Metrics for 2sin (example 3.3)

start0.0ms (0%)

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

analyze55.0ms (0.8%)

Memory

-14.0MiB live, 29.5MiB allocated; 9ms 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)

sample5.1s (72.8%)

Memory

-144.0MiB live, 5 293.9MiB allocated; 2.4s collecting garbage

Samples

2.7s	26 093×	0	invalid
637.0ms	5 608×	1	valid
273.0ms	2 648×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.4s

ival-sin: 729.0ms (30.1% of total)

ival-add!: 698.0ms (28.8% of total)

ival-fabs: 296.0ms (12.2% of total)

ival-<: 199.0ms (8.2% of total)

ival-mult!: 197.0ms (8.1% of total)

adjust: 147.0ms (6.1% of total)

ival-sub!: 84.0ms (3.5% of total)

ival-and: 62.0ms (2.6% of total)

ival-assert: 13.0ms (0.5% of total)

Bogosity

preprocess37.0ms (0.5%)

Memory

-21.4MiB live, 23.5MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	48
1	77	48
2	281	44
3	1622	44

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.0%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 12 to 12 computations (0% saved)

series5.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated; 0ms collecting garbage

Counts

6 → 36

Calls

Call 1

Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)

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

Calls

6 calls:

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

rewrite154.0ms (2.2%)

Memory

25.7MiB live, 201.5MiB allocated; 39ms 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))))

eval11.0ms (0.2%)

Memory: -5.1MiB live, 41.4MiB allocated; 3ms collecting garbage
Compiler: Compiled 1 106 to 384 computations (65.3% saved)

prune7.0ms (0.1%)

Memory

24.5MiB live, 24.5MiB allocated; 0ms collecting garbage

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	86	11	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	12	98

Accuracy

100.0%

Counts

98 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.2%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	7.4%	(/.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))))
✓	62.0%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	60.9%	(-.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)))
	60.8%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
▶	60.3%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
▶	62.0%	(.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))))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
▶	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	97.3%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 296 to 284 computations (4.1% saved)

series40.0ms (0.6%)

Memory

-43.3MiB live, 65.6MiB allocated; 9ms collecting garbage

Counts

42 → 193

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

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 (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 -1/6))
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6)))
#s(approx (* 1/120 (* x x)) #s(hole binary64 (* 1/120 (pow x 2))))
#s(approx (* 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 (- (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 (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* 1/120 (pow x 5))))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* 1/120 (pow x 4))))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (* 1/120 (pow x 2))))
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (* (* 2 (sin (/ (- 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 (- (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 (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))))
#s(approx (* (* 2 (sin (/ (- 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 (- (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 (* (+ (* 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 (- (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)))))

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	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) (- (sin (+ x eps)) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 (* x x) 1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) 2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))
7.0ms	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) (- (sin (+ x eps)) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 (* x x) 1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) 2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))
6.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (* (sin x) eps) (sin x) x 1/24 (* (cos x) -1/6) (cos x) -1/6 (* (sin x) -1/2) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 (* x x) 1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) 2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))
6.0ms	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) (- (sin (+ x eps)) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 (* x x) 1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) 2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))
5.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (* (sin x) eps) (sin x) x 1/24 (* (cos x) -1/6) (cos x) -1/6 (* (sin x) -1/2) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (- (sin (+ x eps)) (sin x)) (sin x) (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (- (* 1/120 (* x x)) 1/6) (* 1/120 (* x x)) 1/120 (* x x) 1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) 2 (sin (/ (- x (- x eps)) 2)) (/ (- x (- x eps)) 2) (- x (- x eps)) (- x eps) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x))

rewrite236.0ms (3.4%)

Memory

25.1MiB live, 284.8MiB allocated; 91ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	761	4659
0	818	4571
1	4269	4551
0	8079	4362

Stop Event

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

Counts

235 → 370

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) x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (sin x) x)
(-.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)))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
#s(literal 1/120 binary64)
(*.f64 x x)
#s(literal 1/6 binary64)
#s(literal 1 binary64)
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))))
#s(literal 2 binary64)
(sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))
(/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))
(-.f64 x (-.f64 x eps))
(-.f64 x eps)
(cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(+.f64 (+.f64 eps x) x)
(+.f64 eps x)
#s(approx (- (sin (+ x eps)) (sin x)) #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 (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 -1/6))
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (- (* 1/120 (pow x 2)) 1/6)))
#s(approx (* 1/120 (* x x)) #s(hole binary64 (* 1/120 (pow x 2))))
#s(approx (* 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 (- (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 (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* 1/120 (pow x 5))))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* 1/120 (pow x 4))))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (* 1/120 (pow x 2))))
#s(approx (- (* 1/120 (* x x)) 1/6) #s(hole binary64 (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))))
#s(approx (* (* 2 (sin (/ (- 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 (- (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 (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))))
#s(approx (* (* 2 (sin (/ (- 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 (- (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 (* (+ (* 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 (- (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)))))

