Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

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

analyze892.0ms (5.8%)

Memory

-391.1MiB live, 290.0MiB allocated; 1.1s 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)

sample8.2s (52.8%)

Memory

147.0MiB live, 7 243.7MiB allocated; 1.3s collecting garbage

Samples

3.3s	26 083×	0	invalid
2.6s	5 745×	2	valid
454.0ms	2 452×	1	valid
7.0ms	59×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 5.0s

ival-cos: 2.1s (41.5% of total)

const: 772.0ms (15.6% of total)

adjust: 457.0ms (9.2% of total)

ival-mult: 320.0ms (6.5% of total)

ival-sub: 301.0ms (6.1% of total)

ival-fabs: 243.0ms (4.9% of total)

ival-<=: 242.0ms (4.9% of total)

ival-add: 209.0ms (4.2% of total)

ival-<: 196.0ms (4% of total)

ival-and: 106.0ms (2.1% of total)

exact: 42.0ms (0.8% of total)

ival-assert: 12.0ms (0.2% of total)

Bogosity

explain472.0ms (3.1%)

Memory

-10.4MiB live, 238.5MiB allocated; 26ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
133	-	1	(-1088.7057802173151 0.003532199836189002)	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
2	-	0	-	`(cos.f64 (+.f64 x eps))`
0	-	0	-	`eps`
0	-	0	-	`(+.f64 x eps)`
0	-	0	-	`(cos.f64 x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	132	1
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	134	0
-	0	122

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	134	0	0
-	0	0	122

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	122
1	134

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

274.0ms	376×	2	valid
17.0ms	126×	1	valid
1.0ms	10×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 267.0ms

ival-sub: 128.0ms (47.9% of total)

ival-cos: 110.0ms (41.2% of total)

adjust: 25.0ms (9.4% of total)

ival-add: 4.0ms (1.5% of total)

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

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

preprocess265.0ms (1.7%)

Memory

-2.4MiB live, 136.9MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	46	41
2	86	41
3	117	41
4	125	41
5	147	41
6	231	41
7	792	41
8	5144	41
0	6	7
0	10	7
1	22	7
2	40	7
3	65	7
4	78	7
5	100	7
6	184	7
7	742	7
8	5073	7
0	8505	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.6%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify191.0ms (1.2%)

Memory

-48.0MiB live, 107.8MiB allocated; 33ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(cos.f64 x)
cost-diff	0	(+.f64 x eps)
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	22	18
2	40	18
3	65	18
4	78	18
5	100	18
6	184	18
7	742	18
8	5073	18
0	8505	18

Stop Event

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

Calls

Call 1

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

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

localize143.0ms (0.9%)

Memory

4.7MiB live, 141.2MiB allocated; 48ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(cos.f64 x)
accuracy	0.06766735772491772	(cos.f64 (+.f64 x eps))
accuracy	29.577512446929912	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

116.0ms	188×	2	valid
9.0ms	63×	1	valid
0.0ms	5×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 112.0ms

ival-cos: 81.0ms (72% of total)

ival-sub: 17.0ms (15.1% of total)

adjust: 13.0ms (11.6% of total)

ival-add: 2.0ms (1.8% of total)

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

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

series4.0ms (0%)

Memory

5.7MiB live, 5.7MiB allocated; 0ms collecting garbage

Counts

4 → 34

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	eps	@	-inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
0.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))

simplify146.0ms (0.9%)

Memory

13.9MiB live, 146.6MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	142	484
1	351	481
2	858	481
3	2728	480
4	6540	480
0	8083	460

Stop Event

1×	iter limit
1×	node limit

Counts

34 → 34

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos x)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

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

rewrite142.0ms (0.9%)

Memory

7.1MiB live, 56.6MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	62	16
2	615	16
0	8141	16

Stop Event

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

Counts

4 → 138

Calls

Call 1

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

Outputs
(.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))))))
(.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))))))
(.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64))))))
(.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))))
(.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))))))
(.f64 (.f64 #s(literal -2 binary64) (sin.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 (sin.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 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 (neg.f64 x))) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 (neg.f64 x))) #s(literal 2 binary64)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 x)) #s(literal 2 binary64)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 eps x))) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 eps x))) x) #s(literal 2 binary64)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 (neg.f64 x))) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 (neg.f64 x))) #s(literal 2 binary64)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) (neg.f64 (neg.f64 x))) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) (neg.f64 (neg.f64 x))) #s(literal 2 binary64)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64)))))
(.f64 #s(literal -2 binary64) (.f64 (sin.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 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))) (.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))))) (.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))))) (+.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (fma.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (*.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (fma.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (*.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))))))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (fma.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))))
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(fma.f64 (/.f64 (neg.f64 (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))))) (/.f64 (.f64 (neg.f64 (cos.f64 x)) (cos.f64 x)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(fma.f64 (/.f64 (neg.f64 (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))))) (/.f64 (.f64 (neg.f64 (cos.f64 x)) (cos.f64 x)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
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(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 x eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps eps (-.f64 (.f64 x x) (.f64 eps x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (.f64 x x) (.f64 eps x))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (.f64 x x) (.f64 eps x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (.f64 x x) (.f64 eps x)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (.f64 x x) (.f64 eps x)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (.f64 x x) (.f64 eps x)))))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(+.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(+.f64 eps x)
(+.f64 x eps)
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (.f64 (sin.f64 x) #s(literal 0 binary64))) (.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))))
(/.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))) (fma.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))))))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(sin.f64 (+.f64 (neg.f64 (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(cos.f64 (neg.f64 (neg.f64 (neg.f64 x))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64)))

eval21.0ms (0.1%)

Memory: -31.6MiB live, 15.9MiB allocated; 4ms collecting garbage
Compiler: Compiled 4 808 to 719 computations (85% saved)

prune11.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	149	15	164
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	149	16	165

Accuracy

99.7%

Counts

165 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.8%	(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
	53.8%	(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
	53.6%	(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
✓	53.6%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	52.4%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
	52.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
▶	51.7%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	51.3%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	83.6%	(.f64 (.f64 (sin.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))
▶	54.0%	(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))))
	53.8%	(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
▶	51.3%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
▶	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
▶	99.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	98.8%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	76.5%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 649 to 404 computations (37.8% saved)

simplify124.0ms (0.8%)

Memory

3.6MiB live, 48.3MiB allocated; 5ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	2	(/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))
cost-diff	2	(cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))
cost-diff	3	(+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
cost-diff	8	(-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
cost-diff	0	(*.f64 (cos.f64 x) eps)
cost-diff	0	(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
cost-diff	0	(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
cost-diff	0	#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
cost-diff	0	(-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
cost-diff	0	(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
cost-diff	1	(fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	449
0	89	449
1	161	449
2	386	409
3	1207	399
4	3784	377
0	8556	371

Stop Event

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

Calls

Call 1

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

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

localize411.0ms (2.7%)

Memory

-9.5MiB live, 134.6MiB allocated; 13ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.13671875	(*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))))
accuracy	0.9687264153926188	(PI.f64)
accuracy	57.18472744862802	(-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
accuracy	57.922604848898104	(cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))
accuracy	0.0078125	(*.f64 (cos.f64 x) eps)
accuracy	0.015625	(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
accuracy	0.12890625	(.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
accuracy	0.8717615398920326	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
accuracy	0.0	(*.f64 x x)
accuracy	0.06766735772491772	(cos.f64 (+.f64 x eps))
accuracy	1.39891919401581	#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	29.103138305964006	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
accuracy	0.0	(cos.f64 eps)
accuracy	28.54909447308266	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	29.992695512456148	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	0.13671875	(.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
accuracy	0.3359375	(.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))
accuracy	0.36328125	(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
accuracy	0.4733026459488449	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))

