Metrics for 2sin (example 3.3)

start0.0ms (0%)

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

analyze52.0ms (0.7%)

Memory

5.8MiB live, 59.7MiB allocated; 19ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample5.7s (73.5%)

Memory

57.4MiB live, 6 053.4MiB allocated; 2.1s collecting garbage

Samples

3.1s	26 689×	0	invalid
872.0ms	5 068×	1	valid
278.0ms	3 188×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.9s

ival-sin: 1.0s (35.9% of total)

const: 492.0ms (17% of total)

ival-add: 286.0ms (9.9% of total)

ival-fabs: 265.0ms (9.1% of total)

adjust: 205.0ms (7.1% of total)

ival-sub: 194.0ms (6.7% of total)

ival-mult: 183.0ms (6.3% of total)

ival-<: 134.0ms (4.6% of total)

ival-and: 83.0ms (2.9% of total)

ival-assert: 18.0ms (0.6% of total)

Bogosity

explain103.0ms (1.3%)

Memory

-3.3MiB live, 98.1MiB allocated; 13ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
230	4	(5.937790170566768e-233 4.19721821820005e-237)	3	(7.695358428596198e-220 8.640229184665769e-222)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
3	0	-	2	(130.88862605248417 7.447438139622618e-13)	`(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	231	6
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	1	2

Confusion

	Predicted +	Predicted -
+	227	3
-	4	22

Precision

0.9826839826839827

Recall

0.9869565217391304

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	227	3	0
-	4	3	19

Precision?

0.9704641350210971

Recall?

1.0

Freqs

test

number	freq
0	25
1	230
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms	326×	1	valid
12.0ms	184×	0	valid
1.0ms	2×	3	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-sin: 12.0ms (35.5% of total)

adjust: 11.0ms (32.5% of total)

ival-add: 7.0ms (20.7% of total)

ival-sub: 4.0ms (11.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

preprocess91.0ms (1.2%)

Memory

-3.4MiB live, 41.0MiB allocated; 10ms 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
0	6	7
0	10	7
1	11	7
0	11	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	node limit

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.6%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

series5.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated; 0ms collecting garbage

Counts

6 → 36

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite135.0ms (1.7%)

Memory

8.5MiB live, 187.6MiB allocated; 34ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

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

Counts

42 → 91

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

eval104.0ms (1.3%)

Memory

6.3MiB live, 152.2MiB allocated; 25ms collecting garbage

Samples

61.0ms	1 444×	0	valid
13.0ms	92×	1	valid

Compiler

Compiled 1 765 to 380 computations (78.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-div: 17.0ms (40.5% of total)

ival-mult: 15.0ms (35.7% of total)

ival-add: 7.0ms (16.7% of total)

adjust: 1.0ms (2.4% of total)

ival-assert: 1.0ms (2.4% of total)

ival-true: 1.0ms (2.4% of total)

prune3.0ms (0%)

Memory

7.5MiB live, 7.5MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	5	90

Accuracy

100.0%

Counts

90 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	61.6%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 x) eps))) eps))
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (+.f64 (.f64 (-.f64 (.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))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 74 to 55 computations (25.7% saved)

series27.0ms (0.3%)

Memory

-8.2MiB live, 36.8MiB allocated; 6ms collecting garbage

Counts

22 → 115

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (* (* (cos x) eps) -1/6) -1/6 (* 1/2 (sin x)) 1/2 (sin x) (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (* 1/2 (* (sin x) eps)) (* (sin x) eps))
6.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (* (* (cos x) eps) -1/6) -1/6 (* 1/2 (sin x)) 1/2 (sin x) (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (* 1/2 (* (sin x) eps)) (* (sin x) eps))
4.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (* (* (cos x) eps) -1/6) -1/6 (* 1/2 (sin x)) 1/2 (sin x) (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (* 1/2 (* (sin x) eps)) (* (sin x) eps))
3.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (* (* (cos x) eps) -1/6) -1/6 (* 1/2 (sin x)) 1/2 (sin x) (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (* 1/2 (* (sin x) eps)) (* (sin x) eps))
3.0ms	x	@	0	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (* (* (cos x) eps) -1/6) -1/6 (* 1/2 (sin x)) 1/2 (sin x) (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (* 1/2 (* (sin x) eps)) (* (sin x) eps))

rewrite201.0ms (2.6%)

Memory

0.4MiB live, 228.1MiB allocated; 50ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	463	2741
0	490	2723
1	2778	2723
0	10316	2723

Stop Event

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

Counts

137 → 211

Calls

Call 1

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

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(*.f64 eps (cos.f64 x))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
x
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))) eps) (cos.f64 x)) eps))
(.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))) eps) (cos.f64 x)) eps)
(.f64 eps (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))) eps) (cos.f64 x)))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) eps) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 (cos.f64 x) eps)) (-.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) eps) (.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) eps)) (.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))) eps) eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (.f64 eps (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps)) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 (cos.f64 x) eps)) (-.f64 (.f64 (.f64 eps (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps)) (.f64 eps (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps))) (.f64 (.f64 (cos.f64 x) eps) (.f64 eps (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))) eps))))))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) eps))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 eps (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) (cos.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 (cos.f64 x) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))) eps) (cos.f64 x))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))) eps))))))
(/.f64 (-.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) (cos.f64 x)))
(/.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64))) (-.f64 (cos.f64 x) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps)))
(/.f64 (+.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))) eps) (cos.f64 x)))))
(/.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))) eps)))))
(-.f64 (/.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)) (-.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) (cos.f64 x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) (cos.f64 x))))
(-.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (cos.f64 x) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps))) (/.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)) (-.f64 (cos.f64 x) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps))))
(-.f64 (cos.f64 x) (.f64 (neg.f64 eps) (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps)))))
(+.f64 (/.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) (cos.f64 x))))))
(+.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps))))) (/.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 3 binary64)) (+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps))))))
(+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) (cos.f64 x))
(+.f64 (cos.f64 x) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps))
(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps)
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))))
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(.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x))
(.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))
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(.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps))
#s(literal -1/6 binary64)
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(+.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (cos.f64 x))
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(.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps))
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(*.f64 eps (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
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#s(approx (* (cos x) eps) eps)
#s(approx (* (cos x) eps) (+.f64 (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) eps))
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#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (+.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
#s(approx (cos x) (+.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal 1 binary64)))
#s(approx (cos x) (+.f64 (.f64 (-.f64 (.f64 (+.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal 1 binary64)))
#s(approx x x)
#s(approx (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (.f64 (+.f64 (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps))
#s(approx (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (+.f64 (.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64)) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (+.f64 (.f64 (+.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) eps) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) x) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)))
#s(approx (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) eps) (.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) x)) x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) x) (.f64 (+.f64 (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)))
#s(approx (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
#s(approx (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (+.f64 (+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))
#s(approx (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (+.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)) x) (.f64 #s(literal -1/2 binary64) eps)) x) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
#s(approx (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (+.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (+.f64 (.f64 eps x) (.f64 eps eps))) #s(literal 1/2 binary64)) x) (.f64 #s(literal -1/2 binary64) eps)) x)))
#s(approx (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
#s(approx (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (-.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) (.f64 #s(literal 1/6 binary64) (.f64 eps eps))))
#s(approx (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/12 binary64) (.f64 (.f64 eps eps) x))) x) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
#s(approx (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (+.f64 (.f64 (+.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 (.f64 eps x) (.f64 eps eps))) x) (.f64 #s(literal -1/2 binary64) eps)) x) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))
#s(approx (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps))
#s(approx (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (-.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal 1/6 binary64) eps)))
#s(approx (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (+.f64 (.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) (.f64 #s(literal -1/6 binary64) eps)))
#s(approx (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (+.f64 (.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x) #s(literal 1/2 binary64)) x) (.f64 #s(literal -1/6 binary64) eps)))
#s(approx (* (* (cos x) eps) -1/6) (*.f64 #s(literal -1/6 binary64) eps))
#s(approx (* (* (cos x) eps) -1/6) (-.f64 (.f64 #s(literal -1/6 binary64) eps) (.f64 #s(literal -1/12 binary64) (.f64 (.f64 x x) eps))))
#s(approx (* (* (cos x) eps) -1/6) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/144 binary64) (.f64 (.f64 x x) eps)) (.f64 #s(literal -1/12 binary64) eps)) (.f64 x x)) (*.f64 #s(literal -1/6 binary64) eps)))
#s(approx (* (* (cos x) eps) -1/6) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/144 binary64) eps) (.f64 #s(literal -1/4320 binary64) (.f64 (.f64 x x) eps))) (.f64 x x)) (.f64 #s(literal 1/12 binary64) eps)) (.f64 x x)) (.f64 #s(literal -1/6 binary64) eps)))
#s(approx (* 1/2 (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (* 1/2 (sin x)) (.f64 (+.f64 (.f64 #s(literal -1/12 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
#s(approx (* 1/2 (sin x)) (.f64 (+.f64 (.f64 (-.f64 (.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 (-.f64 (.f64 (+.f64 (.f64 #s(literal -1/10080 binary64) (.f64 x x)) #s(literal 1/240 binary64)) (.f64 x x)) #s(literal 1/12 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))
#s(approx (sin x) x)
#s(approx (sin x) (.f64 (+.f64 (.f64 (*.f64 x x) #s(literal -1/6 binary64)) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (+.f64 (.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 (+.f64 (.f64 (-.f64 (.f64 (+.f64 (.f64 #s(literal -1/5040 binary64) (.f64 x x)) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x)) #s(literal 1 binary64)) x))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) eps)
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (+.f64 (.f64 (.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64)) eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (.f64 eps x) (.f64 eps eps))) x) eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/12 binary64) (.f64 (.f64 eps eps) x))) x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) x) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(literal 1 binary64))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) eps)) x) #s(literal 1 binary64)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 eps x) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x) (*.f64 #s(literal 1/2 binary64) eps)) x) #s(literal 1 binary64)))
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (.f64 #s(literal 1/2 binary64) eps) x))
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (-.f64 (.f64 #s(literal -1/12 binary64) (.f64 (.f64 x x) eps)) (*.f64 #s(literal -1/2 binary64) eps)) x))
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/12 binary64) eps) (.f64 #s(literal -1/240 binary64) (.f64 (.f64 x x) eps))) (.f64 x x)) (.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/10080 binary64) (.f64 (.f64 x x) eps)) (.f64 #s(literal -1/240 binary64) eps)) (.f64 x x)) (.f64 #s(literal -1/12 binary64) eps)) (.f64 x x)) (*.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (* (sin x) eps) (*.f64 eps x))
#s(approx (* (sin x) eps) (.f64 (+.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/6 binary64)) eps) x))
#s(approx (* (sin x) eps) (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) eps) (.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps))) (*.f64 x x)) eps) x))
#s(approx (* (sin x) eps) (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.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 eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps))
#s(approx (cos x) (cos.f64 x))
#s(approx (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))) eps) (cos.f64 x)) eps))
#s(approx (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) (cos.f64 x)))
#s(approx (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps))
#s(approx (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))))
#s(approx (* (* (cos x) eps) -1/6) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)))
#s(approx (* 1/2 (sin x)) (*.f64 #s(literal 1/2 binary64) (sin.f64 x)))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (-.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))) eps) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 #s(literal -1/24 binary64) (.f64 (sin.f64 x) eps))) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)) eps))
#s(approx (sin eps) eps)
#s(approx (sin eps) (.f64 (+.f64 (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps))
#s(approx (sin eps) (.f64 (+.f64 (.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 (+.f64 (.f64 (-.f64 (.f64 (+.f64 (.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 eps eps)
#s(approx (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (*.f64 (cos.f64 x) eps))
#s(approx (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (.f64 (-.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))) eps) (cos.f64 x)) eps))
#s(approx (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (cos.f64 x))
#s(approx (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (-.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps) (cos.f64 x)))
#s(approx (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (.f64 (cos.f64 x) eps))) eps))
#s(approx (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (*.f64 (cos.f64 x) eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (cos.f64 x))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (-.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (sin eps) (sin.f64 eps))
#s(approx (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (.f64 (.f64 #s(literal -1/6 binary64) (pow.f64 eps #s(literal 3 binary64))) (cos.f64 x)))
#s(approx (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (.f64 (-.f64 (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) #s(literal 1/6 binary64))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (.f64 (-.f64 (+.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) (cos.f64 x)))
#s(approx (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (.f64 (-.f64 (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (.f64 (cos.f64 x) #s(literal 1/6 binary64))) (.f64 eps eps)))
#s(approx (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (.f64 (-.f64 (+.f64 (/.f64 (cos.f64 x) (.f64 eps eps)) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) (*.f64 eps eps)))
#s(approx (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) (cos.f64 x)))
#s(approx (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (.f64 (-.f64 (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (.f64 (cos.f64 x) #s(literal 1/6 binary64))) (.f64 eps eps)))
#s(approx (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64)))
#s(approx (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (.f64 (-.f64 (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (*.f64 (cos.f64 x) #s(literal 1/6 binary64))) eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (/.f64 (cos.f64 x) eps) (.f64 #s(literal 1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 (-.f64 (/.f64 (cos.f64 x) eps) (.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (-.f64 (.f64 (cos.f64 x) #s(literal 1/6 binary64)) (*.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))))
#s(approx (* (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) eps) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (-.f64 (neg.f64 (/.f64 (-.f64 (/.f64 (cos.f64 x) eps) (.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))
#s(approx (+ (* (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (cos.f64 x) eps)) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps)) (.f64 (cos.f64 x) #s(literal 1/6 binary64))) (.f64 eps eps)))
#s(approx (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (.f64 (neg.f64 eps) (-.f64 (.f64 (cos.f64 x) #s(literal 1/6 binary64)) (*.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (cos.f64 x) eps)) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))

