1/5040 binary64)))
#s(approx (+ (* -1/5040 (* x x)) 1/120) (.f64 (-.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/5040 binary64)) (*.f64 x x)))
#s(approx (* (* 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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (+.f64 x x)) (cos.f64 (.f64 (+.f64 eps x) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (+.f64 x x)) (cos.f64 (.f64 (+.f64 eps x) #s(literal 2 binary64))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) (.f64 (cos.f64 (.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
#s(approx (cos (* 2 (+ eps x))) (cos.f64 (*.f64 (+.f64 eps x) #s(literal 2 binary64))))
#s(approx (* 2 (+ eps x)) (+.f64 x x))
#s(approx (* 2 (+ eps x)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 2 binary64) #s(literal 2 binary64)) x))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (cos (* 2 x))) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))
#s(approx (cos (* 2 x)) (cos.f64 (+.f64 x x)))
#s(approx (+ (sin x) (sin (+ eps x))) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (sin (+ eps x)) (sin.f64 (+.f64 eps x)))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
#s(approx (sin (+ eps x)) (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 (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (neg.f64 (.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (pow.f64 x #s(literal 7 binary64)))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (neg.f64 (.f64 (+.f64 #s(literal 1/5040 binary64) (-.f64 (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1/120 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64)))))
#s(approx (* (+ (* (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) x) 1) x) (neg.f64 (.f64 (-.f64 (+.f64 #s(literal 1/5040 binary64) (-.f64 (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1/120 binary64) (*.f64 x x)))) (pow.f64 x #s(literal -6 binary64))) (pow.f64 x #s(literal 7 binary64)))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) (neg.f64 (.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))))
#s(approx (* (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) x) (neg.f64 (.f64 (+.f64 #s(literal 1/5040 binary64) (-.f64 (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1/120 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64)))))
#s(approx (* (+ (* -1/5040 (* x x)) 1/120) x) (neg.f64 (.f64 (-.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (.f64 (.f64 x 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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (+.f64 x x)) (cos.f64 (.f64 (-.f64 eps (neg.f64 x)) #s(literal 2 binary64))))) (+.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (+.f64 x x)) (cos.f64 (.f64 (-.f64 eps (neg.f64 x)) #s(literal 2 binary64))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 (-.f64 eps (neg.f64 x)) #s(literal 2 binary64))) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) (.f64 (cos.f64 (.f64 (-.f64 eps (neg.f64 x)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
#s(approx (cos (* 2 (+ eps x))) (cos.f64 (*.f64 (-.f64 eps (neg.f64 x)) #s(literal 2 binary64))))
#s(approx (* 2 (+ eps x)) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 eps x) #s(literal -2 binary64)) #s(literal 2 binary64))))
#s(approx (+ (sin x) (sin (+ eps x))) (+.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
#s(approx (sin (+ eps x)) (sin.f64 (-.f64 eps (neg.f64 x))))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps 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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (*.f64 (cos.f64 x) eps))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) 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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (cos.f64 x))
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#s(approx eps eps)
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -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 (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
#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 (sin (+ eps x)) (sin.f64 x))
#s(approx (sin (+ eps x)) (fma.f64 (cos.f64 x) eps (sin.f64 x)))
#s(approx (sin (+ eps x)) (fma.f64 eps (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) (sin.f64 x)))
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#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))
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#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))
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#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))
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#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)))
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#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (.f64 (fma.f64 (fma.f64 (/.f64 (cos.f64 (+.f64 x x)) (sin.f64 x)) #s(literal 1/2 binary64) (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (sin.f64 (+.f64 x x)) (cos.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))))) eps (*.f64 (/.f64 (sin.f64 (+.f64 x x)) (sin.f64 x)) #s(literal 1/2 binary64))) eps))
