Metrics for 2sin (example 3.3)

start0.0ms (0%)

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

analyze33.0ms (0.6%)

Memory

-12.4MiB live, 29.6MiB allocated; 7ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50.6%	49.4%	0%	0%	0%	0
0%	0%	50.6%	49.4%	0%	0%	0%	1
0%	0%	50.6%	49.4%	0%	0%	0%	2
0%	0%	25.3%	49.4%	0%	25.3%	0%	3
0%	0%	25.3%	49.4%	0%	25.3%	0%	4
0%	0%	19%	49.4%	0%	31.6%	0%	5
0%	0%	15.8%	49.4%	0%	34.8%	0%	6
0%	0%	11.1%	49.4%	0%	39.5%	0%	7
0%	0%	8.7%	49.4%	0%	41.9%	0%	8
0%	0%	5.9%	49.4%	0%	44.6%	0%	9
0%	0%	4.5%	49.4%	0%	46%	0%	10
0%	0%	3.1%	49.4%	0%	47.5%	0%	11
0%	0%	2.7%	49.4%	0%	47.9%	0%	12

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample3.8s (73.9%)

Memory

139.7MiB live, 2 883.5MiB allocated; 1.3s collecting garbage

Samples

1.6s	26 294×	0	invalid
616.0ms	5 538×	1	valid
420.0ms	2 718×	0	valid

Precisions

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

ival-sin: 816.0ms (47.2% of total)

ival-fabs: 220.0ms (12.7% of total)

adjust: 162.0ms (9.4% of total)

ival-<: 125.0ms (7.2% of total)

ival-add!: 124.0ms (7.2% of total)

ival-mult!: 117.0ms (6.8% of total)

ival-sub!: 90.0ms (5.2% of total)

ival-and: 62.0ms (3.6% of total)

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

Bogosity

preprocess38.0ms (0.7%)

Memory

-19.7MiB live, 25.6MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	48
1	77	48
2	280	44
3	1610	44

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 14 to 12 computations (14.3% saved)

series4.0ms (0.1%)

Memory

5.4MiB live, 5.4MiB allocated; 0ms collecting garbage

Counts

6 → 31

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	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))

rewrite147.0ms (2.8%)

Memory

-32.5MiB live, 97.4MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	145	512
0	150	500
1	926	494
0	8444	463

Stop Event

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

Counts

37 → 100

Calls

Call 1

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

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

eval9.0ms (0.2%)

Memory: 9.3MiB live, 9.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 949 to 371 computations (81% saved)

prune3.0ms (0.1%)

Memory

3.1MiB live, 3.1MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	3	93

Accuracy

100.0%

Counts

93 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Status

Accuracy

Program

▶

100.0%

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

▶

100.0%

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

▶

99.3%

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

Compiler

Compiled 40 to 30 computations (25% saved)

series12.0ms (0.2%)

Memory

7.2MiB live, 7.2MiB allocated; 0ms collecting garbage

Counts

13 → 45

Calls

Call 1

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

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx x #s(hole binary64 x))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (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 (+ 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 (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (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 (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#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
3.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) -1/2)
2.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) -1/2)
2.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) -1/2)
2.0ms	x	@	0	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) -1/2)
1.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) -1/2)

rewrite163.0ms (3.1%)

Memory

-8.2MiB live, 132.3MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	243	894
0	255	884
1	1559	884
0	8676	835

Stop Event

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

Counts

58 → 97

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx x #s(hole binary64 x))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (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 (+ 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 (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (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 (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))

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

eval11.0ms (0.2%)

Memory: 15.1MiB live, 15.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 767 to 479 computations (82.7% saved)

prune6.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated; 0ms collecting garbage

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	87	8	95
Fresh	0	0	0
Picked	2	1	3
Done	0	0	0
Total	89	9	98

Accuracy

100.0%

Counts

98 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
▶	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) eps))

Compiler

Compiled 376 to 259 computations (31.1% saved)

series26.0ms (0.5%)