eval64.0ms (0.8%)

Memory

0.6MiB live, 103.4MiB allocated; 14ms collecting garbage

Samples

22.0ms

512×

valid

Compiler

Compiled 9 224 to 1 353 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 4.0ms (37.6% of total)

ival-div: 3.0ms (28.2% of total)

ival-add: 3.0ms (28.2% of total)

ival-true: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

prune17.0ms (0.2%)

Memory

-10.7MiB live, 35.3MiB allocated; 3ms collecting garbage

Pruning

17 alts after pruning (13 fresh and 4 done)

	Pruned	Kept	Total
New	258	13	271
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	259	17	276

Accuracy

100.0%

Counts

276 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	61.6%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 x) eps))) eps))
✓	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 x) eps))) eps))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 #s(approx (sin x) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/6 binary64)) #s(literal 1 binary64)) x)) eps))) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (sin x) x) eps))) eps))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (+.f64 (.f64 (-.f64 (.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))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (+.f64 (.f64 #s(approx (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps) (cos.f64 x)) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) eps)) x) #s(literal 1 binary64))) eps))
▶	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (+.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal 1 binary64))) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (+.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) eps))
▶	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) eps))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) eps))) (.f64 x x)) eps)))

Compiler

Compiled 716 to 509 computations (28.9% saved)

series42.0ms (0.5%)

Memory

30.1MiB live, 75.2MiB allocated; 7ms collecting garbage

Counts

39 → 135

Calls

Call 1

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

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 (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (sin (* 1/2 (PI))))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* eps (* x (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps)))))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))) (* eps (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps))))))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* eps (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* eps (* x (- (* 1/6 (cos (* 1/2 (PI)))) (* -1/12 eps)))))))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (- (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI)))))) (* 1/2 eps))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (- (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* x (- (* 1/6 (cos (* 1/2 (PI)))) (* -1/12 eps)))))) (* 1/2 eps))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (+ (neg x) (/ (PI) 2)) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ (neg x) (/ (PI) 2)) #s(hole binary64 (+ (* -1 x) (* 1/2 (PI)))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* 1/2 (* eps x))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* x (+ (* -1/12 (* eps (pow x 2))) (* 1/2 eps)))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* x (+ (* 1/2 eps) (* (pow x 2) (+ (* -1/12 eps) (* 1/240 (* eps (pow x 2)))))))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* x (+ (* 1/2 eps) (* (pow x 2) (+ (* -1/12 eps) (* (pow x 2) (+ (* -1/10080 (* eps (pow x 2))) (* 1/240 eps)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 1))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ 1 (* x (- (* -1/2 x) (* 1/2 eps))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ 1 (* x (- (* x (- (* 1/12 (* eps x)) 1/2)) (* 1/2 eps))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 1))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (* (* eps x) -1/2) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 eps))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
#s(approx (* -1/24 (* (* x x) eps)) #s(hole binary64 (* -1/24 (* eps (pow x 2)))))
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (* 1/2 (PI))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* eps (* x (cos (* 1/2 (PI))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))) (* eps (cos (* 1/2 (PI)))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* eps (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* -1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* -1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (- (sin (- (* 1/2 (PI)) x)) (* 1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (- (sin (- (* 1/2 (PI)) x)) (* 1/2 (* eps (sin x))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) x))))
#s(approx (+ (neg x) (/ (PI) 2)) #s(hole binary64 (* -1 x)))
#s(approx (+ (neg x) (/ (PI) 2)) #s(hole binary64 (* x (- (* 1/2 (/ (PI) x)) 1))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* 1/2 (* eps (sin x)))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (- (cos x) (* 1/2 (* eps (sin x)))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (- (cos x) (* 1/2 (* eps (sin x))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* x (+ (* -1/2 eps) (/ 1 x)))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* 1/24 (* eps (pow x 4)))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* (pow x 4) (- (* -1/2 (/ eps (pow x 2))) (* -1/24 eps)))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 2))) (/ eps (pow x 4))) (* -1/24 eps)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* 1/24 (* eps (pow x 4)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* 1/24 (* eps (pow x 2)))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (* -1/2 (/ eps (pow x 2))) (* -1/24 eps)))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (+ x (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 x))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (PI) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (- (sin (+ (* -1 x) (* 1/2 (PI)))) (* 1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (- (sin (+ (* -1 x) (* 1/2 (PI)))) (* 1/2 (* eps (sin x))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (sin (+ (* -1 x) (* 1/2 (PI))))))
#s(approx (+ (neg x) (/ (PI) 2)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ (PI) x)))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* -1 (* x (- (* 1/2 eps) (/ 1 x))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (- (* 1/2 (PI)) (* -1 x))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (PI) x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#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 (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (sin (- (* 1/2 (PI)) x)))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (+ (sin (- (* 1/2 (PI)) x)) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (sin (- (* 1/2 (PI)) x))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (- (* 1/2 (PI)) x)) (* -1/2 (* eps (sin x))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (cos x)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))))))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* -1 (* eps (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/24 (pow x 2)))))))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (sin (- (* 1/2 (PI)) x)) eps)))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* eps (- (/ (sin (- (* 1/2 (PI)) x)) eps) (* 1/2 (sin x))))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* eps (- (/ (cos x) eps) (* 1/2 (sin x))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* eps (+ (* -1/2 x) (/ 1 eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (sin (- (* 1/2 (PI)) x)) eps)) (* -1/2 (sin x)))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (cos x) eps)) (* -1/2 (sin x)))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* -1 (* eps (- (* 1/2 x) (/ 1 eps))))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (- 1/2 (* 1/24 (pow x 2)))) 1)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* -1 (* eps (* (pow x 2) (- 1/2 (* 1/24 (pow x 2))))))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* -1 (* eps (- 1/2 (* 1/24 (pow x 2)))))))