Samples

280.0ms	184×	2	valid
62.0ms	62×	1	valid
13.0ms	4×	5	exit
6.0ms	2×	3	valid
1.0ms	4×	0	valid

Compiler

Compiled 408 to 48 computations (88.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 307.0ms

ival-cos: 112.0ms (36.5% of total)

adjust: 70.0ms (22.8% of total)

ival-mult: 55.0ms (17.9% of total)

ival-add: 19.0ms (6.2% of total)

ival-sin: 13.0ms (4.2% of total)

ival-sub: 11.0ms (3.6% of total)

ival-div: 11.0ms (3.6% of total)

const: 10.0ms (3.3% of total)

ival-neg: 2.0ms (0.7% of total)

ival-pi: 2.0ms (0.7% of total)

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

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

exact: 0.0ms (0% of total)

series33.0ms (0.2%)

Memory

19.2MiB live, 19.2MiB allocated; 0ms collecting garbage

Counts

24 → 160

Calls

Call 1

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

Outputs
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 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 (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -1 eps)))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (- (* -2 x) eps)))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (- (PI) eps)))
#s(approx (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) #s(hole binary64 (cos (* 1/2 (- (PI) eps)))))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (* 1/2 (- (PI) eps))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* 1/6 x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (* 1/24 eps)))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps)))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (+ (* -1 (* x (* (cos (* -1/2 eps)) (cos (* 1/2 (- (PI) eps)))))) (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps))))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (+ (* x (+ (* -1 (* (cos (* -1/2 eps)) (cos (* 1/2 (- (PI) eps))))) (* -1/2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps))))))) (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps))))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (+ (* x (+ (* -1 (* (cos (* -1/2 eps)) (cos (* 1/2 (- (PI) eps))))) (* x (+ (* -1/2 (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps)))) (* 1/6 (* x (* (cos (* -1/2 eps)) (cos (* 1/2 (- (PI) eps)))))))))) (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (sin x) (* 1/2 (* eps (cos x))))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -2 x)))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* x (- (* -1 (/ eps x)) 2))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 (+ eps (* 2 x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -1 (* x (+ 2 (/ eps x))))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 (- (* -2 x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos x)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (sin x)))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (- (* -1 eps) (* 2 x))))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (PI)))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (+ (PI) (* -1 eps))))
#s(approx (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) #s(hole binary64 (cos (* 1/2 (PI)))))
#s(approx (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) #s(hole binary64 (+ (cos (* 1/2 (PI))) (* 1/2 (* eps (sin (* 1/2 (PI))))))))
#s(approx (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) #s(hole binary64 (+ (cos (* 1/2 (PI))) (* eps (- (* -1/8 (* eps (cos (* 1/2 (PI))))) (* -1/2 (sin (* 1/2 (PI)))))))))
#s(approx (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) #s(hole binary64 (+ (cos (* 1/2 (PI))) (* eps (- (* eps (+ (* -1/8 (cos (* 1/2 (PI)))) (* -1/48 (* eps (sin (* 1/2 (PI))))))) (* -1/2 (sin (* 1/2 (PI)))))))))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (* 1/2 (PI))))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (+ (* -1/2 eps) (* 1/2 (PI)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/6 (sin x))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (* (cos (* 1/2 (PI))) (sin (* -1 x)))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (+ (* eps (+ (* -1/2 (* (cos (* -1 x)) (cos (* 1/2 (PI))))) (* 1/2 (* (sin (* -1 x)) (sin (* 1/2 (PI))))))) (* (cos (* 1/2 (PI))) (sin (* -1 x))))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (+ (* eps (+ (* -1/2 (* (cos (* -1 x)) (cos (* 1/2 (PI))))) (+ (* 1/2 (* (sin (* -1 x)) (sin (* 1/2 (PI))))) (* eps (+ (* -1/4 (* (cos (* -1 x)) (sin (* 1/2 (PI))))) (* -1/4 (* (cos (* 1/2 (PI))) (sin (* -1 x))))))))) (* (cos (* 1/2 (PI))) (sin (* -1 x))))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (+ (* eps (+ (* -1/2 (* (cos (* -1 x)) (cos (* 1/2 (PI))))) (+ (* 1/2 (* (sin (* -1 x)) (sin (* 1/2 (PI))))) (* eps (+ (* -1/4 (* (cos (* -1 x)) (sin (* 1/2 (PI))))) (+ (* -1/4 (* (cos (* 1/2 (PI))) (sin (* -1 x)))) (* eps (+ (* -1/16 (* (sin (* -1 x)) (sin (* 1/2 (PI))))) (+ (* -1/48 (* (sin (* -1 x)) (sin (* 1/2 (PI))))) (+ (* 1/48 (* (cos (* -1 x)) (cos (* 1/2 (PI))))) (* 1/16 (* (cos (* -1 x)) (cos (* 1/2 (PI))))))))))))))) (* (cos (* 1/2 (PI))) (sin (* -1 x))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* eps (- (* -2 (/ x eps)) 1))))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* eps (- (/ (PI) eps) 1))))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (* -1/2 eps)))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (* eps (- (* 1/2 (/ (PI) eps)) 1/2))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -1 (* eps (+ 1 (* 2 (/ x eps)))))))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (PI) eps)))))))
#s(approx (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) #s(hole binary64 (cos (* 1/2 (+ (PI) (* -1 eps))))))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/2 (/ (PI) eps)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (* (cos (* 1/2 (+ (PI) (* -1 eps)))) (sin (* 1/2 (- (* -1 eps) (* 2 x)))))))

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	eps	@	0	((+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (* (cos x) eps) 1/24) (* x x) (PI) (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))))
6.0ms	x	@	inf	((+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (* (cos x) eps) 1/24) (* x x) (PI) (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))))
5.0ms	x	@	0	((+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (* (cos x) eps) 1/24) (* x x) (PI) (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))))
5.0ms	x	@	-inf	((+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (* (cos x) eps) 1/24) (* x x) (PI) (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))))
4.0ms	eps	@	-inf	((+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* (* (cos x) eps) 1/24) (* x x) (PI) (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))))

simplify145.0ms (0.9%)

Memory

12.1MiB live, 55.7MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	662	4570
1	1967	4529
2	7301	4462
0	8070	4204