Outputs
#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)
(.f64 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)))
(fma.f64 (cos.f64 x) eps (.f64 (.f64 (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))) eps) eps))
(fma.f64 (cos.f64 x) eps (.f64 eps (.f64 (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))) eps)))
(fma.f64 eps (cos.f64 x) (.f64 (.f64 (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))) eps) eps))
(fma.f64 eps (cos.f64 x) (.f64 eps (.f64 (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))) eps)))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (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))) eps) eps))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 eps (.f64 (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))) eps)))
(/.f64 (-.f64 (pow.f64 (.f64 (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))) eps) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 (.f64 (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))) eps) (cos.f64 x)))
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(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
#s(literal 1/6 binary64)
#s(literal 1 binary64)
(.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (.f64 (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))
(*.f64 (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (+.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)) (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)) (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))))
(+.f64 (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #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 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 x eps) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 x eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (+.f64 x x) (*.f64 #s(literal 2 binary64) (-.f64 x eps))) #s(literal 4 binary64))
(/.f64 (neg.f64 (-.f64 x (-.f64 x eps))) #s(literal -2 binary64))
(/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64))
(-.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 (-.f64 x eps) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 x x) (.f64 (-.f64 x eps) (-.f64 x eps))) (+.f64 x (-.f64 x eps)))
(/.f64 (-.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (-.f64 x eps) (-.f64 x eps)) (-.f64 x eps))) (fma.f64 x x (fma.f64 (-.f64 x eps) (-.f64 x eps) (*.f64 x (-.f64 x eps)))))
(-.f64 x (-.f64 x eps))
(+.f64 (-.f64 x x) eps)
(/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (+.f64 eps x))
(/.f64 (-.f64 (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) (fma.f64 x x (fma.f64 eps eps (*.f64 eps x))))
(-.f64 x eps)
(sin.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(fma.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(-.f64 (.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))
(+.f64 (.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (+.f64 eps x) #s(literal 2 binary64) (+.f64 x x)) #s(literal 4 binary64))
(/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) #s(literal -2 binary64))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))
(+.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))) (+.f64 eps (*.f64 #s(literal -2 binary64) x)))
(/.f64 (-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x x)) (-.f64 (+.f64 eps x) x))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (+.f64 x x) (+.f64 x x))) (-.f64 eps (+.f64 x x)))
(/.f64 (-.f64 (.f64 (.f64 eps eps) eps) (.f64 #s(literal -8 binary64) (.f64 (.f64 x x) x))) (fma.f64 eps eps (fma.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x) (.f64 eps (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (fma.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (+.f64 eps x) (.f64 (.f64 x x) x)) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (*.f64 (+.f64 eps x) x))))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x))) (fma.f64 eps eps (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps (+.f64 x x)))))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
(-.f64 eps (*.f64 #s(literal -2 binary64) x))
(+.f64 (+.f64 x x) eps)
(+.f64 (+.f64 eps x) x)
(+.f64 eps (+.f64 x x))
(+.f64 x (+.f64 eps x))
(/.f64 (-.f64 (.f64 eps eps) (.f64 x x)) (-.f64 eps x))
(/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 x eps))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 eps eps (-.f64 (.f64 x x) (*.f64 eps x))))
(/.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 eps eps) eps)) (fma.f64 x x (-.f64 (.f64 eps eps) (*.f64 eps x))))
(+.f64 eps x)
(+.f64 x eps)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 x (-.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 x (-.f64 (fma.f64 x (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) (cos.f64 eps)) #s(literal 1 binary64)) (sin.f64 eps)))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.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)) 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 (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.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 (+ (* 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)))
#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)))
#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)))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) 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)))
#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 #s(literal -1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/120 binary64) eps)) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (sin x) x)
#s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx 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 (+ x eps)) (sin.f64 eps))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 eps) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 x (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 x (fma.f64 (.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (.f64 (sin.f64 eps) #s(literal -1/2 binary64))) (cos.f64 eps)) x (sin.f64 eps)))
#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) x)
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) #s(literal 1 binary64))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (- (* 1/120 (* x x)) 1/6) #s(literal -1/6 binary64))
#s(approx (- (* 1/120 (* x x)) 1/6) (-.f64 (.f64 (.f64 x x) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)))
#s(approx (* 1/120 (* x x)) (.f64 (.f64 x x) #s(literal 1/120 binary64)))
#s(approx (* 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 (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 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 (+ (* 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 (.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)))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (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))))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (cos x) -1/6) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
#s(approx (cos x) (cos.f64 x))
#s(approx (* (sin x) -1/2) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/120 binary64)))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (.f64 (+.f64 #s(literal 1/120 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64))))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/120 binary64)))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
#s(approx (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) (.f64 (+.f64 #s(literal 1/120 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1/6 binary64) (.f64 x x)))) (.f64 (.f64 x x) (.f64 x x))))
#s(approx (- (* 1/120 (* x x)) 1/6) (.f64 (.f64 x x) #s(literal 1/120 binary64)))
#s(approx (- (* 1/120 (* x x)) 1/6) (.f64 (-.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (*.f64 x x)))
#s(approx (* (* 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 (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (-.f64 eps (neg.f64 x))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (neg.f64 (.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal 1/120 binary64)) (pow.f64 x #s(literal 5 binary64)))))
#s(approx (* (+ (* (- (* 1/120 (* x x)) 1/6) (* x x)) 1) x) (neg.f64 (.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal 1/120 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x)))) (pow.f64 x #s(literal 5 binary64)))))
#s(approx (* (* 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 (- (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 (* (+ (* 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))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
#s(approx 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 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (sin (+ x eps)) (sin.f64 x))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 x) eps (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 eps (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps (sin.f64 x)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (*.f64 (cos.f64 x) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (fma.f64 eps (fma.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) eps) #s(literal 2 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) #s(literal 2 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) eps)
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (sin (/ (- x (- x eps)) 2)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (sin (/ (- x (- x eps)) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (- x (- x eps)) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (- x (- x eps)) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (- x eps) (+.f64 (neg.f64 eps) x))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 x))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 eps (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/48 binary64) (.f64 #s(literal -1/8 binary64) (cos.f64 x))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
#s(approx (* (+ (* eps (+ (* 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 (- (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 #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)) (.f64 (.f64 (neg.f64 eps) (*.f64 eps eps)) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps))) eps))) eps)))))
#s(approx (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2)) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 (cos.f64 x) #s(literal 1/6 binary64))) eps))) (*.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6)) (.f64 (neg.f64 eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/24 binary64)))))
#s(approx (sin (+ x eps)) (sin.f64 (-.f64 x (neg.f64 eps))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (cos.f64 (.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)))
#s(approx (- x eps) (*.f64 (neg.f64 eps) (+.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (+ eps x) x) (.f64 (neg.f64 eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval69.0ms (1%)

Memory: 16.0MiB live, 81.2MiB allocated; 40ms collecting garbage
Compiler: Compiled 4 769 to 1 895 computations (60.3% saved)

prune21.0ms (0.3%)

Memory

-7.6MiB live, 41.5MiB allocated; 9ms collecting garbage

Pruning

22 alts after pruning (18 fresh and 4 done)

	Pruned	Kept	Total
New	339	13	352
Fresh	1	5	6
Picked	2	3	5
Done	0	1	1
Total	342	22	364

Accuracy

100.0%

Counts

364 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.2%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	7.4%	(/.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))))
✓	62.0%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	60.3%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
	5.6%	(-.f64 (sin.f64 #s(approx (+ eps x) x)) #s(approx (sin x) x))
	99.6%	(.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))))
	99.5%	(.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))))
▶	99.3%	(.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 (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 (.f64 (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))) eps) eps)))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (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))) eps) eps)))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
✓	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	97.3%	#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)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* 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))
	97.3%	#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)) (+.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))
✓	97.3%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
▶	97.3%	#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 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
	97.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
▶	97.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
▶	99.8%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))

Compiler

Compiled 794 to 740 computations (6.8% saved)

series53.0ms (0.8%)

Memory

13.0MiB live, 95.8MiB allocated; 18ms collecting garbage

Counts

41 → 216

Calls

Call 1

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

Outputs
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 eps)))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx x #s(hole binary64 x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* eps (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) 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) x) #s(hole binary64 (* (pow eps 2) x)))
#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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (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) #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 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (+ eps (* 2 x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 x))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* eps (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* x (+ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (- eps (* -2 x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos x))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* -1 (* eps (sin x))) (* 2 (cos x)))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos x)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (+ (* eps (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 eps))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* -1/2 (* eps x))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* eps (+ (* -1/2 x) (* -1/6 eps)))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* eps (+ (* -1/2 x) (* eps (- (* 1/24 (* eps x)) 1/6))))))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (* (* eps eps) 1/24) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (+ (* (* eps eps) -1/6) 1) #s(hole binary64 1))
#s(approx (+ (* (* eps eps) -1/6) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (* (+ (* eps (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* 1/24 (* (pow eps 4) x))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (* 1/24 x) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (+ (* -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) #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 (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 (* -1/6 (pow eps 3))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))))
#s(approx (+ (* (* eps eps) -1/6) 1) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (* eps eps) -1/6) 1) #s(hole binary64 (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* eps (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* 1/2 (/ x eps))) eps)) (* 1/24 x)))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* -1 (/ (+ (* -1/2 x) (/ 1 eps)) eps))) eps)) (* 1/24 x)))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))

Calls

6 calls:

Time	Variable		Point	Expression
17.0ms	eps	@	inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) 2 (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (* (* eps eps) x) (* eps eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) eps) (cos x) (* (sin x) -1/2) (sin x) -1/2)
8.0ms	eps	@	0	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) 2 (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (* (* eps eps) x) (* eps eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) eps) (cos x) (* (sin x) -1/2) (sin x) -1/2)
8.0ms	x	@	inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) 2 (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (* (* eps eps) x) (* eps eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) eps) (cos x) (* (sin x) -1/2) (sin x) -1/2)
6.0ms	x	@	-inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) 2 (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (* (* eps eps) x) (* eps eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) eps) (cos x) (* (sin x) -1/2) (sin x) -1/2)
5.0ms	eps	@	-inf	((* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (* 2 (cos (* (+ (* 2 x) eps) 1/2))) 2 (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (* (* eps eps) x) (* eps eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) -1/6 1 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (- (sin (+ x eps)) (sin x)) (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (* (cos x) eps) (cos x) (* (sin x) -1/2) (sin x) -1/2)

rewrite190.0ms (2.7%)

Memory

12.6MiB live, 200.9MiB allocated; 36ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	819	5613
0	873	5441
1	4578	5401
0	8293	5190