Calls

6 calls:

Time	Variable		Point	Expression
12.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (neg x) x (/ (PI) 2) (PI) 2 (* 1/2 (* (sin x) eps)) 1/2 (* (sin x) eps) (sin x) eps (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (+ (* (* eps x) -1/2) 1) (* (* eps x) -1/2) (* eps x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* -1/2 eps) (* -1/24 (* (* x x) eps)) -1/24 (* (* x x) eps) (* x x) (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)))
9.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (neg x) x (/ (PI) 2) (PI) 2 (* 1/2 (* (sin x) eps)) 1/2 (* (sin x) eps) (sin x) eps (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (+ (* (* eps x) -1/2) 1) (* (* eps x) -1/2) (* eps x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* -1/2 eps) (* -1/24 (* (* x x) eps)) -1/24 (* (* x x) eps) (* x x) (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)))
5.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (neg x) x (/ (PI) 2) (PI) 2 (* 1/2 (* (sin x) eps)) 1/2 (* (sin x) eps) (sin x) eps (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (+ (* (* eps x) -1/2) 1) (* (* eps x) -1/2) (* eps x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* -1/2 eps) (* -1/24 (* (* x x) eps)) -1/24 (* (* x x) eps) (* x x) (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)))
4.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (neg x) x (/ (PI) 2) (PI) 2 (* 1/2 (* (sin x) eps)) 1/2 (* (sin x) eps) (sin x) eps (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (+ (* (* eps x) -1/2) 1) (* (* eps x) -1/2) (* eps x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* -1/2 eps) (* -1/24 (* (* x x) eps)) -1/24 (* (* x x) eps) (* x x) (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)))
4.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (neg x) x (/ (PI) 2) (PI) 2 (* 1/2 (* (sin x) eps)) 1/2 (* (sin x) eps) (sin x) eps (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (+ (* (* eps x) -1/2) 1) (* (* eps x) -1/2) (* eps x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* -1/2 eps) (* -1/24 (* (* x x) eps)) -1/24 (* (* x x) eps) (* x x) (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)))

rewrite209.0ms (2.7%)

Memory

-1.6MiB live, 228.0MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	533	3264
0	574	3008
1	2967	3006
0	10890	3006