Memory

-21.1MiB live, 24.5MiB allocated; 4ms collecting garbage

Counts

34 → 89

Calls

Call 1

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

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx x #s(hole binary64 x))
#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 (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (- (* 1/12 (* eps x)) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* 1/12 (* eps x)) 1/2) #s(hole binary64 (- (* 1/12 (* eps x)) 1/2)))
#s(approx (* 1/12 (* eps x)) #s(hole binary64 (* 1/12 (* eps x))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (* 1/2 (PI))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* eps (* x (cos (* 1/2 (PI))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))) (* eps (cos (* 1/2 (PI)))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* eps (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* -1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* -1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (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 (cos x) #s(hole binary64 (cos x)))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* 1/12 (* eps (pow x 3)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* 1/12 (* eps (pow x 2)))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))))
#s(approx (- (* 1/12 (* eps x)) 1/2) #s(hole binary64 (* x (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (+ x (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (PI) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2) x)) (* -1/12 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))))
#s(approx (- (* 1/12 (* eps x)) 1/2) #s(hole binary64 (* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (- (* 1/2 (PI)) (* -1 x))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (PI) x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))))
#s(approx (- (* 1/12 (* eps x)) 1/2) #s(hole binary64 (* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/12 (pow x 2)))))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))))
#s(approx (- (* 1/12 (* eps x)) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))))

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* eps x) eps x -1/2 (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps x)) 1/2) (* 1/12 (* eps x)) 1/12 1/2 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (/ (PI) 2) (PI) 2)
4.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* eps x) eps x -1/2 (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps x)) 1/2) (* 1/12 (* eps x)) 1/12 1/2 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (/ (PI) 2) (PI) 2)
3.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* eps x) eps x -1/2 (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps x)) 1/2) (* 1/12 (* eps x)) 1/12 1/2 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (/ (PI) 2) (PI) 2)
3.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* eps x) eps x -1/2 (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps x)) 1/2) (* 1/12 (* eps x)) 1/12 1/2 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (/ (PI) 2) (PI) 2)
3.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* eps x) eps x -1/2 (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (- (* 1/12 (* eps x)) 1/2) (* 1/12 (* eps x)) 1/12 1/2 (* -1/2 eps) (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (/ (PI) 2) (PI) 2)

rewrite206.0ms (4%)

Memory

-7.9MiB live, 135.7MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	434	2251
0	460	2132
1	2543	2132
0	9039	2038