Stop Event

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

Counts

257 → 416

Calls

Call 1

Inputs
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
#s(literal 2 binary64)
(cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
x
eps
#s(literal 1/2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (sin eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.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)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
(fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
(.f64 (.f64 eps eps) x)
(*.f64 eps eps)
(-.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 1/24 binary64)
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) eps)
(cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(+.f64 (+.f64 eps x) x)
(+.f64 eps x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
(.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps)
(fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x))
(fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(sin.f64 x)
#s(literal -1/2 binary64)
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 eps)))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx x #s(hole binary64 x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* eps (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) 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) x) #s(hole binary64 (* (pow eps 2) x)))
#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 (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 x) (* -1/6 eps))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (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) #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 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (+ eps (* 2 x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 x))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* eps (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* x (+ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (sin x) -1/2) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (- eps (* -2 x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos x))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* -1 (* eps (sin x))) (* 2 (cos x)))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos x)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (+ (* eps (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 eps))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* -1/2 (* eps x))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* eps (+ (* -1/2 x) (* -1/6 eps)))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* eps (+ (* -1/2 x) (* eps (- (* 1/24 (* eps x)) 1/6))))))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (* (* eps eps) 1/24) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (+ (* (* eps eps) -1/6) 1) #s(hole binary64 1))
#s(approx (+ (* (* eps eps) -1/6) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (* (+ (* eps (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* 1/24 (* (pow eps 4) x))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (* 1/24 x) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (+ (* -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) #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 (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 (* -1/6 (pow eps 3))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))))
#s(approx (+ (* (* eps eps) -1/6) 1) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (* eps eps) -1/6) 1) #s(hole binary64 (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* -1/6 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* -1/6 (* (pow eps 2) (cos x)))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1/6 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) #s(hole binary64 (* 2 (cos (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* eps (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* 1/2 (/ x eps))) eps)) (* 1/24 x)))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* -1 (/ (+ (* -1/2 x) (/ 1 eps)) eps))) eps)) (* 1/24 x)))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) #s(hole binary64 (* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))))

Outputs
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
(+.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
#s(literal 2 binary64)
(sin.f64 (+.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)))))
(-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)))))
(cos.f64 (neg.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(cos.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
(cos.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))) (+.f64 eps (*.f64 #s(literal -2 binary64) x)))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (+.f64 x x) (+.f64 x x))) (-.f64 eps (+.f64 x x)))
(/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps eps)) (-.f64 (+.f64 x x) eps))
(/.f64 (-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x x)) (-.f64 (+.f64 eps x) x))
(/.f64 (-.f64 (.f64 (.f64 eps eps) eps) (.f64 #s(literal -8 binary64) (.f64 (.f64 x x) x))) (fma.f64 eps eps (fma.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x) (.f64 eps (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x))) (fma.f64 eps eps (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps (+.f64 x x)))))
(/.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) (fma.f64 (+.f64 x x) (+.f64 x x) (-.f64 (.f64 eps eps) (.f64 (+.f64 x x) eps))))
(/.f64 (fma.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (+.f64 eps x) (.f64 (.f64 x x) x)) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (*.f64 (+.f64 eps x) x))))
(fma.f64 x #s(literal 2 binary64) eps)
(fma.f64 #s(literal 2 binary64) x eps)
(-.f64 eps (*.f64 #s(literal -2 binary64) x))
(+.f64 (+.f64 x x) eps)
(+.f64 (+.f64 eps x) x)
(+.f64 eps (+.f64 x x))
(+.f64 x (+.f64 eps x))
x
eps
#s(literal 1/2 binary64)
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(exp.f64 (.f64 (log.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (sin eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.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)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
(/.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)) (pow.f64 (.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (-.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps) (.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))))
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(/.f64 (fma.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) #s(literal -1/216 binary64) (pow.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)))
(fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (cos.f64 x) (.f64 #s(literal -1/6 binary64) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)))
(-.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps)))
(-.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)) (*.f64 (neg.f64 (sin.f64 x)) #s(literal -1/2 binary64)))
(+.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)))
(+.f64 (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(*.f64 (cos.f64 x) eps)
(*.f64 eps (cos.f64 x))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(sin.f64 x)
#s(literal -1/2 binary64)
#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))))) (.f64 (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.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 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (sin.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (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 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (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 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (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))))) (.f64 (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.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 (cos (* (+ (* 2 x) eps) 1/2))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) x) #s(literal -2 binary64) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (fma.f64 x (fma.f64 (neg.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (fma.f64 x (fma.f64 x (fma.f64 (.f64 #s(literal 1/3 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64))) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) (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 (* (+ (* 2 x) eps) 1/2)) (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 (* (+ (* 2 x) eps) 1/2)) (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 (* (+ (* 2 x) eps) 1/2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (* (+ (* 2 x) eps) 1/2) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (+ eps x) x) eps)
#s(approx (+ (+ eps x) x) (fma.f64 x #s(literal 2 binary64) eps))
#s(approx x x)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 x (-.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 x (-.f64 (fma.f64 x (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) (cos.f64 eps)) #s(literal 1 binary64)) (sin.f64 eps)))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.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)) 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 (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.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 (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (* (* eps eps) x) (.f64 (.f64 eps eps) x))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
#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 x #s(literal 2 binary64) eps))
#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps (.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps (.f64 (fma.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x)))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps (.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (.f64 eps x) #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 eps x (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (* (cos x) eps) eps)
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/24 binary64) eps)) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.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 x) x)
#s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
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#s(approx (+ (* (* eps eps) -1/6) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
#s(approx (+ (* (* eps eps) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)) (*.f64 eps eps)))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (+ eps x) x) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (.f64 (.f64 (cos.f64 x) (.f64 (.f64 eps eps) eps)) #s(literal -1/6 binary64)))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) (.f64 (.f64 eps eps) eps)))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (.f64 eps eps)))) (.f64 (.f64 eps eps) eps)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (.f64 (.f64 (*.f64 eps eps) (cos.f64 x)) #s(literal -1/6 binary64)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) (*.f64 eps eps)))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (/.f64 (cos.f64 x) (.f64 eps eps)))) (*.f64 eps eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) 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 (* (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (sin (* 1/2 eps))) (.f64 (.f64 (cos.f64 (.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)))
#s(approx (* 2 (cos (* (+ (* 2 x) eps) 1/2))) (.f64 (cos.f64 (.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))))
#s(approx (* (+ (* 2 x) eps) 1/2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (+ eps x) x) (.f64 (neg.f64 eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -2 binary64)) #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 #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) (*.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 #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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (.f64 (.f64 eps 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) #s(literal 1/6 binary64)) eps)))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 #s(literal 1/24 binary64) x (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps)) #s(literal 1/6 binary64)) eps))) (.f64 (.f64 eps eps) (.f64 eps eps))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) (.f64 (.f64 (neg.f64 eps) (.f64 eps eps)) (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (+ eps x) x) (.f64 (neg.f64 eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (neg.f64 (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) (cos.f64 x))) (.f64 (.f64 eps eps) eps))))
#s(approx (* (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) eps) (neg.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))) (.f64 (*.f64 eps eps) eps))))
#s(approx (+ (* eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (neg.f64 (/.f64 (fma.f64 (sin.f64 x) #s(literal 1/2 binary64) (neg.f64 (/.f64 (cos.f64 x) eps))) eps))) (.f64 eps eps)))
#s(approx (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2)) (.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) (cos.f64 x)))))

eval49.0ms (0.7%)

Memory: -14.2MiB live, 42.6MiB allocated; 8ms collecting garbage
Compiler: Compiled 5 024 to 2 039 computations (59.4% saved)

prune28.0ms (0.4%)

Memory

-21.3MiB live, 26.7MiB allocated; 2ms collecting garbage

Pruning

33 alts after pruning (28 fresh and 5 done)

	Pruned	Kept	Total
New	332	22	354
Fresh	7	6	13
Picked	2	3	5
Done	2	2	4
Total	343	33	376