Stop Event

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

Counts

174 → 317

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 x) eps))) eps))
(.f64 (-.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 x) eps))) eps)
(-.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps)))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))
(neg.f64 x)
x
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps))
#s(literal 1/2 binary64)
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
eps
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) eps))
(.f64 #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) eps)
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(.f64 (.f64 eps x) #s(literal -1/2 binary64))
(*.f64 eps x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) eps))) (.f64 x x)) eps)))
#s(approx (* (cos x) eps) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) eps))) (.f64 x x)) eps))
(+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) eps))) (.f64 x x)) eps)
(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) eps))) (.f64 x x))
(-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) eps)))
(*.f64 #s(literal -1/2 binary64) eps)
(.f64 #s(literal -1/24 binary64) (.f64 (*.f64 x x) eps))
#s(literal -1/24 binary64)
(.f64 (.f64 x x) eps)
(*.f64 x x)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
(*.f64 (sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) eps)
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))
#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 (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (sin (* 1/2 (PI))))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* eps (* x (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps)))))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))) (* eps (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps))))))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* eps (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* eps (* x (- (* 1/6 (cos (* 1/2 (PI)))) (* -1/12 eps)))))))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (- (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI)))))) (* 1/2 eps))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (- (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* x (- (* 1/6 (cos (* 1/2 (PI)))) (* -1/12 eps)))))) (* 1/2 eps))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (+ (neg x) (/ (PI) 2)) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ (neg x) (/ (PI) 2)) #s(hole binary64 (+ (* -1 x) (* 1/2 (PI)))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* 1/2 (* eps x))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* x (+ (* -1/12 (* eps (pow x 2))) (* 1/2 eps)))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* x (+ (* 1/2 eps) (* (pow x 2) (+ (* -1/12 eps) (* 1/240 (* eps (pow x 2)))))))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* x (+ (* 1/2 eps) (* (pow x 2) (+ (* -1/12 eps) (* (pow x 2) (+ (* -1/10080 (* eps (pow x 2))) (* 1/240 eps)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 1))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ 1 (* x (- (* -1/2 x) (* 1/2 eps))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ 1 (* x (- (* x (- (* 1/12 (* eps x)) 1/2)) (* 1/2 eps))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 1))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (* (* eps x) -1/2) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 eps))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
#s(approx (* -1/24 (* (* x x) eps)) #s(hole binary64 (* -1/24 (* eps (pow x 2)))))
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (* 1/2 (PI))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* eps (* x (cos (* 1/2 (PI))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))) (* eps (cos (* 1/2 (PI)))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* eps (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* -1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* -1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (- (sin (- (* 1/2 (PI)) x)) (* 1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (- (sin (- (* 1/2 (PI)) x)) (* 1/2 (* eps (sin x))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) x))))
#s(approx (+ (neg x) (/ (PI) 2)) #s(hole binary64 (* -1 x)))
#s(approx (+ (neg x) (/ (PI) 2)) #s(hole binary64 (* x (- (* 1/2 (/ (PI) x)) 1))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* 1/2 (* eps (sin x)))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (- (cos x) (* 1/2 (* eps (sin x)))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (- (cos x) (* 1/2 (* eps (sin x))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* x (+ (* -1/2 eps) (/ 1 x)))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* 1/24 (* eps (pow x 4)))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* (pow x 4) (- (* -1/2 (/ eps (pow x 2))) (* -1/24 eps)))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 2))) (/ eps (pow x 4))) (* -1/24 eps)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* 1/24 (* eps (pow x 4)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* 1/24 (* eps (pow x 2)))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (* -1/2 (/ eps (pow x 2))) (* -1/24 eps)))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (+ x (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 x))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (PI) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (- (sin (+ (* -1 x) (* 1/2 (PI)))) (* 1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (- (sin (+ (* -1 x) (* 1/2 (PI)))) (* 1/2 (* eps (sin x))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (sin (+ (* -1 x) (* 1/2 (PI))))))
#s(approx (+ (neg x) (/ (PI) 2)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ (PI) x)))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* -1 (* x (- (* 1/2 eps) (/ 1 x))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (- (* 1/2 (PI)) (* -1 x))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (PI) x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#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 (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (sin (- (* 1/2 (PI)) x)))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (+ (sin (- (* 1/2 (PI)) x)) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (sin (- (* 1/2 (PI)) x))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (- (* 1/2 (PI)) x)) (* -1/2 (* eps (sin x))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (cos x)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))))))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* -1 (* eps (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/24 (pow x 2)))))))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (sin (- (* 1/2 (PI)) x)) eps)))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* eps (- (/ (sin (- (* 1/2 (PI)) x)) eps) (* 1/2 (sin x))))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* eps (- (/ (cos x) eps) (* 1/2 (sin x))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* eps (+ (* -1/2 x) (/ 1 eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (sin (- (* 1/2 (PI)) x)) eps)) (* -1/2 (sin x)))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (cos x) eps)) (* -1/2 (sin x)))))))
#s(approx (+ (* (* eps x) -1/2) 1) #s(hole binary64 (* -1 (* eps (- (* 1/2 x) (/ 1 eps))))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (- 1/2 (* 1/24 (pow x 2)))) 1)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* -1 (* eps (* (pow x 2) (- 1/2 (* 1/24 (pow x 2))))))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* -1 (* eps (- 1/2 (* 1/24 (pow x 2)))))))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
(.f64 (-.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps)
(.f64 eps (-.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) eps) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 (cos.f64 x) eps)) (-.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) eps) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) eps)) (.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 (cos.f64 x) eps)) (-.f64 (.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps))) (.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)))) (.f64 (.f64 (cos.f64 x) eps) (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)))))))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) eps))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (+.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)))))))
(/.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (+.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64))) (-.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps))))
(/.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps))))))
(-.f64 (ratio-square-sum.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (-.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)))))
(-.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))))) (/.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))))))
(-.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))
(+.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)))))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) (cos.f64 x))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)))
(/.f64 (+.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64))) (-.f64 (.f64 (.f64 (cos.f64 x) #s(literal 1 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64))) (.f64 (.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (.f64 (sin.f64 x) #s(literal 0 binary64))) (-.f64 (.f64 (.f64 (cos.f64 x) #s(literal 1 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64))) (.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(sin.f64 (+.f64 (neg.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 #s(literal 1 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(+.f64 (.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64)))
(+.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64)))
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(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps) #s(literal 2 binary64)))) (neg.f64 (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64))) (.f64 #s(literal -1/13824 binary64) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/24 binary64)) eps))))))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) eps)))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps) #s(literal 2 binary64))) (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps)))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps))))
(/.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64))) (.f64 #s(literal -1/13824 binary64) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/24 binary64)) eps)))))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) eps))))))
(-.f64 (ratio-square-sum.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps)) (/.f64 (pow.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps) #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/24 binary64)) eps))))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)))) (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)))))
(-.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps))))) (/.f64 (.f64 #s(literal -1/13824 binary64) (pow.f64 (.f64 (.f64 x x) eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps))))))
(-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps))
(+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)))))) (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)))))))
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)) (.f64 #s(literal -1/2 binary64) eps))
(+.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps)))
(*.f64 #s(literal -1/2 binary64) eps)
(*.f64 eps #s(literal -1/2 binary64))
(.f64 (.f64 (*.f64 x x) #s(literal -1/24 binary64)) eps)
(.f64 (.f64 #s(literal -1/24 binary64) eps) (*.f64 x x))
(.f64 (.f64 (*.f64 x x) eps) #s(literal -1/24 binary64))
(.f64 #s(literal -1/24 binary64) (.f64 (*.f64 x x) eps))
#s(literal -1/24 binary64)
(.f64 (.f64 x x) eps)
(.f64 eps (.f64 x x))
(.f64 x (.f64 eps x))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(fabs.f64 (*.f64 x x))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(*.f64 eps (cos.f64 x))
(/.f64 (+.f64 (pow.f64 (.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64))) (-.f64 (.f64 (.f64 (cos.f64 x) #s(literal 1 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64))) (.f64 (.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (.f64 (sin.f64 x) #s(literal 0 binary64))) (-.f64 (.f64 (.f64 (cos.f64 x) #s(literal 1 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64))) (.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(sin.f64 (+.f64 (neg.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 #s(literal 1 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(+.f64 (.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64)))
(+.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 x x) (.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (.f64 x x) (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64))) (+.f64 (.f64 x x) (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 (.f64 x x) (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))) (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (+.f64 (.f64 x x) (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)
(+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x) (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (.f64 (+.f64 (cos.f64 eps) (-.f64 (.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) x) (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (.f64 (-.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 eps)) #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 x) (* 1/2 (* (sin x) eps))) eps) (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 eps (+.f64 (.f64 (-.f64 (neg.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (neg.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) (.f64 #s(literal 1/2 binary64) eps)) eps) (.f64 (.f64 (.f64 eps x) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) x) (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) eps)))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 eps x) (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)) (.f64 #s(literal -1/12 binary64) eps))) (.f64 (.f64 #s(literal -1/2 binary64) eps) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))))) x) (.f64 (-.f64 (neg.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) (.f64 #s(literal 1/2 binary64) eps)) eps)) x) (.f64 (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) eps)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (-.f64 (neg.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (+.f64 (neg.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) (.f64 #s(literal 1/2 binary64) eps))) x) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (-.f64 (+.f64 (.f64 (+.f64 (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (.f64 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal 1/6 binary64)) (.f64 #s(literal -1/12 binary64) eps)) x)) x) (neg.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))))) (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) (+.f64 (.f64 (neg.f64 x) (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) (+.f64 (.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) (neg.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))))) x) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) x) (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))))) x) (neg.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))))) x) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
#s(approx (+ (neg x) (/ (PI) 2)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
#s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (neg.f64 x) (*.f64 #s(literal -1/2 binary64) (PI.f64))))
#s(approx (neg x) (neg.f64 x))
#s(approx x x)
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (.f64 eps x) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/12 binary64)) (*.f64 #s(literal -1/2 binary64) eps)) x))
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/12 binary64) eps) (.f64 #s(literal -1/240 binary64) (.f64 (.f64 x x) eps))) (.f64 x x)) (.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/10080 binary64) (.f64 (.f64 x x) eps)) (.f64 #s(literal -1/240 binary64) eps)) (.f64 x x)) (.f64 #s(literal -1/12 binary64) eps)) (.f64 x x)) (*.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (* (sin x) eps) (*.f64 eps x))
#s(approx (* (sin x) eps) (.f64 (+.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/6 binary64)) eps) x))
#s(approx (* (sin x) eps) (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) eps) (.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps))) (*.f64 x x)) eps) x))
#s(approx (* (sin x) eps) (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.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 (+.f64 (.f64 (*.f64 x x) #s(literal -1/6 binary64)) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (+.f64 (.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 (+.f64 (.f64 (-.f64 (.f64 (+.f64 (.f64 #s(literal -1/5040 binary64) (.f64 x x)) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x)) #s(literal 1 binary64)) x))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) eps)
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (+.f64 (.f64 (.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64)) eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (.f64 eps x) (.f64 eps eps))) x) eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/12 binary64) (.f64 (.f64 eps eps) x))) x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) x) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(literal 1 binary64))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) eps)) x) #s(literal 1 binary64)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x) (*.f64 #s(literal 1/2 binary64) eps)) x) #s(literal 1 binary64)))
#s(approx (+ (* (* eps x) -1/2) 1) #s(literal 1 binary64))
#s(approx (+ (* (* eps x) -1/2) 1) (+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
#s(approx (* (* eps x) -1/2) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))
#s(approx (* eps x) (*.f64 eps x))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) eps)
#s(approx (* (sin (+ x (/ (PI) 2))) eps) (+.f64 (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) eps))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps)) (.f64 x x)) eps))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps)) (.f64 #s(literal -1/24 binary64) eps)) (.f64 x x)) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) eps)
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (+.f64 (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) eps))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps)) (.f64 x x)) eps))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps)) (.f64 x x)))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps)))
#s(approx (* -1/24 (* (* x x) eps)) (.f64 (.f64 (*.f64 x x) #s(literal -1/24 binary64)) eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (* x x) (*.f64 x x))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) eps))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) (.f64 eps (+.f64 (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) x) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) (+.f64 (.f64 (+.f64 (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) eps) (.f64 (.f64 (.f64 eps x) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))) x) (.f64 (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) eps)))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 eps x) (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) #s(literal -1/6 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) eps) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))))) x) (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) eps)) x) (.f64 (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) eps)))
#s(approx (sin (+ (neg x) (/ (PI) 2))) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) (+.f64 (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) x) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) (+.f64 (.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) x) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) x) (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))))) x) (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) x) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
#s(approx (+ x (/ (PI) 2)) (*.f64 (PI.f64) #s(literal 1/2 binary64)))
#s(approx (+ x (/ (PI) 2)) (+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (-.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)))
#s(approx (+ (neg x) (/ (PI) 2)) (neg.f64 x))
#s(approx (+ (neg x) (/ (PI) 2)) (.f64 (-.f64 (.f64 (/.f64 (PI.f64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (-.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* (* eps x) -1/2) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* eps x) -1/2) 1) (+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) eps) #s(literal 1/24 binary64)))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (.f64 (-.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/24 binary64) eps)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (.f64 (-.f64 (+.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))) (.f64 #s(literal -1/24 binary64) eps)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) eps) #s(literal 1/24 binary64)))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (.f64 (-.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/24 binary64) eps)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) eps)))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 (-.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/24 binary64) eps)) (*.f64 x x)))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) (.f64 (sin.f64 (+.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) eps))
#s(approx (sin (+ (neg x) (/ (PI) 2))) (sin.f64 (+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)))
#s(approx (+ x (/ (PI) 2)) x)
#s(approx (+ x (/ (PI) 2)) (.f64 (+.f64 (.f64 (/.f64 (PI.f64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (sin.f64 (-.f64 (neg.f64 x) (.f64 #s(literal -1/2 binary64) (PI.f64)))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (-.f64 (sin.f64 (-.f64 (neg.f64 x) (.f64 #s(literal -1/2 binary64) (PI.f64)))) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) (sin.f64 (-.f64 (neg.f64 x) (*.f64 #s(literal -1/2 binary64) (PI.f64)))))
#s(approx (+ (neg x) (/ (PI) 2)) (.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (PI.f64) x) #s(literal 1/2 binary64)))))
#s(approx (+ (* (* eps x) -1/2) 1) (.f64 (neg.f64 x) (-.f64 (.f64 #s(literal 1/2 binary64) eps) (pow.f64 x #s(literal -1 binary64)))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) (.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 x))) eps))
#s(approx (sin (+ (neg x) (/ (PI) 2))) (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) (neg.f64 x))))
#s(approx (+ x (/ (PI) 2)) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 (PI.f64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))) eps) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (.f64 #s(literal -1/24 binary64) (.f64 (sin.f64 x) eps))) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)) eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (-.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx eps eps)
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (*.f64 (cos.f64 x) eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (cos.f64 x))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (-.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (.f64 (+.f64 (neg.f64 (.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 (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (.f64 (neg.f64 eps) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 (neg.f64 eps) (+.f64 (.f64 (*.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (* -1/2 eps) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (/.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) eps) (.f64 #s(literal 1/2 binary64) (sin.f64 x))) (.f64 eps eps)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 (-.f64 (/.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) eps) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (/.f64 (cos.f64 x) eps) (.f64 #s(literal 1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 (-.f64 (/.f64 (cos.f64 x) eps) (.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps))
#s(approx (+ (* (* eps x) -1/2) 1) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) eps) #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) eps)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (cos.f64 x) eps)) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
#s(approx (+ (* (* eps x) -1/2) 1) (.f64 (neg.f64 eps) (-.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 eps #s(literal -1 binary64)))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (.f64 (neg.f64 eps) (-.f64 (.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 (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (.f64 (neg.f64 eps) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 (neg.f64 eps) (+.f64 (.f64 (*.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))

eval103.0ms (1.3%)

Memory

11.3MiB live, 158.4MiB allocated; 16ms collecting garbage

Samples

53.0ms

768×

valid

Compiler

Compiled 12 082 to 1 785 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 21.0ms (58.2% of total)

ival-add: 8.0ms (22.2% of total)

ival-div: 5.0ms (13.9% of total)

ival-true: 1.0ms (2.8% of total)

adjust: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

prune17.0ms (0.2%)

Memory

-1.2MiB live, 44.8MiB allocated; 3ms collecting garbage

Pruning

17 alts after pruning (11 fresh and 6 done)