Stop Event

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

Counts

123 → 241

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 x))
#s(approx (* (sin x) eps) (*.f64 eps x))
(*.f64 eps x)
eps
x
#s(literal -1/2 binary64)
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) eps))
#s(approx (* (cos x) eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/12 binary64) (.f64 eps x))
#s(literal 1/12 binary64)
#s(literal 1/2 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps)
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx x #s(hole binary64 x))
#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 (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
#s(approx (- (* 1/12 (* eps x)) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* 1/12 (* eps x)) 1/2) #s(hole binary64 (- (* 1/12 (* eps x)) 1/2)))
#s(approx (* 1/12 (* eps x)) #s(hole binary64 (* 1/12 (* eps x))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (* 1/2 (PI))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* eps (* x (cos (* 1/2 (PI))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))) (* eps (cos (* 1/2 (PI)))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* eps (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* -1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* -1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (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 (cos x) #s(hole binary64 (cos x)))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* 1/12 (* eps (pow x 3)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* 1/12 (* eps (pow x 2)))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/12 eps)) (* 1/2 (/ 1 x))))))
#s(approx (- (* 1/12 (* eps x)) 1/2) #s(hole binary64 (* x (- (* 1/12 eps) (* 1/2 (/ 1 x))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (+ x (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (PI) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1/2) x)) (* -1/12 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* (pow x 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2) x)) (* -1/12 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ eps x))) x)) (* 1/12 eps)))))
#s(approx (- (* 1/12 (* eps x)) 1/2) #s(hole binary64 (* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (- (* 1/2 (PI)) (* -1 x))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (PI) x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (pow x 2)) (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* eps (* x (- (* 1/12 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* eps (+ (* -1/2 (/ (pow x 2) eps)) (+ (* x (- (* 1/12 (pow x 2)) 1/2)) (/ 1 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* eps (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2))))
#s(approx (- (* 1/12 (* eps x)) 1/2) #s(hole binary64 (* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* eps (* x (+ 1/2 (* -1/12 (pow x 2))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* x (+ 1/2 (* -1/12 (pow x 2)))))))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/12 (pow x 2)))))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps))))))))
#s(approx (- (* 1/12 (* eps x)) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(literal -1/2 binary64) #s(approx ( (sin x) eps) (*.f64 eps x)) (cos.f64 x)) eps))
(.f64 (fma.f64 #s(literal -1/2 binary64) #s(approx ( (sin x) eps) (*.f64 eps x)) (cos.f64 x)) eps)
(.f64 eps (fma.f64 #s(literal -1/2 binary64) #s(approx ( (sin x) eps) (*.f64 eps x)) (cos.f64 x)))
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#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 x (-.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 x (-.f64 (fma.f64 x (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) (cos.f64 eps)) #s(literal 1 binary64)) (sin.f64 eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps))) x eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/12 binary64) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
#s(approx (* (sin x) eps) (*.f64 eps x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (fma.f64 (.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 x x)
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.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 (* x x) (*.f64 x x))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (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)))
#s(approx (- (* 1/12 (* eps x)) 1/2) #s(literal -1/2 binary64))
#s(approx (- (* 1/12 (* eps x)) 1/2) (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))
#s(approx (* 1/12 (* eps x)) (.f64 (.f64 eps x) #s(literal 1/12 binary64)))
#s(approx (* (cos x) eps) (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) eps))
#s(approx (* (cos x) eps) (.f64 eps (fma.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) x (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))))
#s(approx (* (cos x) eps) (fma.f64 x (fma.f64 (.f64 (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) eps)) (.f64 (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) eps)))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) x) eps) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) eps) #s(literal -1/2 binary64))) x (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) eps)) x (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) eps)))
#s(approx (cos x) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))
#s(approx (cos x) (fma.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) x (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))))
#s(approx (cos x) (fma.f64 x (fma.f64 (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) x) #s(literal -1/2 binary64) (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))))
#s(approx (cos x) (fma.f64 x (fma.f64 x (fma.f64 (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) x) #s(literal -1/6 binary64) (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal -1/2 binary64))) (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))))
#s(approx (+ x (/ (PI) 2)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
#s(approx (+ x (/ (PI) 2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (cos x) (cos.f64 x))
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* x x) -1/2) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (.f64 (.f64 (.f64 (.f64 x x) x) eps) #s(literal 1/12 binary64)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) x)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x))) (.f64 (*.f64 x x) x)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (.f64 (-.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) x)))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 (.f64 (*.f64 x x) eps) #s(literal 1/12 binary64)))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x)))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x))) (.f64 x x)))
#s(approx (- (* 1/12 (* eps x)) 1/2) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) x))
#s(approx (* (cos x) eps) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (cos x) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
#s(approx (+ x (/ (PI) 2)) (*.f64 (fma.f64 (/.f64 (PI.f64) x) #s(literal 1/2 binary64) #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 (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (.f64 (.f64 (neg.f64 x) (*.f64 x x)) (fma.f64 #s(literal -1/12 binary64) eps (/.f64 #s(literal 1/2 binary64) x))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (.f64 (.f64 (neg.f64 x) (.f64 x x)) (fma.f64 #s(literal -1/12 binary64) eps (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) x)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (.f64 (.f64 (neg.f64 x) (.f64 x x)) (fma.f64 #s(literal -1/12 binary64) eps (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1 binary64) x)) x)) #s(literal 1/2 binary64)) x)))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 (.f64 x x) (fma.f64 #s(literal 1/12 binary64) eps (neg.f64 (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) x)))))
#s(approx (- (* 1/12 (* eps x)) 1/2) (*.f64 (neg.f64 x) (fma.f64 #s(literal -1/12 binary64) eps (/.f64 #s(literal 1/2 binary64) x))))
#s(approx (* (cos x) eps) (.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 x))) eps))
#s(approx (cos x) (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 x))))
#s(approx (+ x (/ (PI) 2)) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 (PI.f64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 eps (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.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 (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (.f64 #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 (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (.f64 (fma.f64 (/.f64 (.f64 x x) eps) #s(literal -1/2 binary64) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (/.f64 #s(literal 1 binary64) eps))) eps))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) eps))
#s(approx (- (* 1/12 (* eps x)) 1/2) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) x) (/.f64 #s(literal 1/2 binary64) eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps)))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (.f64 (neg.f64 eps) (.f64 (fma.f64 #s(literal -1/12 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x)))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (.f64 (neg.f64 eps) (fma.f64 (fma.f64 #s(literal -1/12 binary64) (.f64 x x) #s(literal 1/2 binary64)) x (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 (neg.f64 eps) (fma.f64 #s(literal -1/12 binary64) (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) (.f64 #s(literal -1/12 binary64) (*.f64 x x))) #s(literal 1/2 binary64))))
#s(approx (- (* 1/12 (* eps x)) 1/2) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/12 binary64) x (/.f64 #s(literal 1/2 binary64) eps))))

eval24.0ms (0.5%)