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#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (*.f64 (sin.f64 (+.f64 x x)) eps))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (.f64 (-.f64 (.f64 (cos.f64 (+.f64 x x)) eps) (neg.f64 (sin.f64 (+.f64 x x)))) eps))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 (sin.f64 (+.f64 x x)) eps) #s(literal -2/3 binary64)) (neg.f64 (cos.f64 (+.f64 x x)))) eps) (neg.f64 (sin.f64 (+.f64 x x)))) eps))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (.f64 (-.f64 (.f64 (-.f64 (.f64 (fma.f64 (.f64 (cos.f64 (+.f64 x x)) eps) #s(literal -1/3 binary64) (*.f64 #s(literal -2/3 binary64) (sin.f64 (+.f64 x x)))) eps) (neg.f64 (cos.f64 (+.f64 x x)))) eps) (neg.f64 (sin.f64 (+.f64 x x)))) eps))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (-.f64 (fma.f64 (sin.f64 (+.f64 x x)) eps #s(literal 1/2 binary64)) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (-.f64 (fma.f64 eps (-.f64 (.f64 (cos.f64 (+.f64 x x)) eps) (neg.f64 (sin.f64 (+.f64 x x)))) #s(literal 1/2 binary64)) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (-.f64 (fma.f64 eps (-.f64 (.f64 (-.f64 (.f64 (.f64 (sin.f64 (+.f64 x x)) eps) #s(literal -2/3 binary64)) (neg.f64 (cos.f64 (+.f64 x x)))) eps) (neg.f64 (sin.f64 (+.f64 x x)))) #s(literal 1/2 binary64)) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) (fma.f64 (neg.f64 eps) (sin.f64 (+.f64 x x)) (*.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) (fma.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64) (*.f64 (fma.f64 (neg.f64 eps) (cos.f64 (+.f64 x x)) (neg.f64 (sin.f64 (+.f64 x x)))) eps)))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) (fma.f64 eps (fma.f64 (fma.f64 (.f64 #s(literal 2/3 binary64) eps) (sin.f64 (+.f64 x x)) (neg.f64 (cos.f64 (+.f64 x x)))) eps (neg.f64 (sin.f64 (+.f64 x x)))) (.f64 (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))))
#s(approx (cos (* 2 (+ eps x))) (cos.f64 (+.f64 x x)))
#s(approx (cos (* 2 (+ eps x))) (fma.f64 (*.f64 (sin.f64 (+.f64 x x)) eps) #s(literal -2 binary64) (cos.f64 (+.f64 x x))))
#s(approx (cos (* 2 (+ eps x))) (fma.f64 (fma.f64 (.f64 (cos.f64 (+.f64 x x)) eps) #s(literal -2 binary64) (.f64 #s(literal -2 binary64) (sin.f64 (+.f64 x x)))) eps (cos.f64 (+.f64 x x))))
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#s(approx (+ (sin x) (sin (+ eps x))) (*.f64 (sin.f64 x) #s(literal 2 binary64)))
#s(approx (+ (sin x) (sin (+ eps x))) (fma.f64 (cos.f64 x) eps (*.f64 (sin.f64 x) #s(literal 2 binary64))))
#s(approx (+ (sin x) (sin (+ eps x))) (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (.f64 (sin.f64 x) #s(literal 2 binary64))))
#s(approx (+ (sin x) (sin (+ eps x))) (fma.f64 #s(literal 2 binary64) (sin.f64 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 (+ eps x)) (sin.f64 x))
#s(approx (sin (+ eps x)) (fma.f64 (cos.f64 x) eps (sin.f64 x)))
#s(approx (sin (+ eps x)) (fma.f64 eps (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) (sin.f64 x)))
#s(approx (sin (+ eps x)) (fma.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps (sin.f64 x)))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (.f64 (.f64 (.f64 eps eps) (*.f64 eps eps)) (sin.f64 x)) #s(literal 1/24 binary64)))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal 1/24 binary64))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal 1/24 binary64)))) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (.f64 (.f64 eps eps) eps))))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (.f64 (.f64 (.f64 (.f64 eps eps) eps) (sin.f64 x)) #s(literal 1/24 binary64)))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (.f64 (.f64 (.f64 eps eps) eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal 1/24 binary64)))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (.f64 (.f64 (.f64 eps eps) eps) (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal 1/24 binary64))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (.f64 (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (.f64 (.f64 eps eps) eps))))) (.f64 (.f64 eps eps) eps)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal 1/24 binary64))) (*.f64 eps eps)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (.f64 (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal 1/24 binary64)))) (.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal 1/24 binary64))) eps))
#s(approx (sin eps) (sin.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 (* 2 (+ eps x)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 2 binary64)) eps))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 (cos.f64 x) #s(literal 1/6 binary64))) eps))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/6 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))) eps))) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (neg.f64 (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/24 binary64))) (.f64 (.f64 eps eps) eps))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (neg.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps))) (.f64 (.f64 eps eps) eps))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (neg.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps))) eps))) eps))) (.f64 (*.f64 eps eps) eps))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 (cos.f64 x) #s(literal 1/6 binary64))) eps))) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (.f64 (neg.f64 eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/24 binary64)))))
#s(approx (sin (+ eps x)) (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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (+.f64 x x)) (cos.f64 (.f64 (-.f64 x (neg.f64 eps)) #s(literal 2 binary64))))) (+.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x))))
#s(approx (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (.f64 #s(literal 1/2 binary64) (-.f64 (cos.f64 (+.f64 x x)) (cos.f64 (.f64 (-.f64 x (neg.f64 eps)) #s(literal 2 binary64))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 (-.f64 x (neg.f64 eps)) #s(literal 2 binary64))) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (cos (* 2 (+ eps x)))) (.f64 (cos.f64 (.f64 (-.f64 x (neg.f64 eps)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
#s(approx (cos (* 2 (+ eps x))) (cos.f64 (*.f64 (-.f64 x (neg.f64 eps)) #s(literal 2 binary64))))
#s(approx (* 2 (+ eps x)) (.f64 (neg.f64 eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 2 binary64))))
#s(approx (+ (sin x) (sin (+ eps x))) (+.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (sin (+ eps x)) (sin.f64 (-.f64 x (neg.f64 eps))))