	Pruned	Kept	Total
New	339	4	343
Fresh	1	7	8
Picked	3	2	5
Done	0	4	4
Total	343	17	360

Accuracy

100.0%

Counts

360 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	61.6%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 x) eps))) eps))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 #s(approx (sin x) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/6 binary64)) #s(literal 1 binary64)) x)) eps))) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (sin x) x) eps))) eps))
▶	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 #s(approx (sin (+ (neg x) (/ (PI) 2))) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps))) eps))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (+.f64 (.f64 (-.f64 (.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))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (+.f64 (.f64 #s(approx (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps) (cos.f64 x)) eps))
▶	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ x (/ (PI) 2)) (+.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) eps)) x) #s(literal 1 binary64))) eps))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (+.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal 1 binary64))) eps))
▶	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (+.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) eps))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) eps))
▶	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (.f64 #s(approx (- ( -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 (neg.f64 eps) (+.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))) (.f64 x x)) eps)))

Compiler

Compiled 734 to 522 computations (28.9% saved)

series69.0ms (0.9%)

Memory

-67.3MiB live, 65.8MiB allocated; 57ms collecting garbage

Counts

45 → 183

Calls

Call 1

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

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (sin (* 1/2 (PI))))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* eps (* x (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps)))))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))) (* eps (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps))))))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* eps (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* eps (* x (- (* 1/6 (cos (* 1/2 (PI)))) (* -1/12 eps)))))))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (- (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI)))))) (* 1/2 eps))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (- (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* x (- (* 1/6 (cos (* 1/2 (PI)))) (* -1/12 eps)))))) (* 1/2 eps))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (sin (- (* (PI) 1/2) x)) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (- (* (PI) 1/2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))))
#s(approx (sin (- (* (PI) 1/2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (- (* (PI) 1/2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (- (* (PI) 1/2) x) #s(hole binary64 (* 1/2 (PI))))
#s(approx (- (* (PI) 1/2) x) #s(hole binary64 (+ (* -1 x) (* 1/2 (PI)))))
#s(approx x #s(hole binary64 x))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* 1/2 (* eps x))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* x (+ (* -1/12 (* eps (pow x 2))) (* 1/2 eps)))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* x (+ (* 1/2 eps) (* (pow x 2) (+ (* -1/12 eps) (* 1/240 (* eps (pow x 2)))))))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* x (+ (* 1/2 eps) (* (pow x 2) (+ (* -1/12 eps) (* (pow x 2) (+ (* -1/10080 (* eps (pow x 2))) (* 1/240 eps)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (* (* x x) -1/2) 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) -1/2) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 1))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ 1 (* x (- (* -1/2 x) (* 1/2 eps))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ 1 (* x (- (* x (- (* 1/12 (* eps x)) 1/2)) (* 1/2 eps))))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 1))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) #s(hole binary64 (* x (+ (* -1/2 eps) (* -1/2 x)))))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (- (* -1/2 x) (* 1/2 eps))))
#s(approx (* -1/2 x) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 eps))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) #s(hole binary64 (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
#s(approx (+ (* (* x x) -1/24) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (* x x) -1/24) 1/2) #s(hole binary64 (+ 1/2 (* -1/24 (pow x 2)))))
#s(approx (* (* x x) -1/24) #s(hole binary64 (* -1/24 (pow x 2))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (* 1/2 (PI))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* eps (* x (cos (* 1/2 (PI))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))) (* eps (cos (* 1/2 (PI)))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* eps (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* -1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* -1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (+ (* (PI) 1/2) x) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ (* (PI) 1/2) x) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (- (sin (- (* 1/2 (PI)) x)) (* 1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (- (sin (- (* 1/2 (PI)) x)) (* 1/2 (* eps (sin x))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) x))))
#s(approx (sin (- (* (PI) 1/2) x)) #s(hole binary64 (sin (- (* 1/2 (PI)) x))))
#s(approx (- (* (PI) 1/2) x) #s(hole binary64 (* -1 x)))
#s(approx (- (* (PI) 1/2) x) #s(hole binary64 (* x (- (* 1/2 (/ (PI) x)) 1))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* 1/2 (* eps (sin x)))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (- (cos x) (* 1/2 (* eps (sin x)))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (- (cos x) (* 1/2 (* eps (sin x))))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) #s(hole binary64 (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (* x (- (* -1/2 (/ eps x)) 1/2))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* 1/24 (* eps (pow x 4)))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* (pow x 4) (- (* -1/2 (/ eps (pow x 2))) (* -1/24 eps)))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 2))) (/ eps (pow x 4))) (* -1/24 eps)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* 1/24 (* eps (pow x 4)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* 1/24 (* eps (pow x 2)))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (* -1/2 (/ eps (pow x 2))) (* -1/24 eps)))))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) #s(hole binary64 (* 1/24 (* eps (pow x 2)))))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) #s(hole binary64 (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))))
#s(approx (+ (* (* x x) -1/24) 1/2) #s(hole binary64 (* -1/24 (pow x 2))))
#s(approx (+ (* (* x x) -1/24) 1/2) #s(hole binary64 (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (+ x (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 x))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (PI) x))))))
#s(approx (+ (* (PI) 1/2) x) #s(hole binary64 x))
#s(approx (+ (* (PI) 1/2) x) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (PI) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (- (sin (+ (* -1 x) (* 1/2 (PI)))) (* 1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (- (sin (+ (* -1 x) (* 1/2 (PI)))) (* 1/2 (* eps (sin x))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (sin (+ (* -1 x) (* 1/2 (PI))))))
#s(approx (sin (- (* (PI) 1/2) x)) #s(hole binary64 (sin (+ (* -1 x) (* 1/2 (PI))))))
#s(approx (- (* (PI) 1/2) x) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ (PI) x)))))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (- (* 1/2 (PI)) (* -1 x))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (PI) x)) 1)))))
#s(approx (+ (* (PI) 1/2) x) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (PI) 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 (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (sin (- (* 1/2 (PI)) x)))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (+ (sin (- (* 1/2 (PI)) x)) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (sin (- (* 1/2 (PI)) x))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (- (* 1/2 (PI)) x)) (* -1/2 (* eps (sin x))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (cos x)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))))))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* -1 (* eps (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/24 (pow x 2)))))))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/24 (pow x 2)))))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (sin (- (* 1/2 (PI)) x)) eps)))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* eps (- (/ (sin (- (* 1/2 (PI)) x)) eps) (* 1/2 (sin x))))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* eps (- (/ (cos x) eps) (* 1/2 (sin x))))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) #s(hole binary64 (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (* eps (- (* -1/2 (/ x eps)) 1/2))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (sin (- (* 1/2 (PI)) x)) eps)) (* -1/2 (sin x)))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (cos x) eps)) (* -1/2 (sin x)))))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) #s(hole binary64 (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (- 1/2 (* 1/24 (pow x 2)))) 1)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* -1 (* eps (* (pow x 2) (- 1/2 (* 1/24 (pow x 2))))))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* -1 (* eps (- 1/2 (* 1/24 (pow x 2)))))))

Calls

6 calls:

Time	Variable		Point	Expression
38.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) (sin (+ (neg x) (/ (PI) 2))) (sin (- (* (PI) 1/2) x)) (- (* (PI) 1/2) x) (* (PI) 1/2) (PI) 1/2 x (* 1/2 (* (sin x) eps)) (* (sin x) eps) (sin x) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* (* x x) -1/2) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (* (- (* -1/2 x) (* 1/2 eps)) x) (- (* -1/2 x) (* 1/2 eps)) (* -1/2 x) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* (neg eps) (+ (* (* x x) -1/24) 1/2)) (neg eps) (+ (* (* x x) -1/24) 1/2) (* (* x x) -1/24) -1/24 (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (+ (* (PI) 1/2) x))
5.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) (sin (+ (neg x) (/ (PI) 2))) (sin (- (* (PI) 1/2) x)) (- (* (PI) 1/2) x) (* (PI) 1/2) (PI) 1/2 x (* 1/2 (* (sin x) eps)) (* (sin x) eps) (sin x) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* (* x x) -1/2) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (* (- (* -1/2 x) (* 1/2 eps)) x) (- (* -1/2 x) (* 1/2 eps)) (* -1/2 x) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* (neg eps) (+ (* (* x x) -1/24) 1/2)) (neg eps) (+ (* (* x x) -1/24) 1/2) (* (* x x) -1/24) -1/24 (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (+ (* (PI) 1/2) x))
5.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) (sin (+ (neg x) (/ (PI) 2))) (sin (- (* (PI) 1/2) x)) (- (* (PI) 1/2) x) (* (PI) 1/2) (PI) 1/2 x (* 1/2 (* (sin x) eps)) (* (sin x) eps) (sin x) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* (* x x) -1/2) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (* (- (* -1/2 x) (* 1/2 eps)) x) (- (* -1/2 x) (* 1/2 eps)) (* -1/2 x) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* (neg eps) (+ (* (* x x) -1/24) 1/2)) (neg eps) (+ (* (* x x) -1/24) 1/2) (* (* x x) -1/24) -1/24 (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (+ (* (PI) 1/2) x))
5.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) (sin (+ (neg x) (/ (PI) 2))) (sin (- (* (PI) 1/2) x)) (- (* (PI) 1/2) x) (* (PI) 1/2) (PI) 1/2 x (* 1/2 (* (sin x) eps)) (* (sin x) eps) (sin x) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* (* x x) -1/2) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (* (- (* -1/2 x) (* 1/2 eps)) x) (- (* -1/2 x) (* 1/2 eps)) (* -1/2 x) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* (neg eps) (+ (* (* x x) -1/24) 1/2)) (neg eps) (+ (* (* x x) -1/24) 1/2) (* (* x x) -1/24) -1/24 (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (+ (* (PI) 1/2) x))
5.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) (sin (+ (neg x) (/ (PI) 2))) (sin (- (* (PI) 1/2) x)) (- (* (PI) 1/2) x) (* (PI) 1/2) (PI) 1/2 x (* 1/2 (* (sin x) eps)) (* (sin x) eps) (sin x) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* (* x x) -1/2) (* x x) -1/2 1 (- (sin (+ x eps)) (sin x)) (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) (- (cos x) (* 1/2 (* (sin x) eps))) (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (* (- (* -1/2 x) (* 1/2 eps)) x) (- (* -1/2 x) (* 1/2 eps)) (* -1/2 x) (* 1/2 eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* (neg eps) (+ (* (* x x) -1/24) 1/2)) (neg eps) (+ (* (* x x) -1/24) 1/2) (* (* x x) -1/24) -1/24 (- (sin (+ x eps)) (sin x)) (* (sin (+ x (/ (PI) 2))) eps) (sin (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (+ (* (PI) 1/2) x))

rewrite170.0ms (2.2%)

