Metrics for 2sin (example 3.3)

start0.0ms (0%)

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

analyze58.0ms (0.8%)

Memory

-5.0MiB live, 51.8MiB allocated; 30ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample4.7s (61.9%)

Memory

87.7MiB live, 4 265.7MiB allocated; 2.0s collecting garbage

Samples

2.7s	26 482×	0	invalid
637.0ms	5 604×	1	valid
167.0ms	2 652×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.2s

ival-sin: 1.2s (54.6% of total)

ival-fabs: 260.0ms (11.7% of total)

ival-add!: 171.0ms (7.7% of total)

adjust: 137.0ms (6.1% of total)

ival-mult!: 134.0ms (6% of total)

ival-<: 133.0ms (6% of total)

ival-sub!: 98.0ms (4.4% of total)

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

ival-assert: 15.0ms (0.7% of total)

Bogosity

explain124.0ms (1.6%)

Memory

-36.7MiB live, 100.8MiB allocated; 13ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
232	3	(-7.211058085777366e-77 3.0510035648293696e-79)	1	(-2.3970605403127566e-11 3.145364101702051e-13)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
3	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	234	4
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	3	0

Confusion

	Predicted +	Predicted -
+	231	2
-	3	20

Precision

0.9871794871794872

Recall

0.9914163090128756

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	231	1	1
-	3	3	17

Precision?

0.9747899159663865

Recall?

0.9957081545064378

Freqs

test

number	freq
0	22
1	231
2	3

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

36.0ms	374×	1	valid
6.0ms	136×	0	valid
3.0ms	2×	3	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-sin: 15.0ms (54.8% of total)

adjust: 8.0ms (29.2% of total)

ival-sub!: 2.0ms (7.3% of total)

ival-add!: 2.0ms (7.3% of total)

preprocess87.0ms (1.1%)

Memory

-6.4MiB live, 44.2MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 14 to 12 computations (14.3% saved)

series5.0ms (0.1%)

Memory

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

Counts

6 → 36

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite138.0ms (1.8%)

Memory

35.4MiB live, 124.2MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

42 → 105

Calls

Call 1

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

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

eval14.0ms (0.2%)

Memory: -26.1MiB live, 18.3MiB allocated; 6ms collecting garbage
Compiler: Compiled 1 929 to 372 computations (80.7% saved)

prune5.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated; 0ms collecting garbage

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	90	8	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	9	99

Accuracy

100.0%

Counts

99 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
✓	59.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	57.6%	(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
▶	59.9%	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
▶	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	96.7%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 277 to 192 computations (30.7% saved)

series51.0ms (0.7%)

Memory

21.7MiB live, 71.0MiB allocated; 12ms collecting garbage

Counts

35 → 203

Calls

Call 1

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

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/12 (pow eps 2)) (* eps (* x (+ 1/12 (* -1/144 (pow eps 2)))))) 1/2))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/12 eps) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) 1/2)))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 -1/6))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (- (* 1/24 (* eps x)) 1/6)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* 1/12 x))) 1/6)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* x (+ 1/12 (* -1/144 (* eps x)))))) 1/6)))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx x #s(hole binary64 x))
#s(approx (* (cos x) -1/6) #s(hole binary64 -1/6))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* 1/12 (pow x 2)) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* -1/144 (pow x 2)))) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/4320 (pow x 2)) 1/144)))) 1/6)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 x)))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ (+ eps x) x) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (/ (- (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (sin eps)))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (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 eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (cos eps) 1))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (cos eps))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (+ (cos eps) (* -1/6 (* (pow x 2) (cos eps)))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (+ (cos eps) (* (pow x 2) (+ (* -1/6 (cos eps)) (* 1/120 (* (pow x 2) (cos eps)))))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (+ (cos eps) (* (pow x 2) (+ (* -1/6 (cos eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos eps))) (* 1/120 (cos eps))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (* -1/6 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (- (* (cos eps) (sin x)) (sin x))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* (cos eps) (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 (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* -1/6 (cos x))))
#s(approx eps #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (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 (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (sin x)))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (+ (sin x) (* -1/2 (* (pow eps 2) (sin x))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (+ (sin x) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (+ (sin x) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (sin x)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (sin x)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (sin x)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* 1/24 (* eps (sin x)))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* eps (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* -1 (* eps (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
21.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) 1/24 (* (sin x) eps) (sin x) x eps (* (cos x) -1/6) (cos x) -1/6 (* -1/2 (sin x)) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (- (* (cos eps) (sin x)) (sin x)) (* (cos eps) (sin x)) (cos eps))
6.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) 1/24 (* (sin x) eps) (sin x) x eps (* (cos x) -1/6) (cos x) -1/6 (* -1/2 (sin x)) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (- (* (cos eps) (sin x)) (sin x)) (* (cos eps) (sin x)) (cos eps))
5.0ms	x	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) 1/24 (* (sin x) eps) (sin x) x eps (* (cos x) -1/6) (cos x) -1/6 (* -1/2 (sin x)) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (- (* (cos eps) (sin x)) (sin x)) (* (cos eps) (sin x)) (cos eps))
5.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) 1/24 (* (sin x) eps) (sin x) x eps (* (cos x) -1/6) (cos x) -1/6 (* -1/2 (sin x)) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (- (* (cos eps) (sin x)) (sin x)) (* (cos eps) (sin x)) (cos eps))
5.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) 1/24 (* (sin x) eps) (sin x) x eps (* (cos x) -1/6) (cos x) -1/6 (* -1/2 (sin x)) -1/2 (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x) (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (- (* (cos eps) (sin x)) (sin x)) (* (cos eps) (sin x)) (cos eps))

rewrite191.0ms (2.5%)

Memory

-22.8MiB live, 166.9MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	818	5177
0	868	4892
1	4822	4872
0	8199	4634