Accuracy

100.0%

Counts

376 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.2%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	7.4%	(/.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))))
✓	62.0%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.6%	(.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))))
	99.5%	(.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))))
	99.3%	(.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)))))
	99.3%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))))
✓	99.3%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
▶	99.3%	(.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))))
	98.6%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) x)))
▶	99.3%	(.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%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps)))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps)))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (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))) eps) eps)))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
✓	99.6%	#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))
	97.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 eps x (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	5.7%	#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 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 #s(approx (+ ( (* eps eps) -1/6) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) eps))))
	97.3%	#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 (.f64 (.f64 eps eps) x) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
	97.3%	#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps)) eps #s(literal 1 binary64)) eps))))
▶	97.3%	#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)) eps))))
▶	5.2%	#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) x) (/.f64 #s(literal 1/6 binary64) eps)) (.f64 (.f64 eps eps) (*.f64 eps eps))))))
	5.5%	#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (.f64 (.f64 (.f64 eps eps) (*.f64 eps eps)) x) #s(literal 1/24 binary64)))))
	5.7%	#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))))
	97.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
✓	97.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
	99.7%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
▶	99.8%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (+.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
	99.5%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
	99.6%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( 2 (cos (* (+ (* 2 x) eps) 1/2))) (fma.f64 (cos.f64 x) #s(literal 2 binary64) (.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))

Compiler

Compiled 1 636 to 1 513 computations (7.5% saved)

series37.0ms (0.5%)

Memory

32.0MiB live, 32.0MiB allocated; 0ms collecting garbage

Counts

46 → 210

Calls

Call 1

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

Outputs
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 (PI)) (* 1/2 eps)))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* -2 (* x (* (cos (- (* 1/2 (PI)) (* 1/2 eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 (PI)) (* 1/2 eps))))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 (PI)) (* 1/2 eps))))) (* x (+ (* -2 (* (cos (- (* 1/2 (PI)) (* 1/2 eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (- (* 1/2 (PI)) (* 1/2 eps)))))))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 (PI)) (* 1/2 eps))))) (* x (+ (* -2 (* (cos (- (* 1/2 (PI)) (* 1/2 eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (- (* 1/2 (PI)) (* 1/2 eps))))) (* 1/3 (* x (* (cos (- (* 1/2 (PI)) (* 1/2 eps))) (sin (* 1/2 eps))))))))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (* 2 (sin (- (* 1/2 (PI)) (* 1/2 eps))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (+ (* -2 (* x (cos (- (* 1/2 (PI)) (* 1/2 eps))))) (* 2 (sin (- (* 1/2 (PI)) (* 1/2 eps)))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (sin (- (* 1/2 (PI)) (* 1/2 eps)))) (* x (+ (* -2 (cos (- (* 1/2 (PI)) (* 1/2 eps)))) (* -1 (* x (sin (- (* 1/2 (PI)) (* 1/2 eps))))))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (sin (- (* 1/2 (PI)) (* 1/2 eps)))) (* x (+ (* -2 (cos (- (* 1/2 (PI)) (* 1/2 eps)))) (* x (+ (* -1 (sin (- (* 1/2 (PI)) (* 1/2 eps)))) (* 1/3 (* x (cos (- (* 1/2 (PI)) (* 1/2 eps))))))))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* 1/2 eps)))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (+ (sin (- (* 1/2 (PI)) (* 1/2 eps))) (* -1 (* x (cos (- (* 1/2 (PI)) (* 1/2 eps))))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (+ (sin (- (* 1/2 (PI)) (* 1/2 eps))) (* x (+ (* -1 (cos (- (* 1/2 (PI)) (* 1/2 eps)))) (* -1/2 (* x (sin (- (* 1/2 (PI)) (* 1/2 eps))))))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (+ (sin (- (* 1/2 (PI)) (* 1/2 eps))) (* x (+ (* -1 (cos (- (* 1/2 (PI)) (* 1/2 eps)))) (* x (+ (* -1/2 (sin (- (* 1/2 (PI)) (* 1/2 eps)))) (* 1/6 (* x (cos (- (* 1/2 (PI)) (* 1/2 eps))))))))))))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (- (* 1/2 (PI)) (* 1/2 eps))))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (- (+ (* -1 x) (* 1/2 (PI))) (* 1/2 eps))))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) #s(hole binary64 (* -1/2 eps)))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) #s(hole binary64 (- (* -1 x) (* 1/2 eps))))
#s(approx (* 1/2 (+ (* x 2) eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (* 1/2 (+ (* x 2) eps)) #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 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* (* -1/2 eps) x) 1) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* -1/2 eps) x) 1) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (* -1/2 eps) x) 1) #s(hole binary64 1))
#s(approx (+ (* (* -1/2 eps) x) 1) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) #s(hole binary64 (* -1/6 (pow eps 3))))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) #s(hole binary64 (+ (* -1/6 (pow eps 3)) (* 1/24 (* (pow eps 4) x)))))
#s(approx (- (* 1/24 x) (/ 1/6 eps)) #s(hole binary64 (/ -1/6 eps)))
#s(approx (- (* 1/24 x) (/ 1/6 eps)) #s(hole binary64 (- (* 1/24 x) (* 1/6 (/ 1 eps)))))
#s(approx (* 1/24 x) #s(hole binary64 (* 1/24 x)))
#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 (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x)))))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (* 2 (sin (- (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x))))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x)))))))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (* -1 x)))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (* x (- (* 1/2 (/ (PI) x)) (+ 1 (* 1/2 (/ eps x)))))))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) #s(hole binary64 (* -1 x)))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) #s(hole binary64 (* x (- (* -1/2 (/ eps x)) 1))))