Stop Event

1×	iter limit
1×	node limit

Counts

160 → 160

Calls

Call 1

Inputs
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 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 (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -1 eps)))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (- (* -2 x) eps)))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (- (PI) eps)))
#s(approx (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) #s(hole binary64 (cos (* 1/2 (- (PI) eps)))))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (* 1/2 (- (PI) eps))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* 1/6 x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (* 1/24 eps)))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps)))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (+ (* -1 (* x (* (cos (* -1/2 eps)) (cos (* 1/2 (- (PI) eps)))))) (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps))))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (+ (* x (+ (* -1 (* (cos (* -1/2 eps)) (cos (* 1/2 (- (PI) eps))))) (* -1/2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps))))))) (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps))))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (+ (* x (+ (* -1 (* (cos (* -1/2 eps)) (cos (* 1/2 (- (PI) eps))))) (* x (+ (* -1/2 (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps)))) (* 1/6 (* x (* (cos (* -1/2 eps)) (cos (* 1/2 (- (PI) eps)))))))))) (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (sin x) (* 1/2 (* eps (cos x))))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -2 x)))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* x (- (* -1 (/ eps x)) 2))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 (+ eps (* 2 x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -1 (* x (+ 2 (/ eps x))))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 (- (* -2 x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos x)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (sin x)))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (- (* -1 eps) (* 2 x))))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (PI)))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (+ (PI) (* -1 eps))))
#s(approx (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) #s(hole binary64 (cos (* 1/2 (PI)))))
#s(approx (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) #s(hole binary64 (+ (cos (* 1/2 (PI))) (* 1/2 (* eps (sin (* 1/2 (PI))))))))
#s(approx (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) #s(hole binary64 (+ (cos (* 1/2 (PI))) (* eps (- (* -1/8 (* eps (cos (* 1/2 (PI))))) (* -1/2 (sin (* 1/2 (PI)))))))))
#s(approx (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) #s(hole binary64 (+ (cos (* 1/2 (PI))) (* eps (- (* eps (+ (* -1/8 (cos (* 1/2 (PI)))) (* -1/48 (* eps (sin (* 1/2 (PI))))))) (* -1/2 (sin (* 1/2 (PI)))))))))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (* 1/2 (PI))))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (+ (* -1/2 eps) (* 1/2 (PI)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/6 (sin x))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (* (cos (* 1/2 (PI))) (sin (* -1 x)))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (+ (* eps (+ (* -1/2 (* (cos (* -1 x)) (cos (* 1/2 (PI))))) (* 1/2 (* (sin (* -1 x)) (sin (* 1/2 (PI))))))) (* (cos (* 1/2 (PI))) (sin (* -1 x))))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (+ (* eps (+ (* -1/2 (* (cos (* -1 x)) (cos (* 1/2 (PI))))) (+ (* 1/2 (* (sin (* -1 x)) (sin (* 1/2 (PI))))) (* eps (+ (* -1/4 (* (cos (* -1 x)) (sin (* 1/2 (PI))))) (* -1/4 (* (cos (* 1/2 (PI))) (sin (* -1 x))))))))) (* (cos (* 1/2 (PI))) (sin (* -1 x))))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (+ (* eps (+ (* -1/2 (* (cos (* -1 x)) (cos (* 1/2 (PI))))) (+ (* 1/2 (* (sin (* -1 x)) (sin (* 1/2 (PI))))) (* eps (+ (* -1/4 (* (cos (* -1 x)) (sin (* 1/2 (PI))))) (+ (* -1/4 (* (cos (* 1/2 (PI))) (sin (* -1 x)))) (* eps (+ (* -1/16 (* (sin (* -1 x)) (sin (* 1/2 (PI))))) (+ (* -1/48 (* (sin (* -1 x)) (sin (* 1/2 (PI))))) (+ (* 1/48 (* (cos (* -1 x)) (cos (* 1/2 (PI))))) (* 1/16 (* (cos (* -1 x)) (cos (* 1/2 (PI))))))))))))))) (* (cos (* 1/2 (PI))) (sin (* -1 x))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* eps (- (* -2 (/ x eps)) 1))))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* eps (- (/ (PI) eps) 1))))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (* -1/2 eps)))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (* eps (- (* 1/2 (/ (PI) eps)) 1/2))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -1 (* eps (+ 1 (* 2 (/ x eps)))))))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (PI) eps)))))))
#s(approx (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) #s(hole binary64 (cos (* 1/2 (+ (PI) (* -1 eps))))))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/2 (/ (PI) eps)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (* (cos (* 1/2 (+ (PI) (* -1 eps)))) (sin (* 1/2 (- (* -1 eps) (* 2 x)))))))

Outputs
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64))) x (.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (.f64 (-.f64 (.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps) x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (.f64 (.f64 eps x) eps) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
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#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* x x) (*.f64 x x))
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#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (+ (* -1 (* x (* (cos (* -1/2 eps)) (cos (* 1/2 (- (PI) eps)))))) (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps))))))
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#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (+ (* x (+ (* -1 (* (cos (* -1/2 eps)) (cos (* 1/2 (- (PI) eps))))) (* x (+ (* -1/2 (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps)))) (* 1/6 (* x (* (cos (* -1/2 eps)) (cos (* 1/2 (- (PI) eps)))))))))) (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 eps))))))
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#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
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#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
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#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x))))
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#s(approx (+ x eps) x)
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#s(approx (+ x eps) (fma.f64 (/.f64 eps x) x x))
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#s(approx (cos x) (cos.f64 x))
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#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -2 x)))
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#s(approx (* (* (cos x) eps) 1/24) #s(hole binary64 (* 1/24 (* eps (cos x)))))
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#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (* (cos (* 1/2 (- (PI) eps))) (sin (* -1/2 (+ eps (* 2 x)))))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) (.f64 (sin.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64)))))
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#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/24 binary64)) (cos.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (+.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/24 binary64)) (cos.f64 x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (+.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 3 binary64))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos eps) 1) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (cos eps) (cos.f64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (.f64 (.f64 (*.f64 (cos.f64 x) eps) eps) #s(literal -1/2 binary64)))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (.f64 eps eps)))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 x) eps)))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* eps (- (* -2 (/ x eps)) 1))))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64)) eps))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (neg.f64 eps))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* eps (- (/ (PI) eps) 1))))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (*.f64 (-.f64 (/.f64 (PI.f64) eps) #s(literal 1 binary64)) eps))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (* -1/2 eps)))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (* eps (- (* 1/2 (/ (PI) eps)) 1/2))))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) (.f64 (-.f64 (.f64 (/.f64 (PI.f64) eps) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) eps))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps)) (*.f64 eps eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (neg.f64 eps)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (neg.f64 eps)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x)))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ x eps) (*.f64 (-.f64 (/.f64 x (neg.f64 eps)) #s(literal 1 binary64)) (neg.f64 eps)))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps)))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -1 (* eps (+ 1 (* 2 (/ x eps)))))))
#s(approx (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) #s(literal 1 binary64)) (neg.f64 eps)))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (PI) eps)))))))
#s(approx (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (PI.f64) eps)) (neg.f64 eps)))
#s(approx (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) #s(hole binary64 (cos (* 1/2 (+ (PI) (* -1 eps))))))
#s(approx (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) #s(hole binary64 (* -1 (* eps (+ 1/2 (* -1/2 (/ (PI) eps)))))))
#s(approx (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2) (*.f64 (fma.f64 (/.f64 (PI.f64) eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (neg.f64 eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (.f64 (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64))) (neg.f64 eps)))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) #s(hole binary64 (* (cos (* 1/2 (+ (PI) (* -1 eps)))) (sin (* 1/2 (- (* -1 eps) (* 2 x)))))))
#s(approx (* (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (neg.f64 eps)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64)))))

rewrite105.0ms (0.7%)

Memory

-7.8MiB live, 38.2MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	297
0	87	297
1	342	297
0	3123	297