Stop Event

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

Counts

238 → 380

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/6 binary64)))
#s(literal 1/24 binary64)
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
(*.f64 (cos.f64 x) #s(literal -1/6 binary64))
(cos.f64 x)
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (sin x) x)
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(+.f64 (+.f64 eps x) x)
(+.f64 eps x)
#s(literal 2 binary64)
(sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(-.f64 (+.f64 eps x) x)
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(*.f64 (cos.f64 eps) (sin.f64 x))
(cos.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/12 (pow eps 2)) (* eps (* x (+ 1/12 (* -1/144 (pow eps 2)))))) 1/2))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/6 eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* 1/12 (* eps x))) 1/2)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/6 eps) (* x (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/12 eps) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) 1/2)))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 -1/6))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (- (* 1/24 (* eps x)) 1/6)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* 1/12 x))) 1/6)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (- (* x (+ (* 1/24 eps) (* x (+ 1/12 (* -1/144 (* eps x)))))) 1/6)))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx x #s(hole binary64 x))
#s(approx (* (cos x) -1/6) #s(hole binary64 -1/6))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* 1/12 (pow x 2)) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* -1/144 (pow x 2)))) 1/6)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/4320 (pow x 2)) 1/144)))) 1/6)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 x)))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* 1/12 (pow x 2)) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ (+ eps x) x) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (/ (- (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (sin eps)))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (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 eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (cos eps) 1))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (* -1/6 (cos eps))))) 1))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (* 1/120 (cos eps)) 1/120)))))) 1))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* x (- (+ (cos eps) (* (pow x 2) (+ 1/6 (+ (* -1/6 (cos eps)) (* (pow x 2) (- (+ (* 1/120 (cos eps)) (* (pow x 2) (+ 1/5040 (* -1/5040 (cos eps))))) 1/120)))))) 1))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (cos eps))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (+ (cos eps) (* -1/6 (* (pow x 2) (cos eps)))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (+ (cos eps) (* (pow x 2) (+ (* -1/6 (cos eps)) (* 1/120 (* (pow x 2) (cos eps)))))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* x (+ (cos eps) (* (pow x 2) (+ (* -1/6 (cos eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos eps))) (* 1/120 (cos eps))))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (cos x) -1/6) #s(hole binary64 (* -1/6 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* -1/2 (sin x)) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 x))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (- (* (cos eps) (sin x)) (sin x))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (* (cos eps) (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 (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- eps (* -2 x))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ eps x)) 1)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (cos x)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* -1/2 (sin x))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* -1/6 (cos x))))
#s(approx eps #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (cos x))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (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 (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))))
#s(approx (- (* (cos eps) (sin x)) (sin x)) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (sin x)))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (+ (sin x) (* -1/2 (* (pow eps 2) (sin x))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (+ (sin x) (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x))))))))
#s(approx (* (cos eps) (sin x)) #s(hole binary64 (+ (sin x) (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x)))))))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (sin x)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (sin x)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (sin x)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* 1/24 (* eps (sin x)))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* eps (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(hole binary64 (* -1 (* eps (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Outputs
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(.f64 eps (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
(fma.f64 (cos.f64 x) eps (.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))
(fma.f64 (cos.f64 x) eps (.f64 eps (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))
(fma.f64 eps (cos.f64 x) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))
(fma.f64 eps (cos.f64 x) (.f64 eps (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) eps))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 eps (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))
(/.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64))) (-.f64 (cos.f64 x) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))
(/.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(fma.f64 eps (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))
(-.f64 (cos.f64 x) (.f64 (neg.f64 eps) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(+.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x))
(+.f64 (cos.f64 x) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps))
(fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps))
(fma.f64 eps (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (neg.f64 eps) (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)))))
(-.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) (.f64 #s(literal 1/2 binary64) (sin.f64 x)))
(+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps))
(+.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))))
(/.f64 (fma.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)) #s(literal 1/13824 binary64) (.f64 #s(literal -1/216 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))))
(/.f64 (fma.f64 #s(literal -1/216 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))))))
(fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(fma.f64 (.f64 #s(literal 1/24 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)))
(fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)))
(fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(-.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (*.f64 (neg.f64 (cos.f64 x)) #s(literal -1/6 binary64)))
(-.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 #s(literal -1/24 binary64) (*.f64 (sin.f64 x) eps)))
(+.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
(+.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)))
#s(literal 1/24 binary64)
(*.f64 (sin.f64 x) eps)
(*.f64 eps (sin.f64 x))
(sin.f64 x)
x
eps
(*.f64 (cos.f64 x) #s(literal -1/6 binary64))
(*.f64 #s(literal -1/6 binary64) (cos.f64 x))
(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)))))
(sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 x (/.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)))))
#s(literal -1/6 binary64)
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin.f64 eps))
(sin.f64 eps)
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 #s(approx (sin x) x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 eps x)) #s(approx (sin x) x)))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 #s(approx (sin x) x) #s(literal 3 binary64))) (+.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (fma.f64 #s(approx (sin x) x) #s(approx (sin x) x) (*.f64 (sin.f64 (+.f64 eps x)) #s(approx (sin x) x)))))
(-.f64 (sin.f64 (+.f64 eps x)) #s(approx (sin x) x))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64))) (sin.f64 (-.f64 x eps)))
(/.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))) (+.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 eps))))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
(sin.f64 (+.f64 eps x))
(-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps)))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 eps) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 x) (sin.f64 eps)))
(/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 x eps))
(/.f64 (-.f64 (.f64 eps eps) (.f64 x x)) (-.f64 eps x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 eps eps) (.f64 eps x))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (.f64 x x) (.f64 eps x))))
(+.f64 eps x)
(+.f64 x eps)
#s(approx (sin x) x)
(.f64 (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (pow.f64 (-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))))))
(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 (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 (.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)) (.f64 (cos.f64 x) (sin.f64 eps)))
(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))
(*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(/.f64 (+.f64 (sin.f64 (-.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))) (sin.f64 (+.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) (sin.f64 (+.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) (cos.f64 (+.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))) #s(literal 2 binary64))
(fma.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(-.f64 (.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))
(+.f64 (.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)) #s(literal -2 binary64))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))
(+.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 2 binary64))) (+.f64 eps (*.f64 #s(literal -2 binary64) x)))
(/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (*.f64 x x)) (-.f64 (+.f64 eps x) x))
(/.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (-.f64 eps (*.f64 #s(literal 2 binary64) x)))
(/.f64 (-.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 eps eps (+.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 2 binary64)) (.f64 eps (.f64 #s(literal -2 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (+.f64 eps x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (-.f64 (.f64 x x) (.f64 (+.f64 eps x) x))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) (.f64 eps (.f64 #s(literal 2 binary64) x)))))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
(-.f64 eps (*.f64 #s(literal -2 binary64) x))
(+.f64 (*.f64 #s(literal 2 binary64) x) eps)
(+.f64 (+.f64 eps x) x)
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(+.f64 x (+.f64 eps x))
(/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 x eps))
(/.f64 (-.f64 (.f64 eps eps) (.f64 x x)) (-.f64 eps x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 eps eps) (.f64 eps x))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (.f64 x x) (.f64 eps x))))
(+.f64 eps x)
(+.f64 x eps)
#s(literal 2 binary64)
(sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(-.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (+.f64 eps x) x)) #s(literal -2 binary64))
(/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(-.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64)) (/.f64 x #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (*.f64 x x)) (fma.f64 #s(literal 2 binary64) x eps))
(/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (fma.f64 x x (*.f64 (+.f64 eps x) x))))