#s(approx (* 1/2 (+ (* x 2) eps)) #s(hole binary64 x))
#s(approx (* 1/2 (+ (* x 2) eps)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* x 2) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* x 2) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* eps (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* x (+ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)))))
#s(approx (* (+ (* (* -1/2 eps) x) 1) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (* (+ (* (* -1/2 eps) x) 1) eps) #s(hole binary64 (* x (+ (* -1/2 (pow eps 2)) (/ eps x)))))
#s(approx (+ (* (* -1/2 eps) x) 1) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (* -1/2 eps) x) 1) #s(hole binary64 (* x (+ (* -1/2 eps) (/ 1 x)))))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) #s(hole binary64 (* 1/24 (* (pow eps 4) x))))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) #s(hole binary64 (* x (+ (* -1/6 (/ (pow eps 3) x)) (* 1/24 (pow eps 4))))))
#s(approx (- (* 1/24 x) (/ 1/6 eps)) #s(hole binary64 (* 1/24 x)))
#s(approx (- (* 1/24 x) (/ 1/6 eps)) #s(hole binary64 (* x (- 1/24 (* 1/6 (/ 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 (+ (* 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) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 (PI)) (* 1/2 (- eps (* -2 x)))))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (* 2 (sin (- (* 1/2 (PI)) (* 1/2 (- eps (* -2 x))))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* 1/2 (- eps (* -2 x)))))))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (* -1 (* x (+ 1 (* -1 (/ (- (* 1/2 (PI)) (* 1/2 eps)) x)))))))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ eps x)))))))
#s(approx (* 1/2 (+ (* x 2) eps)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* x 2) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)))))))
#s(approx (* (+ (* (* -1/2 eps) x) 1) eps) #s(hole binary64 (* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))))
#s(approx (+ (* (* -1/2 eps) x) 1) #s(hole binary64 (* -1 (* x (- (* 1/2 eps) (/ 1 x))))))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) #s(hole binary64 (* -1 (* x (+ (* -1/24 (pow eps 4)) (* 1/6 (/ (pow eps 3) x)))))))
#s(approx (- (* 1/24 x) (/ 1/6 eps)) #s(hole binary64 (* -1 (* x (- (* 1/6 (/ 1 (* eps x))) 1/24)))))
#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 (+ (* 1/2 eps) x) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (sin (- (* 1/2 (PI)) x)))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (sin (- (* 1/2 (PI)) x)) (* -1/2 (* eps (cos (- (* 1/2 (PI)) x))))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (sin (- (* 1/2 (PI)) x)) (* eps (+ (* -1/2 (cos (- (* 1/2 (PI)) x))) (* 2 (* eps (+ (* -1/16 (sin (- (* 1/2 (PI)) x))) (* -1/48 (sin (- (* 1/2 (PI)) x))))))))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (sin (- (* 1/2 (PI)) x)) (* eps (+ (* -1/2 (cos (- (* 1/2 (PI)) x))) (* eps (+ (* 1/24 (* eps (cos (- (* 1/2 (PI)) x)))) (* 2 (+ (* -1/16 (sin (- (* 1/2 (PI)) x))) (* -1/48 (sin (- (* 1/2 (PI)) x)))))))))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (* 2 (sin (- (* 1/2 (PI)) x)))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (+ (* -1 (* eps (cos (- (* 1/2 (PI)) x)))) (* 2 (sin (- (* 1/2 (PI)) x))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (sin (- (* 1/2 (PI)) x))) (* eps (+ (* -1 (cos (- (* 1/2 (PI)) x))) (* -1/4 (* eps (sin (- (* 1/2 (PI)) x)))))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (sin (- (* 1/2 (PI)) x))) (* eps (+ (* -1 (cos (- (* 1/2 (PI)) x))) (* eps (+ (* -1/4 (sin (- (* 1/2 (PI)) x))) (* 1/24 (* eps (cos (- (* 1/2 (PI)) x)))))))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) x))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (+ (sin (- (* 1/2 (PI)) x)) (* -1/2 (* eps (cos (- (* 1/2 (PI)) x)))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (+ (sin (- (* 1/2 (PI)) x)) (* eps (+ (* -1/2 (cos (- (* 1/2 (PI)) x))) (* -1/8 (* eps (sin (- (* 1/2 (PI)) x)))))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (+ (sin (- (* 1/2 (PI)) x)) (* eps (+ (* -1/2 (cos (- (* 1/2 (PI)) x))) (* eps (+ (* -1/8 (sin (- (* 1/2 (PI)) x))) (* 1/48 (* eps (cos (- (* 1/2 (PI)) x)))))))))))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (- (* 1/2 (PI)) x)))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (- (+ (* -1/2 eps) (* 1/2 (PI))) x)))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) #s(hole binary64 (- (* -1/2 eps) x)))
#s(approx eps #s(hole binary64 eps))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 eps))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* -1/2 (* eps x))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* eps (+ (* -1/2 x) (* -1/6 eps)))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* eps (+ (* -1/2 x) (* eps (- (* 1/24 (* eps x)) 1/6))))))))
#s(approx (* (+ (* (* -1/2 eps) x) 1) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (* eps x))))))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) #s(hole binary64 (* (pow eps 3) (- (* 1/24 (* eps x)) 1/6))))
#s(approx (- (* 1/24 x) (/ 1/6 eps)) #s(hole binary64 (/ (- (* 1/24 (* eps x)) 1/6) eps)))
#s(approx (/ 1/6 eps) #s(hole binary64 (/ 1/6 eps)))
#s(approx (* (* eps eps) (* eps eps)) #s(hole binary64 (pow eps 4)))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (* eps (- (* 1/2 (/ (PI) eps)) (+ 1/2 (/ x eps))))))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) #s(hole binary64 (* eps (- (* -1 (/ x eps)) 1/2))))
#s(approx (* 1/2 (+ (* x 2) eps)) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* x 2) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* 1/24 (* (pow eps 4) x))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (* 1/24 x) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (/ 1 (pow eps 3)))) (* 1/6 (/ 1 eps))))))
#s(approx (* (+ (* (* -1/2 eps) x) 1) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))))
#s(approx (+ (* (* -1/2 eps) x) 1) #s(hole binary64 (* eps (+ (* -1/2 x) (/ 1 eps)))))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) #s(hole binary64 (* (pow eps 4) (- (* 1/24 x) (* 1/6 (/ 1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (* 2 (sin (- (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1 (/ (- (* 1/2 (PI)) x) eps)))))))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) #s(hole binary64 (* -1 (* eps (+ 1/2 (/ x eps))))))
#s(approx (* 1/2 (+ (* x 2) eps)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* x 2) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* eps (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* 1/2 (/ x eps))) eps)) (* 1/24 x)))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* -1 (/ (+ (* -1/2 x) (/ 1 eps)) eps))) eps)) (* 1/24 x)))))
#s(approx (+ (* (* -1/2 eps) x) 1) #s(hole binary64 (* -1 (* eps (- (* 1/2 x) (/ 1 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 (+ (* 1/2 eps) x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))