Stop Event

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

Counts

24 → 267

Calls

Call 1

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

Outputs
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(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (*.f64 #s(literal -1/6 binary64) (sin.f64 x)))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (*.f64 (neg.f64 (sin.f64 x)) #s(literal 1/6 binary64)))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (.f64 #s(literal 1/6 binary64) (sin.f64 x)))))) (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))))))
(+.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 (neg.f64 (*.f64 (neg.f64 eps) (cos.f64 x))) #s(literal 1/24 binary64)))
(+.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) (.f64 #s(literal 1/24 binary64) (*.f64 eps (cos.f64 x))))
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x))) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(.f64 (.f64 #s(literal 1/24 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal 1/24 binary64) eps) (cos.f64 x))
(.f64 #s(literal 1/24 binary64) (.f64 eps (cos.f64 x)))
(.f64 (.f64 eps (cos.f64 x)) #s(literal 1/24 binary64))
(.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)))
(.f64 (cos.f64 x) (.f64 #s(literal 1/24 binary64) eps))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) 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 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x (neg.f64 x)))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(PI.f64)
(*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x)))) #s(literal -2 binary64))))
(*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x)))) #s(literal -2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (+.f64 (sin.f64 (/.f64 (+.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))))) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))))) #s(literal 2 binary64))))) #s(literal -2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (/.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)) (/.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x)))) #s(literal -2 binary64)))) (sin.f64 (+.f64 (/.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)) (/.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x)))) #s(literal -2 binary64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (/.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)) (/.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x)))) (PI.f64)) #s(literal 2 binary64)))) (cos.f64 (+.f64 (/.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)) (/.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x)))) (PI.f64)) #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (/.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x)))) (PI.f64)) #s(literal 2 binary64)) (/.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))) (cos.f64 (+.f64 (/.f64 (+.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x)))) (PI.f64)) #s(literal 2 binary64)) (/.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (/.f64 (+.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))))) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(+.f64 (/.f64 (sin.f64 (/.f64 (-.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))))) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (sin.f64 (/.f64 (+.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (+.f64 eps x))))) #s(literal 2 binary64))) #s(literal 2 binary64)))

eval84.0ms (0.5%)

Memory: -8.5MiB live, 43.3MiB allocated; 46ms collecting garbage
Compiler: Compiled 17 579 to 2 295 computations (86.9% saved)

prune34.0ms (0.2%)

Memory

-18.3MiB live, 31.9MiB allocated; 4ms collecting garbage

Pruning

35 alts after pruning (33 fresh and 2 done)

	Pruned	Kept	Total
New	399	26	425
Fresh	3	7	10
Picked	4	1	5
Done	0	1	1
Total	406	35	441

Accuracy

100.0%

Counts

441 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.8%	(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
	53.8%	(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
▶	53.6%	(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
✓	53.6%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	52.4%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
	52.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
	83.6%	(.f64 (.f64 (sin.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))
	10.9%	(.f64 #s(literal 2 binary64) #s(approx ( (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) (.f64 (sin.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))))))
	51.3%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
▶	51.2%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/720 binary64) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
▶	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
▶	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
	76.5%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
	97.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
	97.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
▶	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
	97.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
	97.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) (neg.f64 eps)))
	52.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
	52.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
	23.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (+.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 4 binary64)))))
	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (.f64 eps x) #s(literal 1/6 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
	97.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	97.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))

Compiler

Compiled 2 362 to 1 524 computations (35.5% saved)

simplify125.0ms (0.8%)

Memory

14.7MiB live, 66.4MiB allocated; 5ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 x eps)
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
cost-diff	4	(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps)
cost-diff	0	(-.f64 (.f64 #s(approx (+ ( (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x))
cost-diff	0	(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps)))
cost-diff	0	(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
cost-diff	0	#s(approx (cos eps) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
cost-diff	0	(.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
cost-diff	0	(-.f64 (.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
cost-diff	0	(.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	559
0	100	551
1	171	551
2	340	551
3	823	546
4	2248	546
5	6575	546
0	8029	527

Stop Event

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

Calls

Call 1

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

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

localize560.0ms (3.6%)

Memory

7.5MiB live, 337.9MiB allocated; 69ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.06766735772491772	(cos.f64 (+.f64 x eps))
accuracy	0.0755670416083334	(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
accuracy	1.2109080192407735	(PI.f64)
accuracy	29.341576520741267	(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
accuracy	0.13671875	(.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps)
accuracy	0.203125	(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
accuracy	0.4733026459488449	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
accuracy	1.769505835516871	#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
accuracy	0.12890625	(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps))
accuracy	0.3723512816206538	(fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps))
accuracy	0.8717615398920326	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
accuracy	1.3744817712856467	#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps)))
accuracy	0.9269681579281361	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	28.78749415961044	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	30.203018809208782	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
accuracy	0.2265625	(fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal 1/6 binary64) x))
accuracy	0.3515625	(*.f64 #s(literal 1/6 binary64) x)
accuracy	0.4733026459488449	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
accuracy	1.709304907141083	#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal 1/6 binary64) x)))

Samples

421.0ms	183×	2	valid
64.0ms	62×	1	valid
19.0ms	5×	5	exit
4.0ms	1×	3	valid
2.0ms	5×	0	valid

Compiler

Compiled 370 to 52 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 460.0ms

ival-sin: 142.0ms (30.9% of total)

ival-cos: 92.0ms (20% of total)

ival-mult: 82.0ms (17.8% of total)

adjust: 77.0ms (16.7% of total)

ival-add: 29.0ms (6.3% of total)

const: 16.0ms (3.5% of total)

ival-sub: 13.0ms (2.8% of total)

ival-div: 4.0ms (0.9% of total)

ival-pi: 2.0ms (0.4% of total)

exact: 1.0ms (0.2% of total)

ival-neg: 1.0ms (0.2% of total)

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

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

series22.0ms (0.1%)