(-.f64 (+.f64 eps x) x)
(+.f64 eps (-.f64 x x))
(.f64 (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (pow.f64 (-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))))))
(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 (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 (.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)) (.f64 (cos.f64 x) (sin.f64 eps)))
(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (cos.f64 eps) (sin.f64 x) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (fma.f64 (sin.f64 x) (sin.f64 x) (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x))
(*.f64 (cos.f64 eps) (sin.f64 x))
(*.f64 (sin.f64 x) (cos.f64 eps))
(/.f64 (+.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 (+.f64 x (neg.f64 eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 x eps)) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))) x)) (cos.f64 (+.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))) x))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 x (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 x (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(fma.f64 (sin.f64 eps) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 eps) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (fma.f64 #s(literal -1 binary64) eps (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (neg.f64 eps)))
(cos.f64 (neg.f64 eps))
(cos.f64 eps)
(+.f64 (.f64 (sin.f64 eps) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 eps) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin.f64 eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (fma.f64 (-.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 #s(literal 1/12 binary64) (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (.f64 eps x) #s(literal 1/12 binary64) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x (.f64 #s(literal 1/12 binary64) eps)) x (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) #s(literal -1/6 binary64))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (-.f64 (.f64 (.f64 eps x) #s(literal 1/24 binary64)) #s(literal 1/6 binary64)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) x) #s(literal 1/6 binary64)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps x) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) x (*.f64 #s(literal 1/24 binary64) eps)) x) #s(literal 1/6 binary64)))
#s(approx (* (sin x) eps) (*.f64 eps x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (fma.f64 #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 (fma.f64 #s(literal -1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (sin x) x)
#s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx x x)
#s(approx (* (cos x) -1/6) #s(literal -1/6 binary64))
#s(approx (* (cos x) -1/6) (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)))
#s(approx (* (cos x) -1/6) (-.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)))
#s(approx (* (cos x) -1/6) (-.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/4320 binary64) (.f64 x x)) #s(literal 1/144 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/6 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (* -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (* -1/2 (sin x)) (.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x))
#s(approx (* -1/2 (sin x)) (.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/240 binary64) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) x))
#s(approx (* -1/2 (sin x)) (.f64 (-.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/10080 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/12 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) x))
#s(approx (sin (+ x eps)) (sin.f64 eps))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 eps) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) x (sin.f64 eps)))
#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (fma.f64 (.f64 #s(literal -2 binary64) x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (fma.f64 (fma.f64 (neg.f64 x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))) x (sin.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (neg.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) x (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))) x (sin.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (neg.f64 x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) x (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) x (neg.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) x (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (neg.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (+ eps x) x) eps)
#s(approx (+ (+ eps x) x) (fma.f64 #s(literal 2 binary64) x eps))
#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (sin (/ (- (+ eps x) x) 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (/ (- (+ eps x) x) 2) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (- (+ eps x) x) eps)
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (sin.f64 eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (fma.f64 (-.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (-.f64 (fma.f64 (.f64 x x) (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) (cos.f64 eps)) #s(literal 1 binary64)) x))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (-.f64 (fma.f64 (+.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (cos.f64 eps)) #s(literal 1/120 binary64)) (.f64 x x))) (*.f64 x x) (cos.f64 eps)) #s(literal 1 binary64)) x))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (-.f64 (fma.f64 (+.f64 (fma.f64 (-.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (cos.f64 eps) #s(literal 1/5040 binary64)) (.f64 x x) (.f64 #s(literal 1/120 binary64) (cos.f64 eps))) #s(literal 1/120 binary64)) (.f64 x x) (.f64 (cos.f64 eps) #s(literal -1/6 binary64))) #s(literal 1/6 binary64)) (.f64 x x) (cos.f64 eps)) #s(literal 1 binary64)) x))
#s(approx (* (cos eps) (sin x)) (*.f64 (cos.f64 eps) x))
#s(approx (* (cos eps) (sin x)) (.f64 (fma.f64 (.f64 (*.f64 x x) (cos.f64 eps)) #s(literal -1/6 binary64) (cos.f64 eps)) x))
#s(approx (* (cos eps) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) (cos.f64 eps)) #s(literal 1/120 binary64) (.f64 (cos.f64 eps) #s(literal -1/6 binary64))) (*.f64 x x) (cos.f64 eps)) x))
#s(approx (* (cos eps) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x x) (cos.f64 eps)) #s(literal -1/5040 binary64) (.f64 #s(literal 1/120 binary64) (cos.f64 eps))) (.f64 x x) (.f64 (cos.f64 eps) #s(literal -1/6 binary64))) (*.f64 x x) (cos.f64 eps)) x))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (cos x) -1/6) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
#s(approx (cos x) (cos.f64 x))
#s(approx (* -1/2 (sin x)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) x)
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (+ (+ eps x) x) (*.f64 #s(literal 2 binary64) x))
#s(approx (+ (+ eps x) x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
#s(approx (* (cos eps) (sin x)) (*.f64 (cos.f64 eps) (sin.f64 x)))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (-.f64 eps (neg.f64 x))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (.f64 (.f64 #s(literal 2 binary64) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (+ eps x) x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 2 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (cos.f64 x) eps))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (cos.f64 x))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))
#s(approx eps eps)
#s(approx (sin eps) eps)
#s(approx (sin eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 #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)) (sin.f64 x))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 x) eps (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (sin.f64 x)))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) eps) #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) #s(literal 2 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64)))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 (sin.f64 x) eps) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) (sin.f64 x) (.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) eps)) eps (.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/12 binary64) (.f64 #s(literal 1/48 binary64) (.f64 (sin.f64 x) eps))) eps (.f64 #s(literal -1/4 binary64) (sin.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 x))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (cos.f64 x) (.f64 #s(literal 1/48 binary64) (.f64 (sin.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)))
#s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (fma.f64 (.f64 (.f64 eps eps) (sin.f64 x)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/720 binary64) (.f64 eps eps)) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (sin.f64 x))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/40320 binary64) (.f64 eps eps)) (sin.f64 x) (.f64 #s(literal -1/720 binary64) (sin.f64 x))) (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (sin.f64 x))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (* (cos eps) (sin x)) (sin.f64 x))
#s(approx (* (cos eps) (sin x)) (fma.f64 (.f64 (.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x) (sin.f64 x)))
#s(approx (* (cos eps) (sin x)) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) (sin.f64 x)) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps) (sin.f64 x)))
#s(approx (* (cos eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/720 binary64) (.f64 eps eps)) (sin.f64 x) (.f64 #s(literal 1/24 binary64) (sin.f64 x))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 eps eps) (sin.f64 x)))
#s(approx (cos eps) #s(literal 1 binary64))
#s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64)))
#s(approx (cos eps) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal 1/24 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (.f64 (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x)))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (.f64 (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 3 binary64)))))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (.f64 (.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 3 binary64))) (sin.f64 x)))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal 1/24 binary64) (sin.f64 x)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal 1/24 binary64) (sin.f64 x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (.f64 (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (pow.f64 eps #s(literal 3 binary64)))))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) (sin.f64 x)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal 1/24 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (.f64 (fma.f64 (/.f64 (sin.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal 1/24 binary64) (sin.f64 x)))) (.f64 eps eps)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal 1/24 binary64) (sin.f64 x))) eps))
#s(approx (sin eps) (sin.f64 eps))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (+ eps x) x) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (cos eps) (cos.f64 eps))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 (cos.f64 x) #s(literal 1/6 binary64))) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal 1/6 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps))) eps))) eps)))))
#s(approx (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 (cos.f64 x) #s(literal 1/6 binary64))) eps))) (*.f64 eps eps)))
#s(approx (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) (.f64 (neg.f64 eps) (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64)))))
#s(approx (sin (+ x eps)) (sin.f64 (-.f64 x (neg.f64 eps))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x))) (.f64 (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))))
#s(approx (/ (+ (+ eps x) x) 2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (+ eps x) x) (.f64 (neg.f64 eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval61.0ms (0.8%)