Memory

35.1MiB live, 225.0MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	652	4303
0	693	3959
1	3557	3959
0	8305	3959

Stop Event

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

Counts

228 → 360

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 #s(approx (sin (+ (neg x) (/ (PI) 2))) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps))) eps))
(.f64 (-.f64 #s(approx (sin (+ (neg x) (/ (PI) 2))) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps))) eps)
(-.f64 #s(approx (sin (+ (neg x) (/ (PI) 2))) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) (.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 x) eps)))
#s(approx (sin (+ (neg x) (/ (PI) 2))) (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)))
(sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)
(*.f64 (PI.f64) #s(literal 1/2 binary64))
(PI.f64)
#s(literal 1/2 binary64)
x
(.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (+.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (+.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) eps)
#s(approx (cos x) (+.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(+.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(*.f64 x x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) eps)) x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) eps)) x) #s(literal 1 binary64))) eps)
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) eps)) x) #s(literal 1 binary64)))
(+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) eps)) x) #s(literal 1 binary64))
(.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) eps)) x)
(-.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (.f64 #s(approx (- ( -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 (neg.f64 eps) (+.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))) (.f64 x x)) eps)))
#s(approx (* (cos x) eps) (+.f64 (.f64 #s(approx (- ( -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 (neg.f64 eps) (+.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))) (.f64 x x)) eps))
(+.f64 (.f64 #s(approx (- ( -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 (neg.f64 eps) (+.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))) (.f64 x x)) eps)
(.f64 #s(approx (- ( -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 (neg.f64 eps) (+.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))) (.f64 x x))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 (neg.f64 eps) (+.f64 (.f64 (*.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 (neg.f64 eps) (+.f64 (.f64 (*.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(neg.f64 eps)
(+.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
#s(literal -1/24 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ x (/ (PI) 2)) (+.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
(.f64 (sin.f64 #s(approx (+ x (/ (PI) 2)) (+.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps)
(sin.f64 #s(approx (+ x (/ (PI) 2)) (+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)))
#s(approx (+ x (/ (PI) 2)) (+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))
(+.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (sin (* 1/2 (PI))))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* eps (* x (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps)))))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))) (* eps (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps))))))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* eps (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* eps (* x (- (* 1/6 (cos (* 1/2 (PI)))) (* -1/12 eps)))))))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (- (* -1 (cos (* 1/2 (PI)))) (* 1/2 eps))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (- (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI)))))) (* 1/2 eps))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (- (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* x (- (* 1/6 (cos (* 1/2 (PI)))) (* -1/12 eps)))))) (* 1/2 eps))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (sin (- (* (PI) 1/2) x)) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (- (* (PI) 1/2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))))
#s(approx (sin (- (* (PI) 1/2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (- (* (PI) 1/2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (- (* (PI) 1/2) x) #s(hole binary64 (* 1/2 (PI))))
#s(approx (- (* (PI) 1/2) x) #s(hole binary64 (+ (* -1 x) (* 1/2 (PI)))))
#s(approx x #s(hole binary64 x))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* 1/2 (* eps x))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* x (+ (* -1/12 (* eps (pow x 2))) (* 1/2 eps)))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* x (+ (* 1/2 eps) (* (pow x 2) (+ (* -1/12 eps) (* 1/240 (* eps (pow x 2)))))))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* x (+ (* 1/2 eps) (* (pow x 2) (+ (* -1/12 eps) (* (pow x 2) (+ (* -1/10080 (* eps (pow x 2))) (* 1/240 eps)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (* (* x x) -1/2) 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) -1/2) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 1))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ 1 (* x (- (* -1/2 x) (* 1/2 eps))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ 1 (* x (- (* x (- (* 1/12 (* eps x)) 1/2)) (* 1/2 eps))))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 1))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) #s(hole binary64 (* x (+ (* -1/2 eps) (* -1/2 x)))))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (- (* -1/2 x) (* 1/2 eps))))
#s(approx (* -1/2 x) #s(hole binary64 (* -1/2 x)))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 eps))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* -1/2 eps)))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) #s(hole binary64 (* -1/2 eps)))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) #s(hole binary64 (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
#s(approx (+ (* (* x x) -1/24) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (* x x) -1/24) 1/2) #s(hole binary64 (+ 1/2 (* -1/24 (pow x 2)))))
#s(approx (* (* x x) -1/24) #s(hole binary64 (* -1/24 (pow x 2))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (* 1/2 (PI))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* eps (* x (cos (* 1/2 (PI))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))) (* eps (cos (* 1/2 (PI)))))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* eps (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* -1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* -1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (+ (* (PI) 1/2) x) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ (* (PI) 1/2) x) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (- (sin (- (* 1/2 (PI)) x)) (* 1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (- (sin (- (* 1/2 (PI)) x)) (* 1/2 (* eps (sin x))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) x))))
#s(approx (sin (- (* (PI) 1/2) x)) #s(hole binary64 (sin (- (* 1/2 (PI)) x))))
#s(approx (- (* (PI) 1/2) x) #s(hole binary64 (* -1 x)))
#s(approx (- (* (PI) 1/2) x) #s(hole binary64 (* x (- (* 1/2 (/ (PI) x)) 1))))
#s(approx (* 1/2 (* (sin x) eps)) #s(hole binary64 (* 1/2 (* eps (sin x)))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (* x x) -1/2) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (- (cos x) (* 1/2 (* eps (sin x)))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (- (cos x) (* 1/2 (* eps (sin x))))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) #s(hole binary64 (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (* -1/2 x)))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (* x (- (* -1/2 (/ eps x)) 1/2))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* 1/24 (* eps (pow x 4)))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* (pow x 4) (- (* -1/2 (/ eps (pow x 2))) (* -1/24 eps)))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* (pow x 4) (- (+ (* -1/2 (/ eps (pow x 2))) (/ eps (pow x 4))) (* -1/24 eps)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* 1/24 (* eps (pow x 4)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* 1/24 (* eps (pow x 2)))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (* -1/2 (/ eps (pow x 2))) (* -1/24 eps)))))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) #s(hole binary64 (* 1/24 (* eps (pow x 2)))))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) #s(hole binary64 (* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))))
#s(approx (+ (* (* x x) -1/24) 1/2) #s(hole binary64 (* -1/24 (pow x 2))))
#s(approx (+ (* (* x x) -1/24) 1/2) #s(hole binary64 (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (+ x (* 1/2 (PI)))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 x))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (PI) x))))))
#s(approx (+ (* (PI) 1/2) x) #s(hole binary64 x))
#s(approx (+ (* (PI) 1/2) x) #s(hole binary64 (* x (+ 1 (* 1/2 (/ (PI) x))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (- (sin (+ (* -1 x) (* 1/2 (PI)))) (* 1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (- (sin (+ (* -1 x) (* 1/2 (PI)))) (* 1/2 (* eps (sin x))))))
#s(approx (sin (+ (neg x) (/ (PI) 2))) #s(hole binary64 (sin (+ (* -1 x) (* 1/2 (PI))))))
#s(approx (sin (- (* (PI) 1/2) x)) #s(hole binary64 (sin (+ (* -1 x) (* 1/2 (PI))))))
#s(approx (- (* (PI) 1/2) x) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ (PI) x)))))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))))
#s(approx (* (sin (+ x (/ (PI) 2))) eps) #s(hole binary64 (* eps (sin (- (* 1/2 (PI)) (* -1 x))))))
#s(approx (sin (+ x (/ (PI) 2))) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (PI) x)) 1)))))
#s(approx (+ (* (PI) 1/2) x) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ (PI) 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 (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (sin (- (* 1/2 (PI)) x)))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (+ (sin (- (* 1/2 (PI)) x)) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (sin (- (* 1/2 (PI)) x))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (sin (- (* 1/2 (PI)) x)) (* -1/2 (* eps (sin x))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (cos x)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* eps (+ 1 (* -1 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))))))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* -1 (* eps (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/24 (pow x 2)))))))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/24 (pow x 2)))))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (sin (- (* 1/2 (PI)) x)) eps)))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* eps (- (/ (sin (- (* 1/2 (PI)) x)) eps) (* 1/2 (sin x))))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* eps (- (/ (cos x) eps) (* 1/2 (sin x))))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) #s(hole binary64 (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (* eps (- (* -1/2 (/ x eps)) 1/2))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (sin (- (* 1/2 (PI)) x)) eps)) (* -1/2 (sin x)))))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (cos x) eps)) (* -1/2 (sin x)))))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) #s(hole binary64 (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))))
#s(approx (- (* -1/2 x) (* 1/2 eps)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) #s(hole binary64 (* -1 (* eps (- (* (pow x 2) (- 1/2 (* 1/24 (pow x 2)))) 1)))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) #s(hole binary64 (* -1 (* eps (* (pow x 2) (- 1/2 (* 1/24 (pow x 2))))))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) #s(hole binary64 (* -1 (* eps (- 1/2 (* 1/24 (pow x 2)))))))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
(.f64 (-.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps)
(.f64 eps (-.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (+.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (pow.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (+.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (pow.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))))
(-.f64 (ratio-square-sum.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (+.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (pow.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) #s(literal 3 binary64)) (+.f64 (pow.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))))) (/.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (+.f64 (pow.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))))))
(-.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))
(+.f64 #s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x))) (.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)))
(sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))
(-.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) (sin.f64 x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 2 binary64)) (.f64 x x))) (neg.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 2 binary64)) (+.f64 (.f64 x x) (.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 2 binary64)) (.f64 x x)) (+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))
(/.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 2 binary64)) (+.f64 (.f64 x x) (.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))))
(-.f64 (ratio-square-sum.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x) (ratio-square-sum.f64 x (.f64 #s(literal 1/2 binary64) (PI.f64))))
(-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (PI.f64) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 2 binary64)) (+.f64 (.f64 x x) (.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) #s(literal 2 binary64)) (+.f64 (.f64 x x) (.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)
(*.f64 #s(literal 1/2 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 1/2 binary64))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) #s(literal 1/2 binary64)))
(PI.f64)
#s(literal 1/2 binary64)
x
(.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 x)) eps)
(.f64 (.f64 #s(literal 1/2 binary64) eps) (sin.f64 x))
(.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps))
(*.f64 (sin.f64 x) eps)
(*.f64 eps (sin.f64 x))
(sin.f64 x)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (sin (+ x (/ (PI) 2))) (+.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) eps))
(.f64 #s(approx (sin (+ x (/ (PI) 2))) (+.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) eps)
(.f64 eps #s(approx (sin (+ x (/ (PI) 2))) (+.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (sin (+ x (/ (PI) 2))) (+.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(+.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(.f64 x (.f64 #s(literal -1/2 binary64) x))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(fabs.f64 (*.f64 x x))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
#s(literal -1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 1 binary64))) eps)
(.f64 eps #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 1 binary64))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 1 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x))))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (.f64 (neg.f64 x) (.f64 #s(literal -1/2 binary64) (+.f64 eps x))))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x))
(.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x)