Memory

19.8MiB live, 19.8MiB allocated; 0ms collecting garbage

Counts

26 → 169

Calls

Call 1

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

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ (/ (PI) 2) x)) #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 (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos eps) (sin (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (+ (cos (* 1/2 (PI))) (sin eps))))) (sin (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (- (* -1/2 (cos eps)) (* -1/2 (sin (* 1/2 (PI)))))) (+ (cos (* 1/2 (PI))) (sin eps))))) (sin (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (cos (* 1/2 (PI)))) (* -1/6 (sin eps))))) (* -1/2 (cos eps))) (* -1/2 (sin (* 1/2 (PI)))))) (+ (cos (* 1/2 (PI))) (sin eps))))) (sin (* 1/2 (PI))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* 1/6 x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))))
#s(approx (* 1/6 x) #s(hole binary64 (* 1/6 x)))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (* 1/24 eps)))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (+ (* 1/24 eps) (* 1/6 x))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1/4 eps)))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (+ (* -1/4 eps) (* -1/6 x))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (sin x) (* 1/2 (* eps (cos x))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1/6 (pow x 3))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ (* -1/4 (/ eps x)) (/ 1 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ (* -1/4 (/ eps x)) (+ (* 1/2 (/ eps (pow x 3))) (/ 1 (pow x 2)))) 1/6))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos (+ eps x)) (sin (+ x (* 1/2 (PI)))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ 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) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (* 1/6 x)))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (* x (+ 1/6 (* 1/24 (/ eps x))))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1/6 x)))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* x (- (* -1/4 (/ eps x)) 1/6))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/6 (* 1/4 (/ eps x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1) x)) (* -1/4 eps)) x)))))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos (- eps (* -1 x))) (sin (- (* 1/2 (PI)) (* -1 x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (* -1 (* x (- (* -1/24 (/ eps x)) 1/6)))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1 (* x (+ 1/6 (* 1/4 (/ eps x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (sin x)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ (* eps (+ 1/2 (* -1/4 (pow x 2)))) (* x (+ 1 (* -1/6 (pow x 2)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos x) (sin (+ x (* 1/2 (PI)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos x) (* -1 (* eps (sin x)))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos x)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/6 (sin x))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (* (* eps eps) 1/24) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/4 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (* eps (+ 1/24 (* 1/6 (/ x eps))))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* eps (- (* -1/6 (/ x eps)) 1/4))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* eps (- (* 1/4 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* eps (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2)))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos (- x (* -1 eps))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (* -1 (* eps (- (* -1/6 (/ x eps)) 1/24)))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1 (* eps (+ 1/4 (* 1/6 (/ x eps)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin (+ (/ (PI) 2) x)) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (cos (+ x eps)) (+ x eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* 1/6 x) (+ (* 1/24 eps) (* 1/6 x)) (+ (* -1/6 x) (* -1/4 eps)) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (* (* eps eps) 1/24) (PI))
3.0ms	eps	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin (+ (/ (PI) 2) x)) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (cos (+ x eps)) (+ x eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* 1/6 x) (+ (* 1/24 eps) (* 1/6 x)) (+ (* -1/6 x) (* -1/4 eps)) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (* (* eps eps) 1/24) (PI))
3.0ms	x	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin (+ (/ (PI) 2) x)) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (cos (+ x eps)) (+ x eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* 1/6 x) (+ (* 1/24 eps) (* 1/6 x)) (+ (* -1/6 x) (* -1/4 eps)) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (* (* eps eps) 1/24) (PI))
3.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin (+ (/ (PI) 2) x)) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (cos (+ x eps)) (+ x eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* 1/6 x) (+ (* 1/24 eps) (* 1/6 x)) (+ (* -1/6 x) (* -1/4 eps)) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (* (* eps eps) 1/24) (PI))
3.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin (+ (/ (PI) 2) x)) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (cos (+ x eps)) (+ x eps) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (* 1/6 x) (+ (* 1/24 eps) (* 1/6 x)) (+ (* -1/6 x) (* -1/4 eps)) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (* (* eps eps) 1/24) (PI))

simplify166.0ms (1.1%)

Memory

-22.9MiB live, 68.0MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	644	4586
1	1847	4544
2	6661	4539
0	8316	4157

Stop Event

1×	iter limit
1×	node limit

Counts

169 → 169

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ (/ (PI) 2) x)) #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 (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos eps) (sin (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (+ (cos (* 1/2 (PI))) (sin eps))))) (sin (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (- (* -1/2 (cos eps)) (* -1/2 (sin (* 1/2 (PI)))))) (+ (cos (* 1/2 (PI))) (sin eps))))) (sin (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (cos (* 1/2 (PI)))) (* -1/6 (sin eps))))) (* -1/2 (cos eps))) (* -1/2 (sin (* 1/2 (PI)))))) (+ (cos (* 1/2 (PI))) (sin eps))))) (sin (* 1/2 (PI))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* 1/6 x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))))
#s(approx (* 1/6 x) #s(hole binary64 (* 1/6 x)))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (* 1/24 eps)))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (+ (* 1/24 eps) (* 1/6 x))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1/4 eps)))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (+ (* -1/4 eps) (* -1/6 x))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (* 1/24 (pow eps 2)) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (sin x) (* 1/2 (* eps (cos x))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1/6 (pow x 3))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ (* -1/4 (/ eps x)) (/ 1 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ (* -1/4 (/ eps x)) (+ (* 1/2 (/ eps (pow x 3))) (/ 1 (pow x 2)))) 1/6))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos (+ eps x)) (sin (+ x (* 1/2 (PI)))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ 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) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (* 1/6 x)))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (* x (+ 1/6 (* 1/24 (/ eps x))))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1/6 x)))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* x (- (* -1/4 (/ eps x)) 1/6))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/6 (* 1/4 (/ eps x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1) x)) (* -1/4 eps)) x)))))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos (- eps (* -1 x))) (sin (- (* 1/2 (PI)) (* -1 x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (* -1 (* x (- (* -1/24 (/ eps x)) 1/6)))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1 (* x (+ 1/6 (* 1/4 (/ eps x)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (sin x)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ (* eps (+ 1/2 (* -1/4 (pow x 2)))) (* x (+ 1 (* -1/6 (pow x 2)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos x) (sin (+ x (* 1/2 (PI)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos x) (* -1 (* eps (sin x)))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos x)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/6 (sin x))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* -1/2 (cos x))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
#s(approx (* (* eps eps) 1/24) #s(hole binary64 (* 1/24 (pow eps 2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (cos eps) #s(hole binary64 (cos eps)))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/4 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (* eps (+ 1/24 (* 1/6 (/ x eps))))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* eps (- (* -1/6 (/ x eps)) 1/4))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* eps (- (* 1/4 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* eps (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2)))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos (- x (* -1 eps))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (* -1 (* eps (- (* -1/6 (/ x eps)) 1/24)))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1 (* eps (+ 1/4 (* 1/6 (/ x eps)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) x) eps (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/6 binary64) (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/36 binary64) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 eps) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps eps) x) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps)))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (fma.f64 #s(literal 1/2 binary64) eps x))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps)))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ (/ (PI) 2) x)) (fma.f64 (cos.f64 (.f64 (PI.f64) #s(literal -1/2 binary64))) x (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))))
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#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) eps)) #s(literal 1/2 binary64)) eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (.f64 #s(literal 1/24 binary64) (.f64 (cos.f64 x) eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) eps))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (* eps (+ 1/24 (* 1/6 (/ x eps))))))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/24 binary64)) eps))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* eps (- (* -1/6 (/ x eps)) 1/4))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/6 binary64)) #s(literal 1/4 binary64)) eps))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* 1/24 (* (pow eps 2) (cos x)))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (.f64 (.f64 (*.f64 (cos.f64 x) eps) eps) #s(literal 1/24 binary64)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (.f64 (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) (cos.f64 x))) eps) eps))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps)) (*.f64 eps eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps)) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/24 binary64) (cos.f64 x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (neg.f64 eps)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (neg.f64 eps)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/24 binary64) (cos.f64 x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (neg.f64 eps)))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* eps (- (* 1/4 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (-.f64 (.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (neg.f64 eps)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* eps (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2)))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (-.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) (neg.f64 eps)) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos (- x (* -1 eps))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x)))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ x eps) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/24 binary64) (cos.f64 x))) (neg.f64 eps)))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) #s(hole binary64 (* -1 (* eps (- (* -1/6 (/ x eps)) 1/24)))))
#s(approx (+ (* 1/24 eps) (* 1/6 x)) (.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/6 binary64)) #s(literal 1/24 binary64)) (neg.f64 eps)))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1 (* eps (+ 1/4 (* 1/6 (/ x eps)))))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)) (neg.f64 eps)))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps)) (*.f64 eps eps)))

rewrite97.0ms (0.6%)

Memory

37.4MiB live, 37.4MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	471
0	100	463
1	391	463
0	3046	445