Memory: 26.0MiB live, 71.9MiB allocated; 4ms collecting garbage
Compiler: Compiled 11 726 to 1 870 computations (84.1% saved)

prune22.0ms (0.3%)

Memory

-3.2MiB live, 43.1MiB allocated; 3ms collecting garbage

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	355	17	372
Fresh	0	3	3
Picked	4	1	5
Done	0	1	1
Total	359	22	381

Accuracy

100.0%

Counts

381 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
	99.5%	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x))))
✓	59.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.6%	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
	99.6%	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
▶	99.4%	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
	99.0%	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
▶	99.7%	(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
	99.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps))))) eps))
▶	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	96.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 #s(literal 1/12 binary64) (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
▶	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	96.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
	96.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
▶	96.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))

Compiler

Compiled 1 682 to 1 017 computations (39.5% saved)

series38.0ms (0.5%)

Memory

17.0MiB live, 62.7MiB allocated; 4ms collecting garbage

Counts

44 → 236

Calls

Call 1

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

Outputs
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx x #s(hole binary64 x))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/12 (pow eps 2)) (* eps (* x (+ 1/12 (* -1/144 (pow eps 2)))))) 1/2))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2)))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ (+ eps x) x) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (+ eps (* 2 x))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 x))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* 1/2 (/ eps x))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))))
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#s(approx eps #s(hole binary64 eps))
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#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
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#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
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#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 -1/2))
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#s(approx (* 1/12 (* eps eps)) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
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#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (* (* eps eps) 1/24) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (* (* eps eps) -1/6) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos x)))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* -1/48 (pow eps 2))))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (+ 1/2 (* -1/48 (pow eps 2)))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (sin (* 1/2 eps)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
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#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* (pow eps 3) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* 1/24 (pow eps 3))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (+ 1/24 (* 1/12 (/ x eps))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (- (+ 1/24 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* (pow eps 3) (- (+ 1/24 (+ (* -1/2 (/ x (pow eps 3))) (* 1/12 (/ x eps)))) (/ 1/2 (pow eps 2))))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (- (* 1/12 (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* 1/24 (pow eps 3))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* (pow eps 3) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/24) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* -1/48 (pow eps 3))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (* -1/48 (pow eps 2))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (cos (* (+ (* 2 x) eps) 1/2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (* (+ (* 2 x) eps) 1/2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1/12 (/ x eps)) 1/24)))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/12 x) (* 1/2 (/ 1 eps))) eps)) 1/24)))))
#s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1 (/ (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)) eps)) 1/24)))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/24)))))
#s(approx (cos (/ (+ (+ eps x) x) 2)) #s(hole binary64 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
#s(approx (/ (+ (+ eps x) x) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (+ eps x) x) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))))

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	inf	((* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* (- (* (* eps eps) 1/24) 1/2) eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* eps eps) -1/6) -1/6 1 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (sin (/ (- (+ eps x) x) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)
7.0ms	x	@	-inf	((* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* (- (* (* eps eps) 1/24) 1/2) eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* eps eps) -1/6) -1/6 1 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (sin (/ (- (+ eps x) x) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)
5.0ms	eps	@	-inf	((* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* (- (* (* eps eps) 1/24) 1/2) eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* eps eps) -1/6) -1/6 1 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (sin (/ (- (+ eps x) x) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)
4.0ms	x	@	inf	((* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* (- (* (* eps eps) 1/24) 1/2) eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* eps eps) -1/6) -1/6 1 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (sin (/ (- (+ eps x) x) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)
4.0ms	eps	@	0	((* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (cos (* (+ (* 2 x) eps) 1/2)) (sin (* 1/2 eps))) (cos (* (+ (* 2 x) eps) 1/2)) (* (+ (* 2 x) eps) 1/2) (+ (* 2 x) eps) 2 x eps 1/2 (sin (* 1/2 eps)) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (- (* 1/12 (* eps eps)) 1/2) (* 1/12 (* eps eps)) 1/12 (* eps eps) (* (- (* (* eps eps) 1/24) 1/2) eps) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) 1/24 (* (* eps eps) -1/6) -1/6 1 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (cos (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) (sin (/ (- (+ eps x) x) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)

rewrite215.0ms (2.8%)

Memory

-29.2MiB live, 249.1MiB allocated; 42ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	889	7366
0	942	7016
1	4989	6996
0	8489	6666

Stop Event

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

Counts

280 → 430

Calls

Call 1

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

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

eval53.0ms (0.7%)

Memory: 27.8MiB live, 73.0MiB allocated; 5ms collecting garbage
Compiler: Compiled 21 552 to 2 665 computations (87.6% saved)

prune32.0ms (0.4%)

Memory

-3.7MiB live, 43.1MiB allocated; 1ms collecting garbage

Pruning

33 alts after pruning (29 fresh and 4 done)

	Pruned	Kept	Total
New	401	23	424
Fresh	9	6	15
Picked	3	2	5
Done	0	2	2
Total	413	33	446

Accuracy

100.0%

Counts

446 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
	99.5%	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x))))
✓	59.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	99.5%	(.f64 (.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
	99.4%	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) eps)))) #s(literal 2 binary64))
	99.4%	(.f64 (.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
	99.0%	(.f64 (.f64 #s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
▶	100.0%	(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
	99.6%	(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
	99.6%	(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
	99.0%	(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
	99.5%	(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 #s(approx (cos ( (+ (* 2 x) eps) 1/2)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
✓	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	96.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
▶	96.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) x)) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
▶	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
	50.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) x))) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
	97.0%	#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))
	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
▶	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
✓	96.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))

Compiler

Compiled 2 944 to 1 831 computations (37.8% saved)

series66.0ms (0.9%)

Memory

20.3MiB live, 68.3MiB allocated; 16ms collecting garbage

Counts

64 → 339

Calls

Call 1

Inputs
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps)
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
(+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x)
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
(*.f64 eps eps)
#s(literal 1/24 binary64)
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
(fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps)))
(fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps))
(.f64 (.f64 eps eps) x)
(fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64))
#s(literal -1/144 binary64)
#s(literal 1/12 binary64)
(.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)
(-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
(.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(.f64 (.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)

Outputs
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) #s(hole binary64 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
#s(approx (* (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (* (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) #s(hole binary64 (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) #s(hole binary64 (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))))
#s(approx (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) #s(hole binary64 (cos (* 1/2 eps))))
#s(approx (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) #s(hole binary64 (+ (cos (* 1/2 eps)) (* -1/2 (* (pow x 2) (cos (* 1/2 eps)))))))
#s(approx (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) #s(hole binary64 (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* 1/24 (* (pow x 2) (cos (* 1/2 eps)))))))))
#s(approx (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) #s(hole binary64 (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/24 (cos (* 1/2 eps))))))))))
#s(approx (cos (* (* 2 x) 1/2)) #s(hole binary64 1))
#s(approx (cos (* (* 2 x) 1/2)) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos (* (* 2 x) 1/2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos (* (* 2 x) 1/2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (* 2 x) 1/2) #s(hole binary64 x))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2))) #s(hole binary64 (* x (sin (* 1/2 eps)))))
#s(approx (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2))) #s(hole binary64 (* x (+ (sin (* 1/2 eps)) (* -1/6 (* (pow x 2) (sin (* 1/2 eps))))))))
#s(approx (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2))) #s(hole binary64 (* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* 1/120 (* (pow x 2) (sin (* 1/2 eps))))))))))
#s(approx (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2))) #s(hole binary64 (* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/120 (sin (* 1/2 eps)))))))))))
#s(approx (sin (* (* 2 x) 1/2)) #s(hole binary64 x))
#s(approx (sin (* (* 2 x) 1/2)) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin (* (* 2 x) 1/2)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin (* (* 2 x) 1/2)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#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 (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/12 (pow eps 2)) (* eps (* x (+ 1/12 (* -1/144 (pow eps 2)))))) 1/2))))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/12 (pow eps 2)) 1/2))))))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 1))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow eps 2)))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) x) #s(hole binary64 (* x (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) #s(hole binary64 (* eps (- (* 1/12 (pow eps 2)) 1/2))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) #s(hole binary64 (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (* (pow eps 2) (* x (+ 1/12 (* -1/144 (pow eps 2))))))))
#s(approx (* (* eps eps) x) #s(hole binary64 (* (pow eps 2) x)))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* x (+ (* -1 (* x (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))) (* 2 (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (+ (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* x (+ (* 2 (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* -1/3 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps)))) (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* -1/2 (* x (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))) (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))) (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (+ (* x (+ (* x (+ (* -1/2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI)))))) (* -1/6 (* x (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))))) (* (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (sin (* 1/2 eps))))) (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 eps) (* 1/2 (PI))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (cos (+ (* 1/2 eps) (* 1/2 (PI))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (* -1/2 (* x (sin (+ (* 1/2 eps) (* 1/2 (PI)))))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (+ (sin (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (cos (+ (* 1/2 eps) (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ (* 1/2 eps) (* 1/2 (PI))))) (* -1/6 (* x (cos (+ (* 1/2 eps) (* 1/2 (PI)))))))))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ (* 1/2 eps) (* 1/2 (PI)))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (+ x (+ (* 1/2 eps) (* 1/2 (PI))))))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (sin (/ (- (+ eps x) x) 2)) #s(hole binary64 (sin (* 1/2 eps))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))))
#s(approx (* (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) #s(hole binary64 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))))
#s(approx (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) #s(hole binary64 (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
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#s(approx (- (* (* eps eps) 1/12) 1/2) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/12) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) #s(hole binary64 (* 1/24 (pow eps 4))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) #s(hole binary64 (* (pow eps 4) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 (* -1/6 (pow eps 3))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))))
#s(approx (+ (* (* eps eps) -1/6) 1) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (* eps eps) -1/6) 1) #s(hole binary64 (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* eps (+ 1/2 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* -1/48 (pow eps 3))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (* -1/48 (pow eps 2))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 x) (* 1/6 (/ 1 eps)))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1/2 (/ x eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 x) (/ 1 eps)) eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 x) (* 1/6 (/ 1 eps)))))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1/2 (/ x eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* -1/12 (pow x 2))) eps)) (* x (+ 1/24 (* -1/144 (pow x 2))))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (+ (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) eps)) (* -1/12 (pow x 2)))) eps)) (* x (+ 1/24 (* -1/144 (pow x 2))))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))) eps)) (* -1/12 (pow x 2)))) eps)) (* x (+ 1/24 (* -1/144 (pow x 2))))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/2) eps)) (* -1/12 x)) eps)) (* -1/144 (pow x 2)))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2) eps)) (* -1/12 x)) eps)) (* -1/144 (pow x 2)))))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (* -1/12 (/ x eps)) 1/12) eps)) (* -1/144 x)))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (* -1 (/ (- (* 1/12 x) (* 1/2 (/ 1 eps))) eps)) 1/12) eps)) (* -1/144 x)))))
#s(approx (* (- (* (* eps eps) 1/12) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/12)))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1/2)))))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))))