eval66.0ms (1%)

Memory: 19.6MiB live, 66.1MiB allocated; 7ms collecting garbage
Compiler: Compiled 8 354 to 3 117 computations (62.7% saved)

prune20.0ms (0.3%)

Memory

-27.3MiB live, 19.0MiB allocated; 4ms collecting garbage

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	521	11	532
Fresh	8	0	8
Picked	5	0	5
Done	1	0	1
Total	535	11	546

Accuracy

100.0%

Counts

546 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.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))))
	99.9%	(.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))))
▶	99.6%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
	99.6%	#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	99.3%	#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (*.f64 (cos.f64 x) eps))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps #s(approx (+ ( eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
▶	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
▶	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))

Compiler

Compiled 588 to 542 computations (7.8% saved)

series32.0ms (0.5%)

Memory

27.7MiB live, 27.7MiB allocated; 0ms collecting garbage

Counts

42 → 217

Calls

Call 1

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

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 (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 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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
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#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
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#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))))))
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#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
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#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))))))
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#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) 1/24) 1/2) eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* 1/1920 (pow eps 5))))
#s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 5) (- 1/1920 (* 1/24 (/ 1 (pow eps 2)))))))
#s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 5) (- (+ 1/1920 (/ 1 (pow eps 4))) (* 1/24 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 (* 1/1920 (pow eps 4))))
#s(approx (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 (* (pow eps 4) (- 1/1920 (* 1/24 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 (* (pow eps 4) (- (+ 1/1920 (/ 1 (pow eps 4))) (* 1/24 (/ 1 (pow eps 2)))))))
#s(approx (- (* 1/1920 (* eps eps)) 1/24) #s(hole binary64 (* 1/1920 (pow eps 2))))
#s(approx (- (* 1/1920 (* eps eps)) 1/24) #s(hole binary64 (* (pow eps 2) (- 1/1920 (* 1/24 (/ 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 eps) #s(hole binary64 (sin eps)))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (sin x)))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (sin x)))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (* 1/24 x) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (/ 1 (pow eps 3)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (* 1/24 x) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)) (* 1/6 (/ 1 eps))))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) x) #s(hole binary64 (* 1/24 (* (pow eps 2) x))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) x) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (+ (* 1/12 (/ (pow x 2) eps)) (/ 1 (pow eps 3)))))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* 1/24 (pow eps 3))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (+ 1/24 (* 1/12 (/ x eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (- (+ 1/24 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (- (+ 1/24 (+ (* -1/2 (/ x (pow eps 3))) (* 1/12 (/ x eps)))) (/ 1/2 (pow eps 2))))))
#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 eps) 1/24) 1/2) eps) #s(hole binary64 (* 1/24 (pow eps 3))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* (pow eps 3) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#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 (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) 1/1920)))))
#s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) (+ 1/1920 (/ 1 (pow eps 4))))))))
#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)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 x) (* 1/6 (/ 1 eps)))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1/2 (/ x eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 x) (/ 1 eps)) eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 x) (* 1/6 (/ 1 eps)))))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1/2 (/ x eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1/12 (/ x eps)) 1/24)))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/12 x) (* 1/2 (/ 1 eps))) eps)) 1/24)))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)) eps)) 1/24)))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)))))

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (- (* 1/1920 (* eps eps)) 1/24) (* 1/1920 (* eps eps)) 1/1920 (* eps eps) eps 1/24 1 (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) x 2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) (* (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/2 (* (* eps eps) -1/6) -1/6 (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* (- (* (* eps eps) 1/24) 1/2) eps) (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))))
5.0ms	eps	@	-inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (- (* 1/1920 (* eps eps)) 1/24) (* 1/1920 (* eps eps)) 1/1920 (* eps eps) eps 1/24 1 (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) x 2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) (* (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/2 (* (* eps eps) -1/6) -1/6 (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* (- (* (* eps eps) 1/24) 1/2) eps) (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))))
5.0ms	x	@	-inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (- (* 1/1920 (* eps eps)) 1/24) (* 1/1920 (* eps eps)) 1/1920 (* eps eps) eps 1/24 1 (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) x 2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) (* (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/2 (* (* eps eps) -1/6) -1/6 (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* (- (* (* eps eps) 1/24) 1/2) eps) (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))))
4.0ms	x	@	inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (- (* 1/1920 (* eps eps)) 1/24) (* 1/1920 (* eps eps)) 1/1920 (* eps eps) eps 1/24 1 (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) x 2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) (* (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/2 (* (* eps eps) -1/6) -1/6 (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* (- (* (* eps eps) 1/24) 1/2) eps) (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))))
4.0ms	x	@	0	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (- (* 1/1920 (* eps eps)) 1/24) (* 1/1920 (* eps eps)) 1/1920 (* eps eps) eps 1/24 1 (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) x 2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) (* (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/2 (* (* eps eps) -1/6) -1/6 (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* (- (* (* eps eps) 1/24) 1/2) eps) (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))))

rewrite211.0ms (3.3%)

Memory

-9.8MiB live, 85.5MiB allocated; 55ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	880	7399
0	936	7223
1	5054	7203
0	8024	6821