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#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (.f64 (+.f64 (cos.f64 eps) (-.f64 (.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) x) (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (+.f64 (.f64 (-.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 eps)) #s(literal 1/6 binary64)) x) (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x) (cos.f64 eps)) #s(literal 1 binary64)) x) (sin.f64 eps)))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) eps))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (.f64 eps (+.f64 (.f64 (-.f64 (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) (.f64 #s(literal 1/2 binary64) eps)) eps) (.f64 (.f64 (.f64 eps x) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))) x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) eps)))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 eps x) (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/6 binary64)) (.f64 #s(literal -1/12 binary64) eps))) (.f64 (.f64 #s(literal -1/2 binary64) eps) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))))) x) (.f64 (-.f64 (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) (.f64 #s(literal 1/2 binary64) eps)) eps)) x) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) eps)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (-.f64 (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (+.f64 (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) (.f64 #s(literal 1/2 binary64) eps))) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (-.f64 (+.f64 (.f64 (+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (.f64 (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal 1/6 binary64)) (.f64 #s(literal -1/12 binary64) eps)) x)) x) (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))))) (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))
#s(approx (sin (+ x (/ (PI) 2))) (+.f64 (.f64 (neg.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (sin (+ x (/ (PI) 2))) (+.f64 (.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))))) x) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (sin (+ x (/ (PI) 2))) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))))) x) (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))))) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (sin (- (* (PI) 1/2) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))
#s(approx (sin (- (* (PI) 1/2) x)) (+.f64 (.f64 (neg.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (sin (- (* (PI) 1/2) x)) (+.f64 (.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))))) x) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (sin (- (* (PI) 1/2) x)) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal -1/6 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))))) x) (neg.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))))) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (- (* (PI) 1/2) x) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
#s(approx (- (* (PI) 1/2) x) (-.f64 (neg.f64 x) (*.f64 #s(literal -1/2 binary64) (PI.f64))))
#s(approx x x)
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (.f64 eps x) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/12 binary64)) (*.f64 #s(literal -1/2 binary64) eps)) x))
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/12 binary64) eps) (.f64 #s(literal -1/240 binary64) (.f64 (.f64 x x) eps))) (.f64 x x)) (.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/10080 binary64) (.f64 (.f64 x x) eps)) (.f64 #s(literal -1/240 binary64) eps)) (.f64 x x)) (.f64 #s(literal -1/12 binary64) eps)) (.f64 x x)) (*.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (* (sin x) eps) (*.f64 eps x))
#s(approx (* (sin x) eps) (.f64 (+.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/6 binary64)) eps) x))
#s(approx (* (sin x) eps) (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) eps) (.f64 #s(literal -1/120 binary64) (.f64 (.f64 x x) eps))) (*.f64 x x)) eps) x))
#s(approx (* (sin x) eps) (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.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 (+.f64 (.f64 (*.f64 x x) #s(literal -1/6 binary64)) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (+.f64 (.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 (+.f64 (.f64 (-.f64 (.f64 (+.f64 (.f64 #s(literal -1/5040 binary64) (.f64 x x)) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x)) #s(literal 1 binary64)) x))
#s(approx (* (cos x) eps) eps)
#s(approx (* (cos x) eps) (+.f64 (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) eps))
#s(approx (* (cos x) eps) (+.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps))) eps))
#s(approx (* (cos x) eps) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps)) (.f64 #s(literal -1/24 binary64) eps)) (.f64 x x)) (.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x)) eps))
#s(approx (sin (+ x (/ (PI) 2))) #s(literal 1 binary64))
#s(approx (sin (+ x (/ (PI) 2))) (+.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
#s(approx (sin (+ x (/ (PI) 2))) (+.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal 1 binary64)))
#s(approx (sin (+ x (/ (PI) 2))) (+.f64 (.f64 (-.f64 (.f64 (+.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x)) #s(literal 1 binary64)))
#s(approx (+ (* (* x x) -1/2) 1) #s(literal 1 binary64))
#s(approx (+ (* (* x x) -1/2) 1) (+.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
#s(approx (* (* x x) -1/2) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) eps)
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (+.f64 (.f64 (.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64)) eps))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (.f64 eps x) (.f64 eps eps))) x) eps))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/12 binary64) (.f64 (.f64 eps eps) x))) x) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))) x) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) #s(literal 1 binary64))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 1 binary64)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (+.f64 (.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x) (*.f64 #s(literal 1/2 binary64) eps)) x) #s(literal 1 binary64)))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) #s(literal 1 binary64))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 1 binary64)))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x))
#s(approx (- (* -1/2 x) (* 1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (- (* -1/2 x) (* 1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))
#s(approx (* -1/2 x) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) eps)
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (+.f64 (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) eps))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (+.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps))) eps))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps)))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) eps)))
#s(approx (+ (* (* x x) -1/24) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* (* x x) -1/24) 1/2) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))))
#s(approx (* (* x x) -1/24) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
#s(approx (* (cos x) eps) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) eps))
#s(approx (* (cos x) eps) (.f64 eps (+.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) x) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))))))
#s(approx (* (cos x) eps) (+.f64 (.f64 (+.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) eps) (.f64 (.f64 (.f64 eps x) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/2 binary64))) x) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) eps)))
#s(approx (* (cos x) eps) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 eps x) (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) #s(literal -1/6 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) eps) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))))) x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) eps)) x) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) eps)))
#s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))
#s(approx (sin (+ x (/ (PI) 2))) (+.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (sin (+ x (/ (PI) 2))) (+.f64 (.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) x) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (sin (+ x (/ (PI) 2))) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))))) x) (cos.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))) x) (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))))
#s(approx (+ x (/ (PI) 2)) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
#s(approx (+ x (/ (PI) 2)) (+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))
#s(approx (+ (* (PI) 1/2) x) (*.f64 #s(literal 1/2 binary64) (PI.f64)))
#s(approx (+ (* (PI) 1/2) x) (+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (-.f64 (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)))
#s(approx (sin (- (* (PI) 1/2) x)) (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)))
#s(approx (- (* (PI) 1/2) x) (neg.f64 x))
#s(approx (- (* (PI) 1/2) x) (.f64 (-.f64 (.f64 (/.f64 (PI.f64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
#s(approx (* 1/2 (* (sin x) eps)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64)))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps))
#s(approx (sin (+ x (/ (PI) 2))) (cos.f64 x))
#s(approx (+ (* (* x x) -1/2) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* x x) -1/2) 1) (.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (-.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (.f64 (+.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) (*.f64 x x)))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) (.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (- (* -1/2 x) (* 1/2 eps)) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (- (* -1/2 x) (* 1/2 eps)) (.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) x))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) eps) #s(literal 1/24 binary64)))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (.f64 (-.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/24 binary64) eps)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (.f64 (-.f64 (+.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))) (.f64 #s(literal -1/24 binary64) eps)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) eps) #s(literal 1/24 binary64)))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (.f64 (-.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/24 binary64) eps)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) eps)))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 (-.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/24 binary64) eps)) (*.f64 x x)))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) (.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) eps)))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) (.f64 (-.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/24 binary64) eps)) (*.f64 x x)))
#s(approx (+ (* (* x x) -1/24) 1/2) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
#s(approx (+ (* (* x x) -1/24) 1/2) (.f64 (-.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/24 binary64)) (*.f64 x x)))
#s(approx (* (cos x) eps) (.f64 (sin.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x)) eps))
#s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)))
#s(approx (+ x (/ (PI) 2)) x)
#s(approx (+ x (/ (PI) 2)) (.f64 (+.f64 (.f64 (/.f64 (PI.f64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
#s(approx (+ (* (PI) 1/2) x) x)
#s(approx (+ (* (PI) 1/2) x) (.f64 (+.f64 (.f64 (/.f64 (PI.f64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (sin.f64 (-.f64 (neg.f64 x) (.f64 #s(literal -1/2 binary64) (PI.f64)))) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (-.f64 (sin.f64 (-.f64 (neg.f64 x) (.f64 #s(literal -1/2 binary64) (PI.f64)))) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (neg.f64 x) (*.f64 #s(literal -1/2 binary64) (PI.f64)))))
#s(approx (sin (- (* (PI) 1/2) x)) (sin.f64 (-.f64 (neg.f64 x) (*.f64 #s(literal -1/2 binary64) (PI.f64)))))
#s(approx (- (* (PI) 1/2) x) (.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (PI.f64) x) #s(literal 1/2 binary64)))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (pow.f64 x #s(literal -1 binary64))) x)) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (- (* -1/2 x) (* 1/2 eps)) (.f64 (neg.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 (/.f64 eps x) #s(literal -1/2 binary64)))))
#s(approx (* (cos x) eps) (.f64 (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) (neg.f64 x))) eps))
#s(approx (sin (+ x (/ (PI) 2))) (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (neg.f64 x))))
#s(approx (+ x (/ (PI) 2)) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 (PI.f64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (PI) 1/2) x) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 (PI.f64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 #s(literal 1/6 binary64) (*.f64 (cos.f64 x) eps))) eps) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (.f64 #s(literal -1/24 binary64) (.f64 (sin.f64 x) eps))) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps) (cos.f64 x)) eps))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (.f64 (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x)) eps))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x)) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (-.f64 (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx eps eps)
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (*.f64 (cos.f64 x) eps))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))) eps))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (cos.f64 x))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (-.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/2 binary64))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (+.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (+.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (.f64 eps x) (*.f64 x x))) #s(literal 1 binary64)))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) (.f64 #s(literal -1/2 binary64) (+.f64 (.f64 eps x) (*.f64 x x))))
#s(approx (- (* -1/2 x) (* 1/2 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))
#s(approx (* 1/2 eps) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (.f64 (+.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))) (*.f64 x x))) #s(literal 1 binary64)) eps))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (.f64 (neg.f64 eps) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))) (*.f64 x x))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))) (neg.f64 eps)))
#s(approx (* (neg eps) (+ (* (* x x) -1/24) 1/2)) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))) (neg.f64 eps)))
#s(approx (neg eps) (neg.f64 eps))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (/.f64 (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x)) eps) (.f64 #s(literal 1/2 binary64) (sin.f64 x))) (.f64 eps eps)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 (-.f64 (/.f64 (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x)) eps) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (* (- (sin (+ (neg x) (/ (PI) 2))) (* 1/2 (* (sin x) eps))) eps) (.f64 (-.f64 (/.f64 (cos.f64 x) eps) (.f64 #s(literal 1/2 binary64) (sin.f64 x))) (*.f64 eps eps)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 (-.f64 (/.f64 (cos.f64 x) eps) (.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (.f64 (+.f64 (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps) (.f64 #s(literal -1/2 binary64) x)) eps))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))) eps))
#s(approx (- (* -1/2 x) (* 1/2 eps)) (.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x)) eps)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
#s(approx (- (cos x) (* 1/2 (* (sin x) eps))) (.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (cos.f64 x) eps)) (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
#s(approx (+ (* (- (* -1/2 x) (* 1/2 eps)) x) 1) (.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps)) (.f64 #s(literal -1/2 binary64) x))))
#s(approx (* (- (* -1/2 x) (* 1/2 eps)) x) (.f64 (neg.f64 eps) (.f64 #s(literal 1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))))
#s(approx (- (* -1/2 x) (* 1/2 eps)) (.f64 (neg.f64 eps) (-.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))
#s(approx (+ (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) eps) (.f64 (neg.f64 eps) (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))) (*.f64 x x)) #s(literal 1 binary64))))
#s(approx (* (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (* x x)) (.f64 (neg.f64 eps) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))) (*.f64 x x))))
#s(approx (- (* -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))) (neg.f64 eps)))