Calls

6 calls:

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

rewrite170.0ms (2.4%)

Memory

1.1MiB live, 90.9MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	889	6050
0	931	5543
1	5142	5523
0	8098	5261

Stop Event

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

Counts

256 → 405

Calls

Call 1

Inputs
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x
eps
(/.f64 (PI.f64) #s(literal 2 binary64))
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#s(literal 1/24 binary64)
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#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) eps)
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(.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))))
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#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) #s(hole binary64 (* -1/6 (pow eps 3))))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) #s(hole binary64 (+ (* -1/6 (pow eps 3)) (* 1/24 (* (pow eps 4) x)))))
#s(approx (- (* 1/24 x) (/ 1/6 eps)) #s(hole binary64 (/ -1/6 eps)))
#s(approx (- (* 1/24 x) (/ 1/6 eps)) #s(hole binary64 (- (* 1/24 x) (* 1/6 (/ 1 eps)))))
#s(approx (* 1/24 x) #s(hole binary64 (* 1/24 x)))
#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 (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x)))))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (* 2 (sin (- (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x))))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* 1/2 (+ eps (* 2 x)))))))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (* -1 x)))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (* x (- (* 1/2 (/ (PI) x)) (+ 1 (* 1/2 (/ eps x)))))))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) #s(hole binary64 (* -1 x)))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) #s(hole binary64 (* x (- (* -1/2 (/ eps x)) 1))))
#s(approx (* 1/2 (+ (* x 2) eps)) #s(hole binary64 x))
#s(approx (* 1/2 (+ (* x 2) eps)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* x 2) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* x 2) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* eps (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* x (+ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)))))
#s(approx (* (+ (* (* -1/2 eps) x) 1) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (* (+ (* (* -1/2 eps) x) 1) eps) #s(hole binary64 (* x (+ (* -1/2 (pow eps 2)) (/ eps x)))))
#s(approx (+ (* (* -1/2 eps) x) 1) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (* -1/2 eps) x) 1) #s(hole binary64 (* x (+ (* -1/2 eps) (/ 1 x)))))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) #s(hole binary64 (* 1/24 (* (pow eps 4) x))))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) #s(hole binary64 (* x (+ (* -1/6 (/ (pow eps 3) x)) (* 1/24 (pow eps 4))))))
#s(approx (- (* 1/24 x) (/ 1/6 eps)) #s(hole binary64 (* 1/24 x)))
#s(approx (- (* 1/24 x) (/ 1/6 eps)) #s(hole binary64 (* x (- 1/24 (* 1/6 (/ 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 (+ (* 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) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 (PI)) (* 1/2 (- eps (* -2 x)))))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (* 2 (sin (- (* 1/2 (PI)) (* 1/2 (- eps (* -2 x))))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* 1/2 (- eps (* -2 x)))))))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (* -1 (* x (+ 1 (* -1 (/ (- (* 1/2 (PI)) (* 1/2 eps)) x)))))))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ eps x)))))))
#s(approx (* 1/2 (+ (* x 2) eps)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (* x 2) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* -1 (* x (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)))))))
#s(approx (* (+ (* (* -1/2 eps) x) 1) eps) #s(hole binary64 (* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))))
#s(approx (+ (* (* -1/2 eps) x) 1) #s(hole binary64 (* -1 (* x (- (* 1/2 eps) (/ 1 x))))))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) #s(hole binary64 (* -1 (* x (+ (* -1/24 (pow eps 4)) (* 1/6 (/ (pow eps 3) x)))))))
#s(approx (- (* 1/24 x) (/ 1/6 eps)) #s(hole binary64 (* -1 (* x (- (* 1/6 (/ 1 (* eps x))) 1/24)))))
#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 (+ (* 1/2 eps) x) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (sin (- (* 1/2 (PI)) x)))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (sin (- (* 1/2 (PI)) x)) (* -1/2 (* eps (cos (- (* 1/2 (PI)) x))))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (sin (- (* 1/2 (PI)) x)) (* eps (+ (* -1/2 (cos (- (* 1/2 (PI)) x))) (* 2 (* eps (+ (* -1/16 (sin (- (* 1/2 (PI)) x))) (* -1/48 (sin (- (* 1/2 (PI)) x))))))))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* eps (+ (sin (- (* 1/2 (PI)) x)) (* eps (+ (* -1/2 (cos (- (* 1/2 (PI)) x))) (* eps (+ (* 1/24 (* eps (cos (- (* 1/2 (PI)) x)))) (* 2 (+ (* -1/16 (sin (- (* 1/2 (PI)) x))) (* -1/48 (sin (- (* 1/2 (PI)) x)))))))))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (* 2 (sin (- (* 1/2 (PI)) x)))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (+ (* -1 (* eps (cos (- (* 1/2 (PI)) x)))) (* 2 (sin (- (* 1/2 (PI)) x))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (sin (- (* 1/2 (PI)) x))) (* eps (+ (* -1 (cos (- (* 1/2 (PI)) x))) (* -1/4 (* eps (sin (- (* 1/2 (PI)) x)))))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (+ (* 2 (sin (- (* 1/2 (PI)) x))) (* eps (+ (* -1 (cos (- (* 1/2 (PI)) x))) (* eps (+ (* -1/4 (sin (- (* 1/2 (PI)) x))) (* 1/24 (* eps (cos (- (* 1/2 (PI)) x)))))))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) x))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (+ (sin (- (* 1/2 (PI)) x)) (* -1/2 (* eps (cos (- (* 1/2 (PI)) x)))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (+ (sin (- (* 1/2 (PI)) x)) (* eps (+ (* -1/2 (cos (- (* 1/2 (PI)) x))) (* -1/8 (* eps (sin (- (* 1/2 (PI)) x)))))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (+ (sin (- (* 1/2 (PI)) x)) (* eps (+ (* -1/2 (cos (- (* 1/2 (PI)) x))) (* eps (+ (* -1/8 (sin (- (* 1/2 (PI)) x))) (* 1/48 (* eps (cos (- (* 1/2 (PI)) x)))))))))))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (- (* 1/2 (PI)) x)))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (- (+ (* -1/2 eps) (* 1/2 (PI))) x)))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) #s(hole binary64 (- (* -1/2 eps) x)))
#s(approx eps #s(hole binary64 eps))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 eps))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* -1/2 (* eps x))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* eps (+ (* -1/2 x) (* -1/6 eps)))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* eps (+ (* -1/2 x) (* eps (- (* 1/24 (* eps x)) 1/6))))))))
#s(approx (* (+ (* (* -1/2 eps) x) 1) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (* eps x))))))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) #s(hole binary64 (* (pow eps 3) (- (* 1/24 (* eps x)) 1/6))))
#s(approx (- (* 1/24 x) (/ 1/6 eps)) #s(hole binary64 (/ (- (* 1/24 (* eps x)) 1/6) eps)))
#s(approx (/ 1/6 eps) #s(hole binary64 (/ 1/6 eps)))
#s(approx (* (* eps eps) (* eps eps)) #s(hole binary64 (pow eps 4)))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* -1/24 (pow eps 2))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (* eps (- (* 1/2 (/ (PI) eps)) (+ 1/2 (/ x eps))))))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) #s(hole binary64 (* eps (- (* -1 (/ x eps)) 1/2))))
#s(approx (* 1/2 (+ (* x 2) eps)) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* x 2) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* 1/24 (* (pow eps 4) x))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (* 1/24 x) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/24 x)) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (/ 1 (pow eps 3)))) (* 1/6 (/ 1 eps))))))
#s(approx (* (+ (* (* -1/2 eps) x) 1) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))))
#s(approx (+ (* (* -1/2 eps) x) 1) #s(hole binary64 (* eps (+ (* -1/2 x) (/ 1 eps)))))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) #s(hole binary64 (* (pow eps 4) (- (* 1/24 x) (* 1/6 (/ 1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 1/2 eps) x) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) #s(hole binary64 (* 2 (sin (- (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1 (/ (- (* 1/2 (PI)) x) eps)))))))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) #s(hole binary64 (* -1 (* eps (+ 1/2 (/ x eps))))))
#s(approx (* 1/2 (+ (* x 2) eps)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* x 2) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* eps (+ (* 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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* 1/2 (/ x eps))) eps)) (* 1/24 x)))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* -1 (/ (+ (* -1/2 x) (/ 1 eps)) eps))) eps)) (* 1/24 x)))))
#s(approx (+ (* (* -1/2 eps) x) 1) #s(hole binary64 (* -1 (* eps (- (* 1/2 x) (/ 1 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 (+ (* 1/2 eps) x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))