Stop Event

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

Counts

259 → 387

Calls

Call 1

Inputs
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#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))
(.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)
(fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64))
(.f64 #s(literal 1/1920 binary64) (.f64 eps eps))
#s(literal 1/1920 binary64)
(*.f64 eps eps)
eps
#s(literal 1/24 binary64)
#s(literal 1 binary64)
(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)
x
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (sin eps) eps)
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(.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps)
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(-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
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#s(literal 1/12 binary64)
(.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)
(.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)
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#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))))))))))
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#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))
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#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
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#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)))))
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#s(approx (sin eps) #s(hole binary64 eps))
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#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* 1/1920 (pow eps 5))))
#s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 5) (- 1/1920 (* 1/24 (/ 1 (pow eps 2)))))))
#s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* (pow eps 5) (- (+ 1/1920 (/ 1 (pow eps 4))) (* 1/24 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 (* 1/1920 (pow eps 4))))
#s(approx (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 (* (pow eps 4) (- 1/1920 (* 1/24 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) #s(hole binary64 (* (pow eps 4) (- (+ 1/1920 (/ 1 (pow eps 4))) (* 1/24 (/ 1 (pow eps 2)))))))
#s(approx (- (* 1/1920 (* eps eps)) 1/24) #s(hole binary64 (* 1/1920 (pow eps 2))))
#s(approx (- (* 1/1920 (* eps eps)) 1/24) #s(hole binary64 (* (pow eps 2) (- 1/1920 (* 1/24 (/ 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 eps) #s(hole binary64 (sin eps)))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (sin x)))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (sin x)))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (* 1/24 x) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (/ 1 (pow eps 3)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (* 1/24 x) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)) (* 1/6 (/ 1 eps))))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) x) #s(hole binary64 (* 1/24 (* (pow eps 2) x))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) x) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (+ (* 1/12 (/ (pow x 2) eps)) (/ 1 (pow eps 3)))))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* 1/24 (pow eps 3))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (+ 1/24 (* 1/12 (/ x eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (- (+ 1/24 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (- (+ 1/24 (+ (* -1/2 (/ x (pow eps 3))) (* 1/12 (/ x eps)))) (/ 1/2 (pow eps 2))))))
#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 eps) 1/24) 1/2) eps) #s(hole binary64 (* 1/24 (pow eps 3))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* (pow eps 3) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#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 (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) 1/1920)))))
#s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) (+ 1/1920 (/ 1 (pow eps 4))))))))
#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)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 x) (* 1/6 (/ 1 eps)))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1/2 (/ x eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 x) (/ 1 eps)) eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 x) (* 1/6 (/ 1 eps)))))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1/2 (/ x eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1/12 (/ x eps)) 1/24)))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/12 x) (* 1/2 (/ 1 eps))) eps)) 1/24)))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)) eps)) 1/24)))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)))))

Outputs
(.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
(.f64 eps (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) eps (.f64 (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) eps))
(fma.f64 eps #s(literal 1 binary64) (.f64 eps (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps)))
(+.f64 (.f64 eps #s(literal 1 binary64)) (.f64 eps (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps)))
(+.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) eps))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps)))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) #s(literal 1 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps)))))
(fma.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps #s(literal 1 binary64))
(fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(fma.f64 (.f64 eps eps) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (.f64 (neg.f64 (.f64 eps eps)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64))))
(+.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps))
(/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 (.f64 eps eps) #s(literal 1/1920 binary64))) #s(literal 1/576 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/1920 binary64) #s(literal 1/24 binary64)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 3 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)))))
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64))
(.f64 (.f64 #s(literal 1/1920 binary64) eps) eps)
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#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1/24 binary64)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (fma.f64 (/.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/24 binary64)) (.f64 (*.f64 eps eps) eps)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (-.f64 (fma.f64 (/.f64 x eps) #s(literal 1/12 binary64) #s(literal 1/24 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) eps)))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (+.f64 #s(literal 1/24 binary64) (-.f64 (fma.f64 (/.f64 x (.f64 (.f64 eps eps) eps)) #s(literal -1/2 binary64) (.f64 (/.f64 x eps) #s(literal 1/12 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)))) (.f64 (*.f64 eps eps) eps)))
#s(approx (- (* 1/12 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))
#s(approx (- (* 1/12 (* eps eps)) 1/2) (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (*.f64 eps eps)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal 1/24 binary64)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) (.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (.f64 (.f64 eps 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 (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (neg.f64 (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)) (pow.f64 eps #s(literal 5 binary64)))))
#s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (neg.f64 (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (.f64 eps eps)) #s(literal 1/1920 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))) (pow.f64 eps #s(literal 5 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 (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/24 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) (cos.f64 x))) eps))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (sin.f64 x) #s(literal 1/24 binary64) (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))) eps))) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (neg.f64 (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/24 binary64))) (.f64 (.f64 eps eps) eps))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (neg.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps))) (.f64 (.f64 eps eps) eps))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (.f64 (.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps))) eps))) eps)))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/6 binary64) eps))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/6 binary64)) eps)))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps)) eps)) #s(literal 1/6 binary64)) eps)))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) (.f64 (.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/6 binary64) eps))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/6 binary64)) eps)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.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))) eps)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.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)) eps)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.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))) eps)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.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)) eps)))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (-.f64 (.f64 #s(literal -1/12 binary64) (/.f64 x eps)) #s(literal 1/24 binary64))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (-.f64 (neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/12 binary64) x) (/.f64 #s(literal 1/2 binary64) eps)) eps)) #s(literal 1/24 binary64))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 (.f64 (neg.f64 eps) (*.f64 eps eps)) (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 1/12 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) eps))) eps)) #s(literal 1/24 binary64))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) #s(literal 1/24 binary64))))

eval55.0ms (0.9%)

Memory: 4.3MiB live, 51.4MiB allocated; 6ms collecting garbage
Compiler: Compiled 7 436 to 2 572 computations (65.4% saved)

prune20.0ms (0.3%)

Memory

-27.3MiB live, 20.1MiB allocated; 2ms collecting garbage

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	443	13	456
Fresh	6	0	6
Picked	4	1	5
Done	0	0	0
Total	453	14	467