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	x	@	-inf	((* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (cos (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (* 2 x) 1/2)) (* (* 2 x) 1/2) (* 2 x) 2 x (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2))) (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) (* (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) (* eps eps) 1/24 (* (* eps eps) -1/6) -1/6 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12) -1/144 1/12 (* (- (* (* eps eps) 1/12) 1/2) eps) (- (* (* eps eps) 1/12) 1/2) (* (* eps eps) 1/12) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (/ (+ (* 2 x) eps) 2) (+ (* 2 x) eps) (/ (PI) 2) (PI) (sin (/ (- (+ eps x) x) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)
9.0ms	eps	@	inf	((* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (cos (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (* 2 x) 1/2)) (* (* 2 x) 1/2) (* 2 x) 2 x (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2))) (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) (* (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) (* eps eps) 1/24 (* (* eps eps) -1/6) -1/6 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12) -1/144 1/12 (* (- (* (* eps eps) 1/12) 1/2) eps) (- (* (* eps eps) 1/12) 1/2) (* (* eps eps) 1/12) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (/ (+ (* 2 x) eps) 2) (+ (* 2 x) eps) (/ (PI) 2) (PI) (sin (/ (- (+ eps x) x) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)
8.0ms	x	@	inf	((* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (cos (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (* 2 x) 1/2)) (* (* 2 x) 1/2) (* 2 x) 2 x (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2))) (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) (* (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) (* eps eps) 1/24 (* (* eps eps) -1/6) -1/6 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12) -1/144 1/12 (* (- (* (* eps eps) 1/12) 1/2) eps) (- (* (* eps eps) 1/12) 1/2) (* (* eps eps) 1/12) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (/ (+ (* 2 x) eps) 2) (+ (* 2 x) eps) (/ (PI) 2) (PI) (sin (/ (- (+ eps x) x) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)
8.0ms	eps	@	-inf	((* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (cos (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (* 2 x) 1/2)) (* (* 2 x) 1/2) (* 2 x) 2 x (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2))) (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) (* (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) (* eps eps) 1/24 (* (* eps eps) -1/6) -1/6 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12) -1/144 1/12 (* (- (* (* eps eps) 1/12) 1/2) eps) (- (* (* eps eps) 1/12) 1/2) (* (* eps eps) 1/12) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (/ (+ (* 2 x) eps) 2) (+ (* 2 x) eps) (/ (PI) 2) (PI) (sin (/ (- (+ eps x) x) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)
7.0ms	x	@	0	((* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (sin (* 1/2 eps))) (- (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (* (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (cos (* 1/2 eps)) (* 1/2 eps) 1/2 eps (cos (* (* 2 x) 1/2)) (* (* 2 x) 1/2) (* 2 x) 2 x (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2))) (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (+ (* (* x x) -1/2) 1) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) (* (- (* (* eps eps) 1/24) 1/2) x) (- (* (* eps eps) 1/24) 1/2) (* (* eps eps) 1/24) (* eps eps) 1/24 (* (* eps eps) -1/6) -1/6 (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12) -1/144 1/12 (* (- (* (* eps eps) 1/12) 1/2) eps) (- (* (* eps eps) 1/12) 1/2) (* (* eps eps) 1/12) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (* (+ (* (* eps eps) -1/6) 1) eps) (+ (* (* eps eps) -1/6) 1) (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (/ (+ (* 2 x) eps) 2) (+ (* 2 x) eps) (/ (PI) 2) (PI) (sin (/ (- (+ eps x) x) 2)) (* (+ (* -1/48 (* eps eps)) 1/2) eps) (+ (* -1/48 (* eps eps)) 1/2) -1/48)

rewrite212.0ms (2.8%)

Memory

-5.6MiB live, 178.6MiB allocated; 46ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1455	13326
0	1544	12086
0	8911	11568