Memory: 38.3MiB live, 38.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 8 476 to 1 264 computations (85.1% saved)

prune12.0ms (0.2%)

Memory

-31.0MiB live, 13.9MiB allocated; 5ms collecting garbage

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	204	3	207
Fresh	0	3	3
Picked	2	3	5
Done	0	1	1
Total	206	10	216

Accuracy

100.0%

Counts

216 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 #s(approx (+ x (/ (PI) 2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
▶	5.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) #s(approx (+ ( (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) eps))

Compiler

Compiled 409 to 283 computations (30.8% saved)

series23.0ms (0.4%)

Memory

35.2MiB live, 35.2MiB allocated; 0ms collecting garbage

Counts

38 → 100

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (+ (* (PI) 1/2) x) (PI) 1/2 x eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* (* x x) -1/2) (* x x) -1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) -1/2) eps) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (* (- (* 1/12 eps) (/ 1/2 x)) (* x x)) (- (* 1/12 eps) (/ 1/2 x)) (* 1/12 eps) 1/12 (/ 1/2 x))
4.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (+ (* (PI) 1/2) x) (PI) 1/2 x eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* (* x x) -1/2) (* x x) -1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) -1/2) eps) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (* (- (* 1/12 eps) (/ 1/2 x)) (* x x)) (- (* 1/12 eps) (/ 1/2 x)) (* 1/12 eps) 1/12 (/ 1/2 x))
3.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (+ (* (PI) 1/2) x) (PI) 1/2 x eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* (* x x) -1/2) (* x x) -1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) -1/2) eps) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (* (- (* 1/12 eps) (/ 1/2 x)) (* x x)) (- (* 1/12 eps) (/ 1/2 x)) (* 1/12 eps) 1/12 (/ 1/2 x))
3.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (+ (* (PI) 1/2) x) (PI) 1/2 x eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* (* x x) -1/2) (* x x) -1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) -1/2) eps) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (* (- (* 1/12 eps) (/ 1/2 x)) (* x x)) (- (* 1/12 eps) (/ 1/2 x)) (* 1/12 eps) 1/12 (/ 1/2 x))
3.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (+ (* (PI) 1/2) x) (PI) 1/2 x eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* (* x x) -1/2) (* x x) -1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) -1/2) eps) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) x) 1) (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (* (- (* 1/12 eps) (/ 1/2 x)) (* x x)) (- (* 1/12 eps) (/ 1/2 x)) (* 1/12 eps) 1/12 (/ 1/2 x))

rewrite191.0ms (3.7%)

Memory

-22.6MiB live, 121.0MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	460	2661
0	493	2548
1	2652	2548
0	9306	2389

Stop Event

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

Counts

138 → 247

Calls

Call 1

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

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

eval36.0ms (0.7%)

Memory: -18.3MiB live, 27.2MiB allocated; 4ms collecting garbage
Compiler: Compiled 10 986 to 1 599 computations (85.4% saved)

prune9.0ms (0.2%)

Memory

16.1MiB live, 16.1MiB allocated; 0ms collecting garbage

Pruning

11 alts after pruning (3 fresh and 8 done)

	Pruned	Kept	Total
New	268	3	271
Fresh	1	0	1
Picked	1	4	5
Done	0	4	4
Total	270	11	281

Accuracy

100.0%

Counts

281 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 #s(approx (+ x (/ (PI) 2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	46.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 #s(approx (- ( 1/12 eps) (/ 1/2 x)) (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps x))) eps)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(approx (* (- (* 1/12 eps) (/ 1/2 x)) (* x x)) (.f64 (-.f64 (.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) x #s(literal 1 binary64))) eps))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
✓	5.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) #s(approx (+ ( (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) eps))

Compiler

Compiled 784 to 348 computations (55.6% saved)

regimes14.0ms (0.3%)