Accuracy

100.0%

Counts

467 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.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 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
	99.9%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 #s(approx (- ( 1/1920 (* eps eps)) 1/24) #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))) eps) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
	99.6%	(.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))))
	99.3%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) x)))
	99.6%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) #s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (.f64 eps (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 x x)) #s(literal 1 binary64)))) eps))
▶	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
▶	5.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
	5.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/6 binary64)) eps)))))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
✓	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))

Compiler

Compiled 911 to 843 computations (7.5% saved)

series43.0ms (0.7%)

Memory

38.1MiB live, 38.1MiB allocated; 0ms collecting garbage

Counts

53 → 279

Calls

Call 1

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

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 (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 (+ (* 1/2 eps) x) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (+ x (* 1/2 eps))))
#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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/12 (pow eps 2)) (* eps (* x (+ 1/12 (* -1/144 (pow eps 2)))))) 1/2))))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 1))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) #s(hole binary64 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) x) #s(hole binary64 (* x (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 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) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 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) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2)))))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (/ (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))) x)))
#s(approx (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) #s(hole binary64 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))
#s(approx (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) #s(hole binary64 (/ (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2))) x)))
#s(approx (* eps (/ (- (* (* eps eps) 1/24) 1/2) x)) #s(hole binary64 (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))
#s(approx (/ (- (* (* eps eps) 1/24) 1/2) x) #s(hole binary64 (/ (- (* 1/24 (pow eps 2)) 1/2) x)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* x (+ (* -1 (* x (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))) (* 2 (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* x (+ (* 2 (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* -1/3 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 eps) (* 1/2 (PI))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (cos (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (* -1/2 (* x (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ (* 1/2 eps) (* 1/2 (PI))))) (* -1/6 (* x (cos (+ (* 1/2 eps) (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ (* 1/2 eps) (* 1/2 (PI)))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ x (+ (* 1/2 eps) (* 1/2 (PI))))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* x 2) eps) #s(hole binary64 eps))
#s(approx (+ (* x 2) 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 (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 (+ (* 1/2 eps) x) #s(hole binary64 x))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* x (+ (* -1/6 (/ (pow eps 2) x)) (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (/ 1 x))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* x (+ (* -1/2 eps) (/ 1 x)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 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) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (+ (/ 1 (pow x 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)))) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 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) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x))) 1/2))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* (pow x 2) (- (+ (* 1/12 (pow eps 2)) (/ (* eps (- (* 1/24 (pow eps 2)) 1/2)) x)) 1/2))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (- (* 1/12 (pow eps 2)) 1/2)))
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#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (* 1/24 x) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (/ 1 (pow eps 3)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* eps (+ (* -1/2 x) (/ 1 eps)))))
#s(approx (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) x) #s(hole binary64 (* 1/24 (* (pow eps 2) x))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) x) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (+ (* 1/12 (/ (pow x 2) eps)) (/ 1 (pow eps 3)))))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))))) (* 1/6 (/ 1 eps))))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))))))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (* 1/24 (/ (pow eps 3) x))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (* (pow eps 3) (+ (* 1/12 (/ 1 eps)) (* 1/24 (/ 1 x))))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/12 (/ 1 eps)) (* 1/24 (/ 1 x))) (/ 1/2 (* (pow eps 2) x))))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 eps))) (pow eps 2))) (+ (* 1/12 (/ 1 eps)) (* 1/24 (/ 1 x)))))))
#s(approx (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) #s(hole binary64 (* 1/24 (/ (pow eps 3) x))))
#s(approx (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) #s(hole binary64 (* (pow eps 3) (+ (* 1/12 (/ 1 eps)) (* 1/24 (/ 1 x))))))
#s(approx (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/12 (/ 1 eps)) (* 1/24 (/ 1 x))) (/ 1/2 (* (pow eps 2) x))))))
#s(approx (* eps (/ (- (* (* eps eps) 1/24) 1/2) x)) #s(hole binary64 (* 1/24 (/ (pow eps 3) x))))
#s(approx (* eps (/ (- (* (* eps eps) 1/24) 1/2) x)) #s(hole binary64 (* (pow eps 3) (- (* 1/24 (/ 1 x)) (* 1/2 (/ 1 (* (pow eps 2) x)))))))
#s(approx (/ (- (* (* eps eps) 1/24) 1/2) x) #s(hole binary64 (* 1/24 (/ (pow eps 2) x))))
#s(approx (/ (- (* (* eps eps) 1/24) 1/2) x) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (/ 1 x)) (* 1/2 (/ 1 (* (pow eps 2) x)))))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* eps (+ 1/2 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* x 2) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ 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 (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) 1/1920)))))
#s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) (+ 1/1920 (/ 1 (pow eps 4))))))))
#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 (+ (* 1/2 eps) x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 x) (* 1/6 (/ 1 eps)))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1/2 (/ x eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 x) (/ 1 eps)) eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* -1 (* eps (- (* 1/2 x) (/ 1 eps))))))
#s(approx (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 x) (* 1/2 (/ x (pow eps 2))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/12 (/ (pow x 2) eps)) (* -1/24 x))))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) eps)) (* -1/24 x))))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) eps)) (* -1/24 x))))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (/ 1 x)) (* 1/12 (/ 1 eps))))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (- 1/12 (* 1/2 (/ 1 (* eps x)))) eps)) (* 1/24 (/ 1 x)))))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (+ 1/12 (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x))) eps))) eps)) (* 1/24 (/ 1 x)))))))
#s(approx (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (/ 1 x)) (* 1/12 (/ 1 eps))))))
#s(approx (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (- 1/12 (* 1/2 (/ 1 (* eps x)))) eps)) (* 1/24 (/ 1 x)))))))
#s(approx (* eps (/ (- (* (* eps eps) 1/24) 1/2) x)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (* (pow eps 2) x))) (* 1/24 (/ 1 x)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1/2)))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* x 2) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	x	@	-inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (- (* 1/1920 (* eps eps)) 1/24) (* 1/1920 (* eps eps)) 1/1920 (* eps eps) eps 1/24 1 (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (* 1/2 eps) x) 1/2 x (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (+ (* (* eps x) -1/2) 1) (* eps x) -1/2 (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) (* 1/12 eps) 1/12 (* eps (/ (- (* (* eps eps) 1/24) 1/2) x)) (/ (- (* (* eps eps) 1/24) 1/2) x) (* x x) (* (* 2 (sin (/ (- x (- x eps)) 2))) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (* 2 (sin (/ (- x (- x eps)) 2))) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (/ (+ (* x 2) eps) 2) (+ (* x 2) eps) 2 (/ (PI) 2) (PI))
6.0ms	x	@	0	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) (- (* 1/1920 (* eps eps)) 1/24) (* 1/1920 (* eps eps)) 1/1920 (* eps eps) eps 1/24 1 (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (* 1/2 eps) x) 1/2 x (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (+ (* (* eps x) -1/2) 1) (* eps x) -1/2 (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) (* 1/12 eps) 1/12 (* eps (/ (- (* (* eps eps) 1/24) 1/2) x)) (/ (- (* (* eps eps) 1/24) 1/2) x) (* x x) (* (* 2 (sin (/ (- x (- x eps)) 2))) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) (* 2 (sin (/ (- x (- x eps)) 2))) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (/ (+ (* x 2) eps) 2) (+ (* x 2) eps) 2 (/ (PI) 2) (PI))
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rewrite664.0ms (10.5%)