Stop Event

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

Counts

26 → 191

Calls

Call 1

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

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(.f64 eps (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64))))
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(/.f64 (-.f64 (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 eps) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))))))
(fma.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(sin.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
(-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (sin.f64 eps) (sin.f64 x)))
(cos.f64 (neg.f64 (neg.f64 (+.f64 eps x))))
(cos.f64 (neg.f64 (+.f64 eps x)))
(cos.f64 (+.f64 eps x))
(+.f64 (.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) (.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)))
(+.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(/.f64 (-.f64 (.f64 eps eps) (.f64 x x)) (-.f64 eps x))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 x eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (.f64 x x) (.f64 eps x))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(+.f64 eps x)
(+.f64 x eps)
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal 1/6 binary64) x)))
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 x #s(literal 1/6 binary64))
(/.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (.f64 #s(literal 1/576 binary64) (.f64 eps eps))) (-.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 #s(literal 1/24 binary64) eps)))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) eps) #s(literal 3 binary64)) (.f64 #s(literal -1/216 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1/576 binary64) (.f64 eps eps) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 (.f64 #s(literal 1/24 binary64) eps) (*.f64 #s(literal -1/6 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 eps eps)) (.f64 #s(literal 1/36 binary64) (.f64 x x)))) (neg.f64 (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal -1/6 binary64) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/24 binary64) eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/576 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal 1/6 binary64) x) (-.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 #s(literal 1/24 binary64) eps))))))
(/.f64 (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 eps eps)) (.f64 #s(literal 1/36 binary64) (.f64 x x))) (fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal -1/6 binary64) x)))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/24 binary64) eps) #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 (.f64 #s(literal 1/576 binary64) (.f64 eps eps)) (.f64 (.f64 (*.f64 #s(literal 1/24 binary64) eps) #s(literal 1/6 binary64)) x))))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/24 binary64) eps) #s(literal 3 binary64))) (fma.f64 #s(literal 1/576 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal 1/6 binary64) x) (-.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 #s(literal 1/24 binary64) eps)))))
(fma.f64 #s(literal 1/24 binary64) eps (*.f64 (neg.f64 x) #s(literal -1/6 binary64)))
(fma.f64 #s(literal 1/24 binary64) eps (*.f64 #s(literal 1/6 binary64) x))
(fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/24 binary64) eps))
(fma.f64 eps #s(literal 1/24 binary64) (*.f64 (neg.f64 x) #s(literal -1/6 binary64)))
(fma.f64 eps #s(literal 1/24 binary64) (*.f64 #s(literal 1/6 binary64) x))
(fma.f64 x #s(literal 1/6 binary64) (*.f64 #s(literal 1/24 binary64) eps))
(-.f64 (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 eps eps)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal -1/6 binary64) x))) (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal -1/6 binary64) x))))
(-.f64 (.f64 #s(literal 1/24 binary64) eps) (.f64 (neg.f64 x) #s(literal 1/6 binary64)))
(-.f64 (.f64 #s(literal 1/24 binary64) eps) (.f64 #s(literal -1/6 binary64) x))
(-.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 #s(literal -1/24 binary64) eps))
(-.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 (neg.f64 eps) #s(literal 1/24 binary64)))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/24 binary64) eps) #s(literal 3 binary64)) (fma.f64 #s(literal 1/576 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal 1/6 binary64) x) (-.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 #s(literal 1/24 binary64) eps))))) (/.f64 (.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/576 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal 1/6 binary64) x) (-.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 #s(literal 1/24 binary64) eps))))))
(+.f64 (.f64 #s(literal 1/24 binary64) eps) (.f64 (neg.f64 x) #s(literal -1/6 binary64)))
(+.f64 (.f64 #s(literal 1/24 binary64) eps) (.f64 #s(literal 1/6 binary64) x))
(+.f64 (.f64 #s(literal 1/6 binary64) x) (.f64 #s(literal 1/24 binary64) eps))
(/.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps eps)) (.f64 #s(literal 1/36 binary64) (.f64 x x))) (-.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 #s(literal -1/6 binary64) x)))
(/.f64 (-.f64 (.f64 #s(literal -1/216 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (.f64 #s(literal 1/4 binary64) eps) #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (fma.f64 #s(literal 1/16 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1/6 binary64) x) (*.f64 #s(literal 1/4 binary64) eps)))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (.f64 #s(literal 1/16 binary64) (.f64 eps eps)))) (neg.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/216 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/4 binary64) eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/4 binary64) eps) (-.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 #s(literal -1/6 binary64) x))))))
(/.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (.f64 #s(literal 1/16 binary64) (.f64 eps eps))) (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps)))
(/.f64 (fma.f64 #s(literal -1/216 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/4 binary64) eps) #s(literal 3 binary64))) (fma.f64 #s(literal 1/16 binary64) (.f64 eps eps) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (.f64 (.f64 (*.f64 #s(literal -1/6 binary64) x) #s(literal -1/4 binary64)) eps))))
(/.f64 (fma.f64 #s(literal -1/216 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/4 binary64) eps) #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/4 binary64) eps) (-.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 #s(literal -1/6 binary64) x)))))
(fma.f64 #s(literal -1/4 binary64) eps (*.f64 #s(literal -1/6 binary64) x))
(fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps))
(fma.f64 eps #s(literal -1/4 binary64) (*.f64 #s(literal -1/6 binary64) x))
(fma.f64 x #s(literal -1/6 binary64) (*.f64 #s(literal -1/4 binary64) eps))
(-.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps eps)) (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))))
(-.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 (neg.f64 eps) #s(literal -1/4 binary64)))
(-.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 #s(literal 1/4 binary64) eps))
(-.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 (neg.f64 x) #s(literal -1/6 binary64)))
(-.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 #s(literal 1/6 binary64) x))
(+.f64 (/.f64 (.f64 #s(literal -1/216 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/4 binary64) eps) (-.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 #s(literal -1/6 binary64) x))))) (/.f64 (pow.f64 (.f64 #s(literal -1/4 binary64) eps) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1/4 binary64) eps) (-.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 #s(literal -1/6 binary64) x))))))
(+.f64 (.f64 #s(literal -1/6 binary64) x) (.f64 #s(literal -1/4 binary64) eps))
(+.f64 (.f64 #s(literal -1/4 binary64) eps) (.f64 #s(literal -1/6 binary64) x))
#s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1/24 binary64) (fabs.f64 eps)) (fabs.f64 eps))
(.f64 (.f64 #s(literal 1/24 binary64) (neg.f64 eps)) (neg.f64 eps))
(.f64 (fabs.f64 eps) (.f64 (fabs.f64 eps) #s(literal 1/24 binary64)))
(.f64 (.f64 #s(literal 1/24 binary64) eps) eps)
(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
(.f64 (neg.f64 eps) (.f64 (neg.f64 eps) #s(literal 1/24 binary64)))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(.f64 eps (.f64 #s(literal 1/24 binary64) eps))
(PI.f64)

eval47.0ms (0.3%)

Memory: -12.0MiB live, 42.2MiB allocated; 5ms collecting garbage
Compiler: Compiled 14 225 to 1 796 computations (87.4% saved)

prune64.0ms (0.4%)

Memory

-19.5MiB live, 27.3MiB allocated; 3ms collecting garbage

Pruning

33 alts after pruning (29 fresh and 4 done)