Stop Event

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

Counts

403 → 592

Calls

Call 1

Inputs
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(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
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#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (+ (* 1/12 (/ (pow x 2) eps)) (+ (* x (+ 1/24 (* -1/144 (pow x 2)))) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (pow eps 2)))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (- (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/12 (/ (pow x 2) eps)) (+ (* x (+ 1/24 (* -1/144 (pow x 2)))) (+ (/ 1 (pow eps 3)) (/ (* x (- (* 1/12 (pow x 2)) 1/2)) (pow eps 2)))))) (* 1/6 (/ 1 eps))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (* -1/144 (pow x 2))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (+ (* -1/144 (pow x 2)) (* 1/12 (/ x eps)))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (- (+ 1/24 (+ (* -1/144 (pow x 2)) (+ (* 1/12 (/ x eps)) (* 1/12 (/ (pow x 2) (pow eps 2)))))) (/ 1/2 (pow eps 2))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (- (+ 1/24 (+ (* -1/2 (/ x (pow eps 3))) (+ (* -1/144 (pow x 2)) (+ (* 1/12 (/ x eps)) (* 1/12 (/ (pow x 2) (pow eps 2))))))) (/ 1/2 (pow eps 2))))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) #s(hole binary64 (* -1/144 (* (pow eps 4) x))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1/144 x) (* 1/12 (/ 1 eps))))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1/144 x) (+ (* 1/12 (/ x (pow eps 2))) (* 1/12 (/ 1 eps)))))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) #s(hole binary64 (* (pow eps 4) (- (+ (* -1/144 x) (+ (* 1/12 (/ x (pow eps 2))) (* 1/12 (/ 1 eps)))) (* 1/2 (/ 1 (pow eps 3)))))))
#s(approx (+ (* -1/144 (* eps eps)) 1/12) #s(hole binary64 (* -1/144 (pow eps 2))))
#s(approx (+ (* -1/144 (* eps eps)) 1/12) #s(hole binary64 (* (pow eps 2) (- (* 1/12 (/ 1 (pow eps 2))) 1/144))))
#s(approx (* (- (* (* eps eps) 1/12) 1/2) eps) #s(hole binary64 (* 1/12 (pow eps 3))))
#s(approx (* (- (* (* eps eps) 1/12) 1/2) eps) #s(hole binary64 (* (pow eps 3) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (- (* (* eps eps) 1/12) 1/2) #s(hole binary64 (* 1/12 (pow eps 2))))
#s(approx (- (* (* eps eps) 1/12) 1/2) #s(hole binary64 (* (pow eps 2) (- 1/12 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) #s(hole binary64 (* 1/24 (pow eps 4))))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) #s(hole binary64 (* (pow eps 4) (- 1/24 (* 1/2 (/ 1 (pow eps 2)))))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 (* -1/6 (pow eps 3))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))))
#s(approx (+ (* (* eps eps) -1/6) 1) #s(hole binary64 (* -1/6 (pow eps 2))))
#s(approx (+ (* (* eps eps) -1/6) 1) #s(hole binary64 (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* eps (+ 1/2 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* eps (+ 1/2 (/ x eps)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* -1/48 (pow eps 3))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (* -1/48 (pow eps 2))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) #s(hole binary64 (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 x) (* 1/6 (/ 1 eps)))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1/2 (/ x eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ (- (* 1/2 x) (/ 1 eps)) eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/24 x) (* 1/6 (/ 1 eps)))))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1/2 (/ x eps)) 1/6) eps)) (* -1/24 x))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* -1/12 (pow x 2))) eps)) (* x (+ 1/24 (* -1/144 (pow x 2))))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (+ (* -1 (/ (* x (- (* 1/12 (pow x 2)) 1/2)) eps)) (* -1/12 (pow x 2)))) eps)) (* x (+ 1/24 (* -1/144 (pow x 2))))))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* x (- (* 1/12 (pow x 2)) 1/2))) eps)) (* -1/12 (pow x 2)))) eps)) (* x (+ 1/24 (* -1/144 (pow x 2))))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/12 (pow x 2)) 1/2) eps)) (* -1/12 x)) eps)) (* -1/144 (pow x 2)))))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) #s(hole binary64 (* (pow eps 4) (+ 1/24 (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/2) eps)) (* -1/12 x)) eps)) (* -1/144 (pow x 2)))))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (* -1/12 (/ x eps)) 1/12) eps)) (* -1/144 x)))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (* -1 (/ (- (* 1/12 x) (* 1/2 (/ 1 eps))) eps)) 1/12) eps)) (* -1/144 x)))))
#s(approx (* (- (* (* eps eps) 1/12) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/12)))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))))
#s(approx (* (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) 2) #s(hole binary64 (* 2 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))))
#s(approx (* (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin (/ (- (+ eps x) x) 2))) #s(hole binary64 (* (sin (* 1/2 eps)) (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps))))))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) #s(hole binary64 (sin (+ (* 1/2 (PI)) (* 1/2 (- (* 2 x) (* -1 eps)))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1/2)))))
#s(approx (/ (+ (* 2 x) eps) 2) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) #s(hole binary64 (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))))

Outputs
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))) (fma.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (fma.f64 (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))
(fma.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (neg.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (.f64 (neg.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))))
(sin.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))))
(-.f64 (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(cos.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))))
(cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))
(+.f64 (.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (neg.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))))
(.f64 (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (+.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
eps
(sin.f64 (fma.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) x))
(.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(+.f64 x x)
#s(literal 2 binary64)
x
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(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/48 binary64) (.f64 eps eps)))
(+.f64 (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
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#s(approx (* (* 2 x) 1/2) x)
#s(approx (* 2 x) (*.f64 #s(literal 2 binary64) x))
#s(approx x x)
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#s(approx (sin (* (* 2 x) 1/2)) x)
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#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (sin.f64 eps))
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#s(approx (+ (* (* x x) -1/2) 1) #s(literal 1 binary64))
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#s(approx (* x x) (*.f64 x x))
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#s(approx (cos (* (* 2 x) 1/2)) (cos.f64 x))
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#s(approx (sin (* (* 2 x) 1/2)) (sin.f64 x))
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#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) x)
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#s(approx (/ (+ (* 2 x) eps) 2) x)
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#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (/.f64 (.f64 x x) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1/2 binary64) (-.f64 (fma.f64 (/.f64 (.f64 x x) eps) #s(literal 1/12 binary64) (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/144 binary64) #s(literal 1/24 binary64)) x (fma.f64 x (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)) (pow.f64 eps #s(literal -3 binary64))))) (/.f64 #s(literal 1/6 binary64) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/144 binary64) #s(literal 1/24 binary64))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (+.f64 (fma.f64 (/.f64 x eps) #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal -1/144 binary64))) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal -1/144 binary64) (.f64 #s(literal 1/12 binary64) (+.f64 (/.f64 x eps) (/.f64 (.f64 x x) (.f64 eps eps))))) #s(literal 1/24 binary64)) (.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/2 binary64))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (-.f64 (+.f64 (fma.f64 (/.f64 x (pow.f64 eps #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (.f64 x x) #s(literal -1/144 binary64) (.f64 #s(literal 1/12 binary64) (+.f64 (/.f64 x eps) (/.f64 (.f64 x x) (.f64 eps eps)))))) #s(literal 1/24 binary64)) (.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/2 binary64))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) x) #s(literal -1/144 binary64)))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (*.f64 (fma.f64 #s(literal -1/144 binary64) x (/.f64 #s(literal 1/12 binary64) eps)) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (fma.f64 #s(literal -1/144 binary64) x (fma.f64 (/.f64 x (.f64 eps eps)) #s(literal 1/12 binary64) (/.f64 #s(literal 1/12 binary64) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (-.f64 (fma.f64 #s(literal -1/144 binary64) x (fma.f64 (/.f64 x (.f64 eps eps)) #s(literal 1/12 binary64) (/.f64 #s(literal 1/12 binary64) eps))) (*.f64 (pow.f64 eps #s(literal -3 binary64)) #s(literal 1/2 binary64))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* -1/144 (* eps eps)) 1/12) (.f64 (.f64 eps eps) #s(literal -1/144 binary64)))
#s(approx (+ (* -1/144 (* eps eps)) 1/12) (.f64 (-.f64 (.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/12 binary64)) #s(literal 1/144 binary64)) (*.f64 eps eps)))
#s(approx (* (- (* (* eps eps) 1/12) 1/2) eps) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/12 binary64)))
#s(approx (* (- (* (* eps eps) 1/12) 1/2) eps) (.f64 (-.f64 #s(literal 1/12 binary64) (.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/2 binary64))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))
#s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (-.f64 #s(literal 1/12 binary64) (.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/2 binary64))) (*.f64 eps eps)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/24 binary64)))
#s(approx (* (- (* (* eps eps) 1/24) 1/2) (* eps eps)) (.f64 (-.f64 #s(literal 1/24 binary64) (.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/2 binary64))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64)))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) (*.f64 (-.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/6 binary64)) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (+ (* (* eps eps) -1/6) 1) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
#s(approx (+ (* (* eps eps) -1/6) 1) (.f64 (-.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/6 binary64)) (.f64 eps eps)))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (*.f64 (+.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps) #s(literal 1/2 binary64)) eps))
#s(approx (/ (+ (* 2 x) eps) 2) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* 2 x) eps) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/48 binary64)))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) (.f64 (-.f64 (.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/48 binary64)) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))
#s(approx (+ (* -1/48 (* eps eps)) 1/2) (.f64 (-.f64 (.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/48 binary64)) (*.f64 eps eps)))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (.f64 (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) (cos.f64 x))) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (neg.f64 (.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/24 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (neg.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (neg.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (sin.f64 x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 x) (neg.f64 (/.f64 (fma.f64 (sin.f64 x) #s(literal 1/2 binary64) (neg.f64 (/.f64 (cos.f64 x) eps))) eps))) eps))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (neg.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64)) eps))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (neg.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (.f64 (*.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/6 binary64))) eps))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (neg.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))) eps))) #s(literal 1/6 binary64)) eps))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (neg.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/6 binary64) eps)) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (neg.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/6 binary64)) eps))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (neg.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 eps #s(literal -1 binary64))) eps)) #s(literal 1/6 binary64)) eps))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) (neg.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) x (/.f64 #s(literal 1/6 binary64) eps)) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) (neg.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/6 binary64)) eps))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/144 binary64) #s(literal 1/24 binary64)) x (neg.f64 (/.f64 (fma.f64 #s(literal -1/12 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/144 binary64) #s(literal 1/24 binary64)) x (neg.f64 (/.f64 (+.f64 (fma.f64 #s(literal -1/12 binary64) (.f64 x x) (neg.f64 (/.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) eps))) #s(literal 1/6 binary64)) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) x) (* (+ (* (* eps eps) -1/6) 1) eps)) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/144 binary64) #s(literal 1/24 binary64)) x (neg.f64 (/.f64 (+.f64 (fma.f64 #s(literal -1/12 binary64) (.f64 x x) (neg.f64 (/.f64 (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (neg.f64 (/.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) eps))) eps))) #s(literal 1/6 binary64)) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal -1/144 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -1/12 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps))) eps))) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal -1/144 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -1/12 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))) eps))) eps))) #s(literal 1/24 binary64)) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (fma.f64 #s(literal -1/144 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 #s(literal -1/12 binary64) (/.f64 x eps)) #s(literal 1/12 binary64)) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (fma.f64 #s(literal -1/144 binary64) x (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/12 binary64) x) (/.f64 #s(literal 1/2 binary64) eps)) eps)) #s(literal 1/12 binary64)) eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (- (* (* eps eps) 1/12) 1/2) eps) (neg.f64 (.f64 (-.f64 (.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/12 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (* (+ (* (* eps eps) -1/6) 1) eps) (neg.f64 (*.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal -2 binary64))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (PI.f64) (fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal 1 binary64) eps)))))))
#s(approx (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (PI.f64) (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps))))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (sin (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (PI.f64) (fma.f64 #s(literal 2 binary64) x (.f64 #s(literal 1 binary64) eps))))))
#s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps)) #s(literal 1/2 binary64))))
#s(approx (/ (+ (* 2 x) eps) 2) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* 2 x) eps) (.f64 (neg.f64 eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64))))
#s(approx (* (+ (* -1/48 (* eps eps)) 1/2) eps) (neg.f64 (.f64 (-.f64 #s(literal 1/48 binary64) (.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/2 binary64))) (pow.f64 eps #s(literal 3 binary64)))))