eval123.0ms (1.6%)

Memory

-5.7MiB live, 188.2MiB allocated; 18ms collecting garbage

Samples

60.0ms

1 280×

valid

Compiler

Compiled 16 007 to 2 280 computations (85.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-div: 14.0ms (44.8% of total)

ival-mult: 9.0ms (28.8% of total)

ival-add: 6.0ms (19.2% of total)

ival-true: 1.0ms (3.2% of total)

ival-assert: 1.0ms (3.2% of total)

adjust: 0.0ms (0% of total)

prune23.0ms (0.3%)

Memory

-1.4MiB live, 44.4MiB allocated; 3ms collecting garbage

Pruning

17 alts after pruning (7 fresh and 10 done)

	Pruned	Kept	Total
New	419	2	421
Fresh	1	5	6
Picked	1	4	5
Done	0	6	6
Total	421	17	438

Accuracy

100.0%

Counts

438 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	61.6%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 x) eps))) eps))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 #s(approx (sin x) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/6 binary64)) #s(literal 1 binary64)) x)) eps))) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (sin x) x) eps))) eps))
✓	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (-.f64 #s(approx (sin (+ (neg x) (/ (PI) 2))) (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps))) eps))
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (+.f64 (.f64 (-.f64 (.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))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (+.f64 (.f64 #s(approx (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) (*.f64 #s(literal -1/6 binary64) eps)) eps) (cos.f64 x)) eps))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ x (/ (PI) 2)) (+.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
✓	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x) #s(literal 1 binary64))) eps))
	99.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (- (cos x) ( 1/2 (* (sin x) eps))) (sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (- (* (* (cos x) eps) -1/6) (* 1/2 (sin x))) eps) (cos x)) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64))) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (sin (+ x (/ (PI) 2))) (+.f64 (.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x)) #s(literal 1 binary64))) eps))
✓	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (+.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))) eps))
✓	98.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) eps))
✓	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (+.f64 (.f64 #s(approx (- ( -1/2 eps) (* -1/24 (* (* x x) eps))) (.f64 (neg.f64 eps) (+.f64 (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))) (.f64 x x)) eps)))

Compiler

Compiled 1 004 to 477 computations (52.5% saved)

regimes20.0ms (0.3%)

Memory

21.1MiB live, 21.1MiB allocated; 0ms collecting garbage

Counts

24 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes74.0ms (0.9%)

Memory

-26.3MiB live, 20.7MiB allocated; 2ms collecting garbage

Counts

23 → 1

Calls

Call 1

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

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

Calls

3 calls:

61.0ms	eps
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.2%)

Memory

18.4MiB live, 18.4MiB allocated; 0ms collecting garbage

Counts

20 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes14.0ms (0.2%)

Memory

-34.0MiB live, 16.4MiB allocated; 3ms collecting garbage

Counts

13 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	x
4.0ms	eps
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory

17.8MiB live, 17.8MiB allocated; 0ms collecting garbage

Counts

11 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory

14.5MiB live, 14.5MiB allocated; 0ms collecting garbage

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps
2.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory

-32.3MiB live, 13.4MiB allocated; 3ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0.1%)

Memory

13.4MiB live, 13.4MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.7%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory

9.0MiB live, 9.0MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) eps))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (- (cos x) (* 1/2 (* (sin x) eps))) eps) eps))

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify41.0ms (0.5%)

Memory

-15.1MiB live, 29.1MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	81	216
1	127	214
2	241	214
3	616	214
4	1220	214
5	3433	214

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations264.0ms (3.4%)

Memory

13.1MiB live, 257.1MiB allocated; 21ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 216 to 84 computations (61.1% saved)

preprocess41.0ms (0.5%)

Memory: 15.2MiB live, 62.9MiB allocated; 9ms collecting garbage
Compiler: Compiled 446 to 180 computations (59.6% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze52.0ms (0.7%)

sample5.7s (73.5%)

explain103.0ms (1.3%)

preprocess91.0ms (1.2%)

eval0.0ms (0%)

prune0.0ms (0%)

series5.0ms (0.1%)

rewrite135.0ms (1.7%)

eval104.0ms (1.3%)

prune3.0ms (0%)

series27.0ms (0.3%)

rewrite201.0ms (2.6%)

eval64.0ms (0.8%)

prune17.0ms (0.2%)

series42.0ms (0.5%)

rewrite209.0ms (2.7%)

eval103.0ms (1.3%)

prune17.0ms (0.2%)

series69.0ms (0.9%)

rewrite170.0ms (2.2%)

eval123.0ms (1.6%)

prune23.0ms (0.3%)

regimes20.0ms (0.3%)

regimes74.0ms (0.9%)

regimes16.0ms (0.2%)

regimes14.0ms (0.2%)

regimes10.0ms (0.1%)

regimes8.0ms (0.1%)

regimes10.0ms (0.1%)

regimes6.0ms (0.1%)

regimes3.0ms (0%)

simplify41.0ms (0.5%)

derivations264.0ms (3.4%)

preprocess41.0ms (0.5%)

end0.0ms (0%)

Profiling