Memory

-136.8MiB live, 103.2MiB allocated; 801ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1098	10037
0	1150	9546
1	6344	9526
0	8147	9013

Stop Event

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

Counts

332 → 466

Calls

Call 1

Inputs
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(fma.f64 #s(literal 1/2 binary64) eps x)
#s(literal 1/2 binary64)
x
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#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (+ (* 1/12 (/ (pow x 2) eps)) (/ 1 (pow eps 3)))))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))))) (* 1/6 (/ 1 eps))))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* 1/24 (* (pow eps 3) x))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))))))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (* 1/24 (/ (pow eps 3) x))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (* (pow eps 3) (+ (* 1/12 (/ 1 eps)) (* 1/24 (/ 1 x))))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/12 (/ 1 eps)) (* 1/24 (/ 1 x))) (/ 1/2 (* (pow eps 2) x))))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 eps))) (pow eps 2))) (+ (* 1/12 (/ 1 eps)) (* 1/24 (/ 1 x)))))))
#s(approx (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) #s(hole binary64 (* 1/24 (/ (pow eps 3) x))))
#s(approx (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) #s(hole binary64 (* (pow eps 3) (+ (* 1/12 (/ 1 eps)) (* 1/24 (/ 1 x))))))
#s(approx (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) #s(hole binary64 (* (pow eps 3) (- (+ (* 1/12 (/ 1 eps)) (* 1/24 (/ 1 x))) (/ 1/2 (* (pow eps 2) x))))))
#s(approx (* eps (/ (- (* (* eps eps) 1/24) 1/2) x)) #s(hole binary64 (* 1/24 (/ (pow eps 3) x))))
#s(approx (* eps (/ (- (* (* eps eps) 1/24) 1/2) x)) #s(hole binary64 (* (pow eps 3) (- (* 1/24 (/ 1 x)) (* 1/2 (/ 1 (* (pow eps 2) x)))))))
#s(approx (/ (- (* (* eps eps) 1/24) 1/2) x) #s(hole binary64 (* 1/24 (/ (pow eps 2) x))))
#s(approx (/ (- (* (* eps eps) 1/24) 1/2) x) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (/ 1 x)) (* 1/2 (/ 1 (* (pow eps 2) x)))))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* eps (+ 1/2 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* x 2) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ 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 (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) 1/1920)))))
#s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) #s(hole binary64 (* -1 (* (pow eps 5) (- (* 1/24 (/ 1 (pow eps 2))) (+ 1/1920 (/ 1 (pow eps 4))))))))
#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 (+ (* 1/2 eps) x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 x) (* 1/6 (/ 1 eps)))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1/2 (/ x eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 x) (/ 1 eps)) eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* -1 (* eps (- (* 1/2 x) (/ 1 eps))))))
#s(approx (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 x) (* 1/2 (/ x (pow eps 2))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/12 (/ (pow x 2) eps)) (* -1/24 x))))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) eps)) (* -1/24 x))))))
#s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) eps)) (* -1/24 x))))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (/ 1 x)) (* 1/12 (/ 1 eps))))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (- 1/12 (* 1/2 (/ 1 (* eps x)))) eps)) (* 1/24 (/ 1 x)))))))
#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (+ 1/12 (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/2 (/ 1 x))) eps))) eps)) (* 1/24 (/ 1 x)))))))
#s(approx (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (/ 1 x)) (* 1/12 (/ 1 eps))))))
#s(approx (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (- 1/12 (* 1/2 (/ 1 (* eps x)))) eps)) (* 1/24 (/ 1 x)))))))
#s(approx (* eps (/ (- (* (* eps eps) 1/24) 1/2) x)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (* (pow eps 2) x))) (* 1/24 (/ 1 x)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))))
#s(approx (sin (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1/2)))))
#s(approx (/ (+ (* x 2) eps) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* x 2) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))