eval89.0ms (1.2%)

Memory: -21.7MiB live, 114.4MiB allocated; 14ms collecting garbage
Compiler: Compiled 42 576 to 4 000 computations (90.6% saved)

prune42.0ms (0.6%)

Memory

6.2MiB live, 59.9MiB allocated; 6ms collecting garbage

Pruning

36 alts after pruning (31 fresh and 5 done)

	Pruned	Kept	Total
New	626	14	640
Fresh	7	17	24
Picked	4	1	5
Done	0	4	4
Total	637	36	673

Accuracy

100.0%

Counts

673 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
	99.5%	(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x))))
✓	59.9%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.7%	(.f64 (.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 #s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)) x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
	99.4%	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) eps)))) #s(literal 2 binary64))
	99.4%	(.f64 (.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
	99.0%	(.f64 (.f64 #s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
	100.0%	(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( (* 2 x) 1/2) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
	99.6%	(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
	99.6%	(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
	99.0%	(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
	99.5%	(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 #s(approx (- ( (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
✓	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	96.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) x)) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
✓	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
	4.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
	96.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
	5.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))) eps))
	97.0%	#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))
	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
	96.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 x eps)) eps) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
	96.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (.f64 (.f64 eps eps) x) (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (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)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
	97.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 x eps (.f64 x x))) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
	96.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (.f64 x x)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
✓	96.7%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
	98.1%	#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))

Compiler

Compiled 4 977 to 1 600 computations (67.9% saved)

regimes49.0ms (0.6%)

Memory

8.4MiB live, 53.9MiB allocated; 3ms collecting garbage

Counts

63 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (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 (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (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)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
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#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 #s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)) x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) eps)))) #s(literal 2 binary64))
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(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
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(.f64 (.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
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(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 #s(approx (cos ( (+ (* 2 x) eps) 1/2)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
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(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
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#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (/.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps))))) eps))

Outputs

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

Calls

3 calls:

16.0ms	x
15.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
14.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes46.0ms (0.6%)

Memory

4.8MiB live, 50.5MiB allocated; 2ms collecting garbage

Counts

60 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (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 (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (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)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (.f64 x x)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 x eps (.f64 x x))) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) x)) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 x eps)) eps) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (.f64 (.f64 eps eps) x) (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 #s(literal 1/12 binary64) (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) x))) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 #s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)) x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) eps)))) #s(literal 2 binary64))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(.f64 (.f64 #s(approx (cos (/ (+ (+ eps x) x) 2)) (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(approx (- (* (cos eps) (sin x)) (sin x)) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 #s(approx (cos ( (+ (* 2 x) eps) 1/2)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 #s(approx (- ( (cos (* 1/2 eps)) (cos (* (* 2 x) 1/2))) (* (sin (* 1/2 eps)) (sin (* (* 2 x) 1/2)))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))

Outputs

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

Calls

3 calls:

15.0ms	x
14.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
14.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes40.0ms (0.5%)

Memory

-1.6MiB live, 44.2MiB allocated; 3ms collecting garbage

Counts

51 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (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 (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (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)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (.f64 x x)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 x eps (.f64 x x))) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) x)) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 x eps)) eps) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (.f64 (.f64 eps eps) x) (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 #s(literal 1/12 binary64) (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) x))) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 #s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)) x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) eps)))) #s(literal 2 binary64))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))

Outputs

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

Calls

3 calls:

13.0ms	x
12.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
12.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes39.0ms (0.5%)

Memory

-6.5MiB live, 42.2MiB allocated; 5ms collecting garbage

Counts

48 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (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 (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (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)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (.f64 x x)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 x eps (.f64 x x))) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) x)) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 x eps)) eps) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (.f64 (.f64 eps eps) x) (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 #s(literal 1/12 binary64) (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) x))) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 #s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)) x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) eps)))) #s(literal 2 binary64))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

14.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
11.0ms	eps
11.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes36.0ms (0.5%)

Memory

-5.7MiB live, 40.1MiB allocated; 2ms collecting garbage

Counts

46 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (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 (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (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)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (.f64 x x)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 x eps (.f64 x x))) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) x)) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 x eps)) eps) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (.f64 (.f64 eps eps) x) (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 #s(literal 1/12 binary64) (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) x))) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 #s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)) x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) eps)))) #s(literal 2 binary64))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

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

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)

regimes33.0ms (0.4%)

Memory

37.8MiB live, 37.8MiB allocated; 0ms collecting garbage

Counts

43 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (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 (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (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)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (.f64 x x)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 x eps (.f64 x x))) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) x)) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 x eps)) eps) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (.f64 (.f64 eps eps) x) (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 #s(literal 1/12 binary64) (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) x))) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.f64 (.f64 (sin.f64 #s(approx (+ (/ (+ (* 2 x) eps) 2) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (PI.f64)) x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/48 binary64)) eps)))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

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

regimes32.0ms (0.4%)