	Pruned	Kept	Total
New	336	10	346
Fresh	9	19	28
Picked	3	2	5
Done	0	2	2
Total	348	33	381

Accuracy

100.0%

Counts

381 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.8%	(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
	53.8%	(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
✓	53.6%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	53.6%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
	52.4%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
▶	52.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
	83.6%	(.f64 (.f64 (sin.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))
	10.9%	(.f64 #s(literal 2 binary64) #s(approx ( (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) (.f64 (sin.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))))))
	51.3%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
✓	51.2%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/720 binary64) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
▶	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(approx (+ (* 1/24 eps) (* 1/6 x)) (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
✓	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
	76.5%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
	97.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
▶	97.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x))) (neg.f64 eps)))
	97.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
	97.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
	52.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
	52.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
▶	52.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
	23.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (+.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 4 binary64)))))
	97.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))

Compiler

Compiled 2 171 to 1 395 computations (35.7% saved)

simplify122.0ms (0.8%)

Memory

17.5MiB live, 64.9MiB allocated; 1ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
cost-diff	0	#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(cos.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
cost-diff	0	(fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps)))
cost-diff	0	(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
cost-diff	0	(*.f64 eps eps)
cost-diff	0	(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
cost-diff	0	#s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
cost-diff	0	(.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
cost-diff	0	(-.f64 (.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
cost-diff	0	(.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	575
0	112	567
1	202	567
2	452	567
3	1220	567
4	3612	567
0	8540	552

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) x (*.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64))
(fma.f64 #s(literal -1/36 binary64) x (*.f64 #s(literal -1/48 binary64) eps))
#s(literal -1/36 binary64)
x
(*.f64 #s(literal -1/48 binary64) eps)
#s(literal -1/48 binary64)
eps
#s(literal 1/6 binary64)
(*.f64 #s(literal 1/24 binary64) eps)
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
(cos.f64 x)
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps)))
(fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))
(fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (*.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) (*.f64 #s(literal -1/6 binary64) x))
(*.f64 #s(literal -1/6 binary64) x)
#s(literal -1/6 binary64)
x
#s(literal 1 binary64)
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(neg.f64 eps)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
#s(literal 1/24 binary64)
(*.f64 x x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) x)
(PI.f64)
#s(literal 1/2 binary64)

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) x (*.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64))
(fma.f64 #s(literal -1/36 binary64) x (*.f64 #s(literal -1/48 binary64) eps))
#s(literal -1/36 binary64)
x
(*.f64 #s(literal -1/48 binary64) eps)
#s(literal -1/48 binary64)
eps
#s(literal 1/6 binary64)
(*.f64 #s(literal 1/24 binary64) eps)
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
(cos.f64 x)
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(.f64 (.f64 #s(literal -1/2 binary64) eps) eps)
(*.f64 eps eps)
eps
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (.f64 x x) #s(approx (+ ( -1/6 x) (* -1/4 eps)) (*.f64 #s(literal -1/6 binary64) x)) (fma.f64 #s(literal 1/2 binary64) eps x)))))
(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps))
(.f64 (neg.f64 eps) #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (.f64 x x) #s(approx (+ ( -1/6 x) (* -1/4 eps)) (*.f64 #s(literal -1/6 binary64) x)) (fma.f64 #s(literal 1/2 binary64) eps x))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps)))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (.f64 x x) #s(approx (+ ( -1/6 x) (* -1/4 eps)) (*.f64 #s(literal -1/6 binary64) x)) (fma.f64 #s(literal 1/2 binary64) eps x)))
(fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (.f64 x x) #s(approx (+ ( -1/6 x) (* -1/4 eps)) (*.f64 #s(literal -1/6 binary64) x)) (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (*.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) (*.f64 #s(literal -1/6 binary64) x))
(*.f64 #s(literal -1/6 binary64) x)
#s(literal -1/6 binary64)
x
#s(literal 1 binary64)
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(neg.f64 eps)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(-.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(cos.f64 (+.f64 x eps))
(cos.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
#s(literal 1/24 binary64)
(*.f64 x x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
(-.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
(cos.f64 (+.f64 x eps))
(cos.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
#s(approx (cos x) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) x)
(PI.f64)
#s(literal 1/2 binary64)

localize643.0ms (4.2%)

Memory

-32.0MiB live, 304.5MiB allocated; 40ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.06766735772491772	(cos.f64 (+.f64 x eps))
accuracy	0.0755670416083334	(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))
accuracy	1.4530896230889283	(PI.f64)
accuracy	29.108411323990804	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
accuracy	0.00390625	(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
accuracy	0.06766735772491772	(cos.f64 (+.f64 x eps))
accuracy	1.2336583110219244	#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	29.108411323990804	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
accuracy	0.3515625	(*.f64 #s(literal -1/6 binary64) x)
accuracy	0.8717615398920326	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
accuracy	1.3744817712856467	#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps)))
accuracy	28.59820273446164	#s(approx (+ (* -1/6 x) (* -1/4 eps)) (*.f64 #s(literal -1/6 binary64) x))
accuracy	0.0	(*.f64 eps eps)
accuracy	0.0078125	(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
accuracy	0.8419384374535545	#s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
accuracy	29.95933106189276	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
accuracy	0.33984375	(*.f64 #s(literal -1/48 binary64) eps)
accuracy	0.35546875	(fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))
accuracy	0.4733026459488449	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
accuracy	1.3807794020301285	#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps)))

Samples

469.0ms	182×	2	valid
75.0ms	61×	1	valid
26.0ms	6×	5	exit
8.0ms	2×	3	valid
2.0ms	5×	0	valid

Compiler

Compiled 342 to 66 computations (80.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 508.0ms

ival-sin: 173.0ms (34% of total)

adjust: 112.0ms (22% of total)

ival-cos: 78.0ms (15.3% of total)

ival-mult: 67.0ms (13.2% of total)

ival-add: 29.0ms (5.7% of total)

const: 28.0ms (5.5% of total)

ival-sub: 12.0ms (2.4% of total)

ival-div: 4.0ms (0.8% of total)

ival-pi: 2.0ms (0.4% of total)

exact: 1.0ms (0.2% of total)

ival-neg: 1.0ms (0.2% of total)

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

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

series25.0ms (0.2%)