Outputs
(.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)
(.f64 eps (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) eps (.f64 (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) eps))
(fma.f64 eps #s(literal 1 binary64) (.f64 eps (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps)))
(+.f64 (.f64 eps #s(literal 1 binary64)) (.f64 eps (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps)))
(+.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) eps))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps)) #s(literal 1 binary64)) (-.f64 (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps)) (.f64 #s(literal 1 binary64) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) #s(literal 1 binary64)))))
(fma.f64 (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps #s(literal 1 binary64))
(fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(fma.f64 (.f64 eps eps) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (.f64 (neg.f64 (.f64 eps eps)) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64))))
(+.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)) eps) eps))
(/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 (.f64 eps eps) #s(literal 1/1920 binary64))) #s(literal 1/576 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/1920 binary64) #s(literal 1/24 binary64)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 3 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64)))))
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64))
(.f64 (.f64 #s(literal 1/1920 binary64) eps) eps)
(.f64 (.f64 eps eps) #s(literal 1/1920 binary64))
(.f64 #s(literal 1/1920 binary64) (.f64 eps eps))
#s(literal 1/1920 binary64)
(*.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)))
(*.f64 (fabs.f64 eps) (fabs.f64 eps))
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 eps eps)
(pow.f64 eps #s(literal 2 binary64))
(+.f64 (cosh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
eps
#s(literal 1/24 binary64)
#s(literal 1 binary64)
(sin.f64 (+.f64 (neg.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) (/.f64 (PI.f64) #s(literal 2 binary64))))
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#s(approx (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (neg.f64 (.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) eps)) #s(literal 1/12 binary64)) eps)) (/.f64 #s(literal 1/24 binary64) x)) (.f64 (*.f64 eps eps) eps))))
#s(approx (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) (.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) x) (/.f64 #s(literal 1/12 binary64) eps)) (.f64 (*.f64 eps eps) eps)))
#s(approx (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) (neg.f64 (.f64 (-.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps x))) eps)) (/.f64 #s(literal 1/24 binary64) x)) (.f64 (.f64 eps eps) eps))))
#s(approx (* eps (/ (- (* (* eps eps) 1/24) 1/2) x)) (neg.f64 (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) x)) (/.f64 #s(literal 1/24 binary64) x)) (.f64 (*.f64 eps eps) eps))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (PI.f64) (-.f64 (+.f64 x x) (neg.f64 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (PI.f64) (-.f64 (+.f64 x x) (neg.f64 eps))))))
#s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) 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 (+ (* x 2) eps) (.f64 (neg.f64 eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))))

eval58.0ms (0.9%)

Memory: 8.4MiB live, 53.2MiB allocated; 6ms collecting garbage
Compiler: Compiled 7 771 to 2 920 computations (62.4% saved)

prune23.0ms (0.4%)

Memory

26.4MiB live, 26.4MiB allocated; 0ms collecting garbage

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	431	9	440
Fresh	2	6	8
Picked	3	2	5
Done	0	1	1
Total	436	18	454

Accuracy

100.0%

Counts

454 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.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 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
	99.9%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 #s(approx (- ( 1/1920 (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
	99.6%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) #s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) eps)) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
	6.1%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 #s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) x)))
	99.3%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) x)))
	99.6%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) #s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))))
	99.6%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) #s(approx (cos (/ (+ (+ eps x) x) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (PI.f64) (fma.f64 x #s(literal 2 binary64) eps))))))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 #s(approx (+ ( (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) eps)) #s(literal 1/2 binary64)) (*.f64 x x))) #s(literal 1 binary64))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x))) #s(literal 1 binary64))) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 x x)) #s(literal 1 binary64)))) eps))
✓	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
	5.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/6 binary64)) eps)))))) eps))
	5.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) x) eps))) eps))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* eps x) -1/2) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps)))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
✓	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
	99.3%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))

Compiler

Compiled 1 305 to 933 computations (28.5% saved)

regimes40.0ms (0.6%)

Memory

-19.8MiB live, 26.5MiB allocated; 2ms 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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* eps x) -1/2) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 #s(approx (+ ( (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) eps)) #s(literal 1/2 binary64)) (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/6 binary64)) eps)))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x))) #s(literal 1 binary64))) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 #s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) x)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps 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)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (.f64 eps (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
(.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))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) #s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) 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 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -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 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #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 (fma.f64 eps #s(approx (+ ( eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
(.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) #s(approx (cos (/ (+ (+ eps x) x) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (PI.f64) (fma.f64 x #s(literal 2 binary64) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
(.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))) (.f64 (fma.f64 #s(approx (- ( 1/1920 (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
(.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))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 #s(approx (- ( 1/1920 (* eps eps)) 1/24) #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)) #s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)))
(.f64 #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 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
(.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)) #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)))
(-.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 (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps x)))) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) #s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))))
(-.f64 (sin.f64 #s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))) (sin.f64 x))
(.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 (- (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))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.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)))