Memory

-9.6MiB live, 36.4MiB allocated; 2ms collecting garbage

Counts

40 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (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 (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (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)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (.f64 x x)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 x eps (.f64 x x))) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) x)) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 x eps)) eps) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (.f64 (.f64 eps eps) x) (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 #s(literal 1/12 binary64) (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) x))) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 #s(approx (/ (+ (+ eps x) x) 2) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (/ (- (+ eps x) x) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))

Outputs

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

Calls

3 calls:

11.0ms	eps
10.0ms	x
9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

Accuracy	Segments	Branch
99.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.4%	1	`x`
99.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes31.0ms (0.4%)

Memory

-11.8MiB live, 33.9MiB allocated; 2ms collecting garbage

Counts

37 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (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 (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (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)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (.f64 x x)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 x eps (.f64 x x))) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) x)) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 x eps)) eps) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (.f64 (.f64 eps eps) x) (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 #s(literal 1/12 binary64) (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) x))) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(.f64 #s(approx ( (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64))) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

11.0ms	x
9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	eps

Results

Accuracy	Segments	Branch
99.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.0%	1	`x`
99.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes32.0ms (0.4%)

Memory

-15.6MiB live, 32.6MiB allocated; 6ms collecting garbage

Counts

36 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (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 (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (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)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (.f64 x x)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 x eps (.f64 x x))) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) x)) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 x eps)) eps) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (.f64 (.f64 eps eps) x) (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 #s(literal 1/12 binary64) (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) x))) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))
#s(approx (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 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 (* (* (cos (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) 2) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps))

Calls

3 calls:

12.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	x
8.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes26.0ms (0.3%)

Memory

31.0MiB live, 31.0MiB allocated; 0ms collecting garbage

Counts

33 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (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 (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (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)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (.f64 x x)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 x eps (.f64 x x))) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) x)) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 x eps)) eps) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (.f64 (.f64 eps eps) x) (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 #s(literal 1/12 binary64) (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) x))) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(-.f64 (sin.f64 (+.f64 x eps)) #s(approx (sin x) x))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes26.0ms (0.3%)

Memory

-16.6MiB live, 29.6MiB allocated; 1ms collecting garbage

Counts

31 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) #s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 x eps (*.f64 x x)) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (* (- (* (* eps eps) 1/24) 1/2) x) eps) (* (* eps eps) -1/6)) 1) (.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (.f64 #s(literal -1/2 binary64) (+.f64 x eps))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (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 (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 #s(approx (- ( (* eps eps) 1/24) 1/2) #s(literal -1/2 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (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)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)) (.f64 x x)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 #s(approx (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (fma.f64 x eps (.f64 x x))) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 #s(approx (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) (.f64 (-.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) (/.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) x)) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 eps x) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (.f64 x eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 x eps)) eps) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (.f64 (.f64 (.f64 eps eps) x) (fma.f64 (.f64 eps eps) #s(literal -1/144 binary64) #s(literal 1/12 binary64)))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 #s(literal 1/12 binary64) (.f64 eps eps))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) #s(literal 1/2 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) #s(approx (+ (+ (* (+ (* (- (* 1/12 (* eps eps)) 1/2) x) (* (- (* (* eps eps) 1/24) 1/2) eps)) x) (* (* eps eps) -1/6)) 1) (.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (neg.f64 (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps (/.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) x))) #s(literal 1/2 binary64)) (*.f64 x x)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(approx (- (* (* eps eps) 1/12) 1/2) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) (fma.f64 #s(literal -1/144 binary64) (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) eps)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 eps eps))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Outputs

#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/144 binary64) (*.f64 eps eps) #s(literal 1/12 binary64)) x) eps (*.f64 #s(literal 1/12 binary64) (*.f64 eps eps))) #s(literal 1/2 binary64)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64))) eps))

Calls

3 calls:

9.0ms	x
8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps

Results

Accuracy	Segments	Branch
97.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.0%	1	`x`
97.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.3%)

Memory

24.1MiB live, 24.1MiB allocated; 0ms collecting garbage

Counts

24 → 1

Calls

Call 1

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

Outputs

#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/12 binary64) (+.f64 x eps)) eps) #s(literal 1/2 binary64)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.0%	1	`x`
97.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.3%)

Memory

-24.2MiB live, 22.0MiB allocated; 2ms collecting garbage

Counts

22 → 1

Calls

Call 1

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

Outputs

#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (fma.f64 x eps (*.f64 x x))) #s(literal 1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps)) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.0%	1	`eps`
97.0%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.2%)

Memory

18.7MiB live, 18.7MiB allocated; 0ms collecting garbage

Counts

17 → 1

Calls

Call 1

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

Outputs

#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (+ (* (+ (* 1/24 (* (sin x) eps)) (* (cos x) -1/6)) eps) (* -1/2 (sin x))) eps) (cos x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* eps eps) x) (+ (* -1/144 (* eps eps)) 1/12)) (* (- (* (* eps eps) 1/12) 1/2) eps)) x) (* (- (* (* eps eps) 1/24) 1/2) (* eps eps))) (*.f64 (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)) eps)) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.0%	1	`x`
97.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.2%)

Memory

-29.8MiB live, 16.6MiB allocated; 2ms collecting garbage

Counts

14 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.0%	1	`x`
97.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.2%)

Memory

15.6MiB live, 15.6MiB allocated; 0ms collecting garbage

Counts

13 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
97.0%	1	`x`
97.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

12.8MiB live, 12.8MiB allocated; 0ms collecting garbage

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory

11.2MiB live, 11.3MiB allocated; 0ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.2%)

Memory

-38.7MiB live, 9.7MiB allocated; 19ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

12.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
96.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
96.8%	1	`eps`
96.8%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0.1%)

Memory

8.2MiB live, 8.2MiB allocated; 0ms collecting garbage

Accuracy

Total -58.8b remaining (-2791%)

Threshold costs -58.8b (-2791%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
96.7%	1	`x`
96.7%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

derivations757.0ms (9.9%)

Memory

9.3MiB live, 566.4MiB allocated; 107ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 1 039 to 231 computations (77.8% saved)

preprocess143.0ms (1.9%)

Memory: -16.7MiB live, 198.5MiB allocated; 85ms collecting garbage
Compiler: Compiled 2 174 to 540 computations (75.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze58.0ms (0.8%)

sample4.7s (61.9%)

explain124.0ms (1.6%)

preprocess87.0ms (1.1%)

series5.0ms (0.1%)

rewrite138.0ms (1.8%)

eval14.0ms (0.2%)

prune5.0ms (0.1%)

series51.0ms (0.7%)

rewrite191.0ms (2.5%)

eval61.0ms (0.8%)

prune22.0ms (0.3%)

series38.0ms (0.5%)

rewrite215.0ms (2.8%)

eval53.0ms (0.7%)

prune32.0ms (0.4%)

series66.0ms (0.9%)

rewrite212.0ms (2.8%)

eval89.0ms (1.2%)

prune42.0ms (0.6%)

regimes49.0ms (0.6%)

regimes46.0ms (0.6%)

regimes40.0ms (0.5%)

regimes39.0ms (0.5%)

regimes36.0ms (0.5%)

regimes33.0ms (0.4%)

regimes32.0ms (0.4%)

regimes31.0ms (0.4%)

regimes32.0ms (0.4%)

regimes26.0ms (0.3%)

regimes26.0ms (0.3%)

regimes20.0ms (0.3%)

regimes20.0ms (0.3%)

regimes15.0ms (0.2%)

regimes14.0ms (0.2%)

regimes12.0ms (0.2%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

regimes16.0ms (0.2%)

regimes5.0ms (0.1%)

derivations757.0ms (9.9%)

preprocess143.0ms (1.9%)

end0.0ms (0%)

Profiling