Outputs
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
(+.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
#s(literal 2 binary64)
(sin.f64 (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))))
(fma.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal 0 binary64) (.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 1 binary64)))
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 0 binary64) (.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 #s(literal 0 binary64) (sin.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(-.f64 (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)))))
(-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)))))
(cos.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))))
(cos.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(+.f64 (.f64 (sin.f64 (.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))) #s(literal 0 binary64)) (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))) (.f64 #s(literal 0 binary64) (sin.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 0 binary64)) (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 3 binary64)) (.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) (-.f64 (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps)))
(*.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(neg.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(fma.f64 (+.f64 x x) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 #s(literal 1/2 binary64) (+.f64 x x) (*.f64 #s(literal 1/2 binary64) eps))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (+.f64 x x)))
(+.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) eps))
(+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)) (.f64 #s(literal 1/2 binary64) eps))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) (+.f64 x x)))
#s(literal 1/2 binary64)
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))) (+.f64 eps (*.f64 #s(literal -2 binary64) x)))
(/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps eps)) (-.f64 (+.f64 x x) eps))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (+.f64 x x) (+.f64 x x))) (-.f64 eps (+.f64 x x)))
(/.f64 (-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x x)) (-.f64 (+.f64 eps x) x))
(/.f64 (-.f64 (.f64 (.f64 eps eps) eps) (.f64 #s(literal -8 binary64) (.f64 (.f64 x x) x))) (fma.f64 eps eps (fma.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x) (.f64 eps (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) (.f64 (.f64 eps eps) eps)) (fma.f64 (+.f64 x x) (+.f64 x x) (-.f64 (.f64 eps eps) (.f64 (+.f64 x x) eps))))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x))) (fma.f64 eps eps (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps (+.f64 x x)))))
(/.f64 (fma.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (+.f64 eps x) (.f64 (.f64 x x) x)) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (*.f64 (+.f64 eps x) x))))
(fma.f64 x #s(literal 2 binary64) eps)
(fma.f64 #s(literal 2 binary64) x eps)
(-.f64 eps (*.f64 #s(literal -2 binary64) x))
(+.f64 (+.f64 x x) eps)
(+.f64 (+.f64 eps x) x)
(+.f64 eps (+.f64 x x))
(+.f64 x (+.f64 eps x))
x
eps
(/.f64 (neg.f64 (PI.f64)) #s(literal -2 binary64))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) 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)) eps) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)) eps)))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)) eps))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)) eps)
(.f64 eps (fma.f64 (.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) eps (.f64 (.f64 (*.f64 #s(literal -1/2 binary64) eps) x) eps))
(fma.f64 eps #s(literal 1 binary64) (.f64 eps (.f64 (*.f64 #s(literal -1/2 binary64) eps) x)))
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#s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (* 1/2 eps) x) (*.f64 #s(literal 1/2 binary64) eps))
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#s(approx (sin x) x)
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#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)))
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#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) (neg.f64 x))
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#s(approx (neg (* 1/2 (+ (* x 2) eps))) (neg.f64 x))
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#s(approx (* 1/2 (+ (* x 2) eps)) x)
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#s(approx (+ (* (* -1/2 eps) x) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) x))
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#s(approx (/ (+ (+ eps x) x) 2) x)
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#s(approx (+ (* 1/2 eps) x) x)
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#s(approx (sin x) (sin.f64 x))
#s(approx (cos x) (cos.f64 x))
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#s(approx (+ (* (* -1/2 eps) x) 1) (.f64 (neg.f64 x) (-.f64 (.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1 binary64) x))))
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#s(approx (- (* 1/24 x) (/ 1/6 eps)) (.f64 (neg.f64 x) (-.f64 (/.f64 #s(literal 1/6 binary64) (.f64 eps x)) #s(literal 1/24 binary64))))
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#s(approx (+ (* 1/2 eps) x) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (*.f64 (cos.f64 x) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (fma.f64 eps (fma.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) eps) #s(literal 2 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
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#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) (.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) eps))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) (.f64 (fma.f64 eps (fma.f64 (.f64 (.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) #s(literal -1/12 binary64)) eps) #s(literal 2 binary64) (.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) #s(literal -1/2 binary64))) (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) #s(literal -1/12 binary64)) #s(literal 2 binary64) (.f64 (.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) eps) #s(literal 1/24 binary64))) eps (.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) #s(literal -1/2 binary64))) eps (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) #s(literal 2 binary64)))
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#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (fma.f64 eps (fma.f64 #s(literal -1/4 binary64) (.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) eps) (neg.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)))) (.f64 (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)) #s(literal 2 binary64))))
#s(approx (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) eps) (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) (.f64 #s(literal -1/4 binary64) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)))) eps (neg.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)))) eps (.f64 (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)) #s(literal 2 binary64))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) (.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) #s(literal -1/2 binary64))) eps (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) (fma.f64 (fma.f64 eps (fma.f64 (.f64 #s(literal 1/48 binary64) eps) (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) (.f64 #s(literal -1/8 binary64) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)))) (.f64 (cos.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) #s(literal -1/2 binary64))) eps (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) (-.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps)) x))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) (-.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
#s(approx eps eps)
#s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (* 1/2 eps) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#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 (cos.f64 x) #s(literal -1/6 binary64) (.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps))) (.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) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) eps)
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)) eps))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps)) eps #s(literal 1 binary64)) eps))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps #s(literal 1 binary64)) eps))
#s(approx (* (+ (* (* -1/2 eps) x) 1) eps) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)) eps))
#s(approx (* -1/2 eps) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) (.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) (.f64 (*.f64 eps eps) eps)))
#s(approx (- (* 1/24 x) (/ 1/6 eps)) (/.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/24 binary64)) #s(literal 1/6 binary64)) eps))
#s(approx (/ 1/6 eps) (/.f64 #s(literal 1/6 binary64) eps))
#s(approx (* (* eps eps) (* eps eps)) (.f64 (.f64 (*.f64 eps eps) eps) eps))
#s(approx (* eps eps) (*.f64 eps eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) eps)
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (* 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 x))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 eps (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) #s(literal -1/8 binary64) (.f64 #s(literal 1/48 binary64) (.f64 (sin.f64 x) eps))) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (cos.f64 x))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) (.f64 (-.f64 (-.f64 (.f64 (/.f64 (PI.f64) eps) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 x eps)) eps))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) (*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps))
#s(approx (* 1/2 (+ (* x 2) eps)) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* x 2) eps) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))
#s(approx (sin (* 1/2 eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (.f64 (.f64 (.f64 (.f64 (*.f64 eps 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)) 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 (*.f64 eps eps) 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 (.f64 eps eps) 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 (*.f64 eps eps) eps) eps)))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (.f64 (.f64 (.f64 (*.f64 eps eps) eps) eps) x) #s(literal 1/24 binary64)))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (-.f64 (*.f64 #s(literal 1/24 binary64) x) (/.f64 #s(literal 1/6 binary64) eps))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (/.f64 x (.f64 eps eps)) #s(literal -1/2 binary64) (-.f64 (.f64 #s(literal 1/24 binary64) x) (/.f64 #s(literal 1/6 binary64) eps))) (.f64 (.f64 (.f64 eps eps) eps) eps)))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (-.f64 (fma.f64 (/.f64 x (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/24 binary64) x (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) eps)))) (/.f64 #s(literal 1/6 binary64) eps)) (.f64 (.f64 (*.f64 eps eps) eps) eps)))
#s(approx (* (+ (* (* -1/2 eps) x) 1) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) (.f64 eps eps)))
#s(approx (+ (* (* -1/2 eps) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps))
#s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (-.f64 (*.f64 #s(literal 1/24 binary64) x) (/.f64 #s(literal 1/6 binary64) eps))))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* 1/2 eps) x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))
#s(approx (* (* 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 (* (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (sin (* 1/2 eps))) (.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 (* 2 (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) (-.f64 (+.f64 x x) (neg.f64 eps))))) #s(literal 2 binary64)))
#s(approx (sin (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) (-.f64 (+.f64 x x) (neg.f64 eps))))))
#s(approx (+ (neg (* 1/2 (+ (* x 2) eps))) (/ (PI) 2)) (.f64 (neg.f64 eps) (+.f64 (neg.f64 (/.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x) eps)) #s(literal 1/2 binary64))))
#s(approx (neg (* 1/2 (+ (* x 2) eps))) (*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (+ (* x 2) eps)) (*.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))))
#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 #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 (*.f64 eps eps) 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 #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 (.f64 eps eps) eps) eps)))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (.f64 (.f64 (.f64 eps eps) eps) eps) (fma.f64 #s(literal 1/24 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) #s(literal 1/6 binary64)) eps)))))
#s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 #s(literal 1/24 binary64) x (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps)) #s(literal 1/6 binary64)) eps))) (.f64 (.f64 (.f64 eps eps) eps) eps)))
#s(approx (+ (* (* -1/2 eps) x) 1) (.f64 (neg.f64 eps) (-.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 (-.f64 (+.f64 x x) (neg.f64 eps)) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* 1/2 eps) x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 (sin.f64 x) #s(literal 1/2 binary64) (neg.f64 (/.f64 (cos.f64 x) eps)))))

eval87.0ms (1.2%)

Memory: -2.4MiB live, 43.9MiB allocated; 65ms collecting garbage
Compiler: Compiled 5 161 to 2 223 computations (56.9% saved)

prune35.0ms (0.5%)

Memory

-20.1MiB live, 31.3MiB allocated; 6ms collecting garbage

Pruning

32 alts after pruning (24 fresh and 8 done)

	Pruned	Kept	Total
New	354	12	366
Fresh	11	12	23
Picked	2	3	5
Done	0	5	5
Total	367	32	399

Accuracy

100.0%

Counts

399 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.2%	(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	7.4%	(/.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))))
✓	62.0%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.6%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (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))) (.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))))
	99.5%	(.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 #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) (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)))))
	99.3%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
✓	99.3%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
✓	99.3%	(.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))))
	98.6%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) #s(approx (+ (* 1/2 eps) x) x))))
✓	99.3%	(.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))))
	97.7%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) #s(approx (cos (/ (+ (+ eps x) x) 2)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))))
	97.7%	(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) #s(approx (cos (/ (+ (+ eps x) x) 2)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64)))))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps)))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps)))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (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))) eps) eps)))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
✓	99.6%	#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))
	97.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 eps x (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	97.3%	#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 (.f64 (.f64 eps eps) x) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
✓	97.3%	#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)) eps))))
	5.2%	#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal -1/6 binary64))))))
	5.7%	#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(approx (* (+ (* (* -1/2 eps) x) 1) eps) (.f64 (.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64))))))
	97.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
✓	97.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
	99.7%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
	99.5%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (+.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (/.f64 (PI.f64) #s(literal 2 binary64))))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
	99.6%	#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( 2 (cos (* (+ (* 2 x) eps) 1/2))) (fma.f64 (cos.f64 x) #s(literal 2 binary64) (.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))