Memory

18.6MiB live, 18.6MiB allocated; 0ms collecting garbage

Counts

18 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) #s(approx (+ ( (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(approx (* (- (* 1/12 eps) (/ 1/2 x)) (* x x)) (.f64 (-.f64 (.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 #s(approx (- ( 1/12 eps) (/ 1/2 x)) (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps x))) eps)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 #s(approx (+ x (/ (PI) 2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes19.0ms (0.4%)

Memory

-26.7MiB live, 17.7MiB allocated; 4ms collecting garbage

Counts

17 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) #s(approx (+ ( (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(approx (* (- (* 1/12 eps) (/ 1/2 x)) (* x x)) (.f64 (-.f64 (.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 #s(approx (- ( 1/12 eps) (/ 1/2 x)) (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps x))) eps)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 #s(approx (+ x (/ (PI) 2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

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

Calls

3 calls:

10.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	eps
4.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.2%)

Memory

17.0MiB live, 17.0MiB allocated; 0ms collecting garbage

Counts

15 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) #s(approx (+ ( (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(approx (* (- (* 1/12 eps) (/ 1/2 x)) (* x x)) (.f64 (-.f64 (.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 #s(approx (- ( 1/12 eps) (/ 1/2 x)) (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps x))) eps)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 #s(approx (+ x (/ (PI) 2)) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes11.0ms (0.2%)

Memory

18.9MiB live, 18.9MiB allocated; 0ms collecting garbage

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) #s(approx (+ ( (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(approx (* (- (* 1/12 eps) (/ 1/2 x)) (* x x)) (.f64 (-.f64 (.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 #s(approx (- ( 1/12 eps) (/ 1/2 x)) (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps x))) eps)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.3%)

Memory

-25.4MiB live, 18.8MiB allocated; 4ms collecting garbage

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) #s(approx (+ ( (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) #s(approx (* (- (* 1/12 eps) (/ 1/2 x)) (* x x)) (.f64 (-.f64 (.f64 (*.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) eps) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps x)) 1/2) x) (* -1/2 eps)) (.f64 #s(approx (- ( 1/12 eps) (/ 1/2 x)) (.f64 (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps x))) eps)) (*.f64 x x))) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (sin (+ x (/ (PI) 2))) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Outputs

#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))

Calls

3 calls:

8.0ms	eps
3.0ms	x
3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 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 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.2%)

Memory

12.2MiB live, 12.2MiB allocated; 0ms collecting garbage

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps
2.0ms	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 9 to 10 computations (-11.1% saved)

regimes5.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

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 9 to 10 computations (-11.1% saved)

regimes4.0ms (0.1%)

Memory

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

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

1.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms	eps
1.0ms	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 9 to 10 computations (-11.1% saved)

regimes21.0ms (0.4%)

Memory

-140.3MiB live, 7.2MiB allocated; 35ms collecting garbage

Accuracy

Total -60.3b remaining (-13291.3%)

Threshold costs -60.3b (-13291.3%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

18.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms	x
1.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

derivations213.0ms (4.1%)

Memory

42.9MiB live, 136.7MiB allocated; 4ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 182 to 61 computations (66.5% saved)

preprocess75.0ms (1.5%)

Memory: -6.5MiB live, 136.1MiB allocated; 11ms collecting garbage
Compiler: Compiled 230 to 100 computations (56.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze33.0ms (0.6%)

sample3.8s (73.9%)

preprocess38.0ms (0.7%)

series4.0ms (0.1%)

rewrite147.0ms (2.8%)

eval9.0ms (0.2%)

prune3.0ms (0.1%)

series12.0ms (0.2%)

rewrite163.0ms (3.1%)

eval11.0ms (0.2%)

prune6.0ms (0.1%)

series26.0ms (0.5%)

rewrite206.0ms (4%)

eval24.0ms (0.5%)

prune12.0ms (0.2%)

series23.0ms (0.4%)

rewrite191.0ms (3.7%)

eval36.0ms (0.7%)

prune9.0ms (0.2%)

regimes14.0ms (0.3%)

regimes19.0ms (0.4%)

regimes12.0ms (0.2%)

regimes11.0ms (0.2%)

regimes15.0ms (0.3%)

regimes8.0ms (0.2%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes21.0ms (0.4%)

derivations213.0ms (4.1%)

preprocess75.0ms (1.5%)

end0.0ms (0%)

Profiling