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

Calls

3 calls:

15.0ms	x
11.0ms	(-.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)

regimes25.0ms (0.4%)

Memory

19.2MiB live, 19.2MiB allocated; 0ms 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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* eps x) -1/2) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 #s(approx (+ ( (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) eps)) #s(literal 1/2 binary64)) (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/6 binary64)) eps)))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x))) #s(literal 1 binary64))) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 #s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) x)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps 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)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (.f64 eps (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
(.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))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) #s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) 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 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -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 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #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 (fma.f64 eps #s(approx (+ ( eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
(.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) #s(approx (cos (/ (+ (+ eps x) x) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (PI.f64) (fma.f64 x #s(literal 2 binary64) eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
(.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))) (.f64 (fma.f64 #s(approx (- ( 1/1920 (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))
(.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))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 #s(approx (- ( 1/1920 (* eps eps)) 1/24) #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)) #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)))

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

Outputs

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

Calls

3 calls:

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

regimes22.0ms (0.3%)

Memory

16.6MiB live, 16.6MiB allocated; 0ms collecting garbage

Counts

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

Calls

3 calls:

7.0ms	(-.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)

regimes23.0ms (0.4%)

Memory

-38.4MiB live, 15.0MiB 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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* eps x) -1/2) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 #s(approx (+ ( (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) eps)) #s(literal 1/2 binary64)) (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/6 binary64)) eps)))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x))) #s(literal 1 binary64))) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 #s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) x)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps 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)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (.f64 eps (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
(.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))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) #s(approx (* (+ (* (- (* 1/1920 (* eps eps)) 1/24) (* eps eps)) 1) eps) 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 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -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 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #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 (fma.f64 eps #s(approx (+ ( eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) (cos.f64 x)) eps))
(.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 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))))

Calls

3 calls:

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

regimes16.0ms (0.2%)

Memory

13.6MiB live, 13.6MiB allocated; 0ms 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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 #s(approx (- (* (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* eps x) -1/2) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 #s(approx (+ ( (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) eps)) #s(literal 1/2 binary64)) (*.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.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 (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/6 binary64)) eps)))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(approx (* (- (+ (* (* 1/12 eps) eps) (* eps (/ (- (* (* eps eps) 1/24) 1/2) x))) 1/2) (* x x)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x)) x))) #s(literal 1 binary64))) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 #s(approx (+ (/ (+ (* x 2) eps) 2) (/ (PI) 2)) x)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (/ (- (- 1/2 (* 1/2 (cos (* 2 (+ eps x))))) (- 1/2 (* 1/2 (cos (* 2 x))))) (+ (sin x) (sin (+ eps 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)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (.f64 eps (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x))) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes15.0ms (0.2%)

Memory

13.1MiB live, 13.1MiB allocated; 0ms collecting garbage

Counts

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes14.0ms (0.2%)

Memory

-35.7MiB live, 11.2MiB allocated; 1ms collecting garbage

Counts

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

Outputs

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

Calls

3 calls:

5.0ms	x
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	eps

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes11.0ms (0.2%)

Memory

9.9MiB live, 9.9MiB allocated; 0ms collecting garbage

Counts

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.8%	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)

regimes8.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated; 0ms collecting garbage

Counts

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes7.0ms (0.1%)

Memory

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

Counts

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

Outputs

#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 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
98.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes5.0ms (0.1%)

Memory

6.0MiB live, 6.0MiB allocated; 0ms collecting garbage

Counts

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

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes4.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated; 0ms collecting garbage

Accuracy

Total -59.2b remaining (-4648.8%)

Threshold costs -59.2b (-4648.8%)

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

derivations384.0ms (6.1%)

Memory

-34.3MiB live, 105.1MiB allocated; 10ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 244 to 145 computations (40.6% saved)

preprocess91.0ms (1.4%)

Memory: 42.5MiB live, 135.1MiB allocated; 8ms collecting garbage
Compiler: Compiled 287 to 184 computations (35.9% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze29.0ms (0.5%)

sample3.8s (60.3%)

preprocess88.0ms (1.4%)

series5.0ms (0.1%)

rewrite151.0ms (2.4%)

eval10.0ms (0.2%)

prune9.0ms (0.1%)

series68.0ms (1.1%)

rewrite299.0ms (4.7%)

eval66.0ms (1%)

prune20.0ms (0.3%)

series32.0ms (0.5%)

rewrite211.0ms (3.3%)

eval55.0ms (0.9%)

prune20.0ms (0.3%)

series43.0ms (0.7%)

rewrite664.0ms (10.5%)

eval58.0ms (0.9%)

prune23.0ms (0.4%)

regimes40.0ms (0.6%)

regimes25.0ms (0.4%)

regimes22.0ms (0.3%)

regimes23.0ms (0.4%)

regimes16.0ms (0.2%)

regimes15.0ms (0.2%)

regimes14.0ms (0.2%)

regimes11.0ms (0.2%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

derivations384.0ms (6.1%)

preprocess91.0ms (1.4%)

end0.0ms (0%)

Profiling