Compiler

Compiled 1 545 to 1 132 computations (26.7% saved)

regimes45.0ms (0.6%)

Memory

-14.2MiB live, 32.4MiB allocated; 2ms collecting garbage

Counts

59 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) 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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(approx (* (+ (* (* -1/2 eps) x) 1) eps) (.f64 (.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64))))))
#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal -1/6 binary64))))))
#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( 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 (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) #s(approx (cos (/ (+ (+ eps x) x) 2)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (.f64 (.f64 (.f64 eps eps) (*.f64 eps eps)) x) #s(literal 1/24 binary64)))))
#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps)) eps #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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) x) (/.f64 #s(literal 1/6 binary64) eps)) (.f64 (.f64 eps eps) (*.f64 eps eps))))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) #s(approx (cos (/ (+ (+ eps x) x) 2)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 (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)) (+.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)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 #s(approx (+ ( (* eps eps) -1/6) 1) (.f64 (.f64 eps eps) #s(literal -1/6 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 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
(-.f64 (sin.f64 #s(approx (+ eps x) x)) #s(approx (sin x) x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) x)))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) #s(approx (+ (* 1/2 eps) x) x))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 eps x (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) 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))))
#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 ( 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) (sin.f64 (+.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (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)))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.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 #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 (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)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #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))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (+.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (/.f64 (PI.f64) #s(literal 2 binary64))))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps 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))
(.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))))
#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 (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (fma.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (/.f64 (-.f64 x (-.f64 x eps)) #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (+.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (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)) (fma.f64 (cos.f64 x) eps (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 (.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))) eps))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 #s(approx ( 2 (cos (* (+ (* 2 x) eps) 1/2))) (fma.f64 (cos.f64 x) #s(literal 2 binary64) (.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (.f64 (.f64 (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))) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (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))) eps) 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))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))

Outputs

#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))))

Calls

3 calls:

14.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
13.0ms	x
13.0ms	eps

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes33.0ms (0.5%)

Memory

25.3MiB live, 25.3MiB allocated; 0ms collecting garbage

Counts

44 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) 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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(approx (* (+ (* (* -1/2 eps) x) 1) eps) (.f64 (.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64))))))
#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal -1/6 binary64))))))
#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( 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 (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) #s(approx (cos (/ (+ (+ eps x) x) 2)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (.f64 (.f64 (.f64 eps eps) (*.f64 eps eps)) x) #s(literal 1/24 binary64)))))
#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps)) eps #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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) x) (/.f64 #s(literal 1/6 binary64) eps)) (.f64 (.f64 eps eps) (*.f64 eps eps))))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) #s(approx (cos (/ (+ (+ eps x) x) 2)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 (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)) (+.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)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 #s(approx (+ ( (* eps eps) -1/6) 1) (.f64 (.f64 eps eps) #s(literal -1/6 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 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
(-.f64 (sin.f64 #s(approx (+ eps x) x)) #s(approx (sin x) x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) x)))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) #s(approx (+ (* 1/2 eps) x) x))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( eps (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 eps x (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) 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))))
#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 ( 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) (sin.f64 (+.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (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)))))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) (sin.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(.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 #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 (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)))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #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))))
#s(approx (* (* 2 (sin (/ (- x (- x eps)) 2))) (cos (/ (+ (+ eps x) x) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (+.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 2 binary64) eps))) (/.f64 (PI.f64) #s(literal 2 binary64))))) #s(approx (sin ( 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (.f64 eps eps) #s(literal 1/1920 binary64)) (.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps 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))
(.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))))

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

Calls

3 calls:

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

regimes31.0ms (0.4%)

Memory

-22.9MiB live, 23.8MiB allocated; 2ms collecting garbage

Counts

40 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

regimes28.0ms (0.4%)

Memory

21.4MiB live, 21.4MiB allocated; 0ms collecting garbage

Counts

37 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.5%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.5%	1	`x`
99.5%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes25.0ms (0.4%)

Memory

19.9MiB live, 19.9MiB allocated; 0ms collecting garbage

Counts

33 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.3%	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)

regimes23.0ms (0.3%)

Memory

-31.5MiB live, 17.1MiB allocated; 3ms collecting garbage

Counts

27 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	eps
7.0ms	x
7.0ms	(-.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)

regimes20.0ms (0.3%)

Memory

16.8MiB live, 16.8MiB allocated; 0ms collecting garbage

Counts

25 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes17.0ms (0.2%)

Memory

14.3MiB live, 14.3MiB allocated; 0ms collecting garbage

Counts

20 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes16.0ms (0.2%)

Memory

-33.6MiB live, 13.4MiB allocated; 2ms 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)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(approx (* (+ (* (* -1/2 eps) x) 1) eps) (.f64 (.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64))))))
#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(approx (* (- (* 1/24 x) (/ 1/6 eps)) (* (* eps eps) (* eps eps))) (.f64 (.f64 (*.f64 eps eps) eps) #s(literal -1/6 binary64))))))
#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( 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 (+ (* (* (cos x) eps) -1/6) (* (sin x) -1/2))) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) #s(approx (cos (/ (+ (+ eps x) x) 2)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (.f64 (.f64 (.f64 eps eps) (*.f64 eps eps)) x) #s(literal 1/24 binary64)))))
#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x (.f64 #s(literal -1/6 binary64) eps)) eps #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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps)))
#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) #s(approx (+ (* (* (* eps eps) x) (- (* (* eps eps) 1/24) 1/2)) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) x) (/.f64 #s(literal 1/6 binary64) eps)) (.f64 (.f64 eps eps) (*.f64 eps eps))))))
(.f64 #s(approx ( 2 (sin (/ (- x (- x eps)) 2))) eps) #s(approx (cos (/ (+ (+ eps x) x) 2)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(approx (- (* (* eps eps) 1/24) 1/2) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 (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)) (+.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)) #s(approx (* (+ (* eps (+ (* eps (+ (* (* (sin x) eps) 1/24) (* (cos x) -1/6))) (* (sin x) -1/2))) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 #s(approx (+ ( (* eps eps) -1/6) 1) (.f64 (.f64 eps eps) #s(literal -1/6 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 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Outputs

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

Calls

3 calls:

6.0ms	eps
5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	x

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes7.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated; 0ms collecting garbage

Accuracy

Total -59.0b remaining (-3429.7%)

Threshold costs -59b (-3429.7%)

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.3%	1	`x`
97.3%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

derivations289.0ms (4.1%)

Memory

-11.3MiB live, 81.1MiB allocated; 4ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 143 to 96 computations (32.9% saved)

preprocess84.0ms (1.2%)

Memory: 30.0MiB live, 124.0MiB allocated; 9ms collecting garbage
Compiler: Compiled 186 to 135 computations (27.4% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze55.0ms (0.8%)

sample5.1s (72.8%)

preprocess37.0ms (0.5%)

series5.0ms (0.1%)

rewrite154.0ms (2.2%)

eval11.0ms (0.2%)

prune7.0ms (0.1%)

series40.0ms (0.6%)

rewrite236.0ms (3.4%)

eval69.0ms (1%)

prune21.0ms (0.3%)

series53.0ms (0.8%)

rewrite190.0ms (2.7%)

eval49.0ms (0.7%)

prune28.0ms (0.4%)

series37.0ms (0.5%)

rewrite170.0ms (2.4%)

eval87.0ms (1.2%)

prune35.0ms (0.5%)

regimes45.0ms (0.6%)

regimes33.0ms (0.5%)

regimes31.0ms (0.4%)

regimes28.0ms (0.4%)

regimes25.0ms (0.4%)

regimes23.0ms (0.3%)

regimes20.0ms (0.3%)

regimes17.0ms (0.2%)

regimes16.0ms (0.2%)

regimes7.0ms (0.1%)

derivations289.0ms (4.1%)

preprocess84.0ms (1.2%)

end0.0ms (0%)

Profiling