Memory

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

Counts

26 → 180

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 eps eps)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps)))
(fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
#s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))
(*.f64 #s(literal -1/48 binary64) eps)
#s(approx (+ (* -1/6 x) (* -1/4 eps)) (*.f64 #s(literal -1/6 binary64) x))
(*.f64 #s(literal -1/6 binary64) x)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(PI.f64)
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos eps) (sin (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (+ (cos (* 1/2 (PI))) (sin eps))))) (sin (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (- (* -1/2 (cos eps)) (* -1/2 (sin (* 1/2 (PI)))))) (+ (cos (* 1/2 (PI))) (sin eps))))) (sin (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (cos (* 1/2 (PI)))) (* -1/6 (sin eps))))) (* -1/2 (cos eps))) (* -1/2 (sin (* 1/2 (PI)))))) (+ (cos (* 1/2 (PI))) (sin eps))))) (sin (* 1/2 (PI))))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ (/ (PI) 2) x)) #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 (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* 1/6 x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* 1/24 eps)))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (+ (* 1/24 eps) (* 1/6 x))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1/4 eps)))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (+ (* -1/4 eps) (* -1/6 x))))
#s(approx (* -1/6 x) #s(hole binary64 (* -1/6 x)))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(hole binary64 -1/2))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(hole binary64 (- (* 1/24 (pow x 2)) 1/2)))
#s(approx (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))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ (* (PI) 1/2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (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 (+ (cos (* 1/2 (PI))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* -1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (sin x) (* 1/2 (* eps (cos x))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1/6 (pow x 3))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ (* -1/4 (/ eps x)) (/ 1 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ (* -1/4 (/ eps x)) (+ (* 1/2 (/ eps (pow x 3))) (/ 1 (pow x 2)))) 1/6))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos (+ eps x)) (sin (+ x (* 1/2 (PI)))))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* -1/36 (pow x 3))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* (pow x 3) (- (* -1/48 (/ eps x)) 1/36))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* (pow x 3) (- (+ (* -1/48 (/ eps x)) (/ 1/6 (pow x 2))) 1/36))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* (pow x 3) (- (+ (* -1/48 (/ eps x)) (+ (* 1/24 (/ eps (pow x 3))) (/ 1/6 (pow x 2)))) 1/36))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1/6 x)))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* x (- (* -1/4 (/ eps x)) 1/6))))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(hole binary64 (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sin (+ (* (PI) 1/2) x)) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/6 (* 1/4 (/ eps x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1) x)) (* -1/4 eps)) x)))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos (- eps (* -1 x))) (sin (- (* 1/2 (PI)) (* -1 x))))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/36 (* 1/48 (/ eps x)))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/36 (* -1 (/ (+ (* -1/48 eps) (* 1/6 (/ 1 x))) x)))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/36 (* -1 (/ (+ (* -1 (/ (- (* -1/24 (/ eps x)) 1/6) x)) (* -1/48 eps)) x)))))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1 (* x (+ 1/6 (* 1/4 (/ eps x)))))))
#s(approx (sin (+ (* (PI) 1/2) x)) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (* (* eps eps) -1/2) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (sin x)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ (* eps (+ 1/2 (* -1/4 (pow x 2)))) (* x (+ 1 (* -1/6 (pow x 2)))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos x)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos x) (sin (+ x (* 1/2 (PI)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos x) (* -1 (* eps (sin x)))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/6 (sin x))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* x (+ 1/6 (* -1/36 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (+ (* eps (+ 1/24 (* -1/48 (pow x 2)))) (* x (+ 1/6 (* -1/36 (pow x 2)))))))
#s(approx (* -1/48 eps) #s(hole binary64 (* -1/48 eps)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/4 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* eps (+ 1/24 (* -1/48 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* eps (+ 1/24 (+ (* -1/48 (pow x 2)) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps))))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* eps (- (* -1/6 (/ x eps)) 1/4))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* eps (- (* 1/4 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* eps (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos (- x (* -1 eps))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* -1 (* eps (- (* 1/48 (pow x 2)) 1/24)))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* -1 (* eps (- (+ (* -1 (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)) (* 1/48 (pow x 2))) 1/24)))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1 (* eps (+ 1/4 (* 1/6 (/ x eps)))))))

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (* (* eps eps) -1/2) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (sin (+ (/ (PI) 2) x)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) (* -1/48 eps) (+ (* -1/6 x) (* -1/4 eps)) (* -1/6 x) (+ (* 1/24 (* x x)) -1/2) (PI) (sin (+ (* (PI) 1/2) x)))
4.0ms	eps	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (* (* eps eps) -1/2) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (sin (+ (/ (PI) 2) x)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) (* -1/48 eps) (+ (* -1/6 x) (* -1/4 eps)) (* -1/6 x) (+ (* 1/24 (* x x)) -1/2) (PI) (sin (+ (* (PI) 1/2) x)))
4.0ms	eps	@	-inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (* (* eps eps) -1/2) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (sin (+ (/ (PI) 2) x)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) (* -1/48 eps) (+ (* -1/6 x) (* -1/4 eps)) (* -1/6 x) (+ (* 1/24 (* x x)) -1/2) (PI) (sin (+ (* (PI) 1/2) x)))
3.0ms	x	@	inf	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (* (* eps eps) -1/2) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (sin (+ (/ (PI) 2) x)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) (* -1/48 eps) (+ (* -1/6 x) (* -1/4 eps)) (* -1/6 x) (+ (* 1/24 (* x x)) -1/2) (PI) (sin (+ (* (PI) 1/2) x)))
3.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (* (* eps eps) -1/2) (* eps eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (sin (+ (/ (PI) 2) x)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) (* -1/48 eps) (+ (* -1/6 x) (* -1/4 eps)) (* -1/6 x) (+ (* 1/24 (* x x)) -1/2) (PI) (sin (+ (* (PI) 1/2) x)))

simplify154.0ms (1%)

Memory

13.3MiB live, 103.8MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	702	4830
1	1985	4786
2	7339	4780
0	8321	4334

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ x (* 1/2 eps))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos eps) (sin (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (+ (cos (* 1/2 (PI))) (sin eps))))) (sin (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (- (* -1/2 (cos eps)) (* -1/2 (sin (* 1/2 (PI)))))) (+ (cos (* 1/2 (PI))) (sin eps))))) (sin (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (cos (* 1/2 (PI)))) (* -1/6 (sin eps))))) (* -1/2 (cos eps))) (* -1/2 (sin (* 1/2 (PI)))))) (+ (cos (* 1/2 (PI))) (sin eps))))) (sin (* 1/2 (PI))))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (sin (* 1/2 (PI)))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (cos (* 1/2 (PI))) (* -1/2 (* x (sin (* 1/2 (PI))))))))))
#s(approx (sin (+ (/ (PI) 2) x)) #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 (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 eps)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* 1/6 x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* 1/24 eps)))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (+ (* 1/24 eps) (* 1/6 x))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1/4 eps)))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (+ (* -1/4 eps) (* -1/6 x))))
#s(approx (* -1/6 x) #s(hole binary64 (* -1/6 x)))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(hole binary64 -1/2))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(hole binary64 (- (* 1/24 (pow x 2)) 1/2)))
#s(approx (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))) (* x (cos (* 1/2 (PI)))))))
#s(approx (sin (+ (* (PI) 1/2) x)) #s(hole binary64 (+ (sin (* 1/2 (PI))) (* x (+ (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 (+ (cos (* 1/2 (PI))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* -1/6 (* x (cos (* 1/2 (PI))))))))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (+ eps x)) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (+ (sin x) (* 1/2 (* eps (cos x))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1/6 (pow x 3))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ (* -1/4 (/ eps x)) (/ 1 (pow x 2))) 1/6))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* (pow x 3) (- (+ (* -1/4 (/ eps x)) (+ (* 1/2 (/ eps (pow x 3))) (/ 1 (pow x 2)))) 1/6))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos (+ eps x)) (sin (+ x (* 1/2 (PI)))))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* -1/36 (pow x 3))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* (pow x 3) (- (* -1/48 (/ eps x)) 1/36))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* (pow x 3) (- (+ (* -1/48 (/ eps x)) (/ 1/6 (pow x 2))) 1/36))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* (pow x 3) (- (+ (* -1/48 (/ eps x)) (+ (* 1/24 (/ eps (pow x 3))) (/ 1/6 (pow x 2)))) 1/36))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1/6 x)))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* x (- (* -1/4 (/ eps x)) 1/6))))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* 1/24 (* x x)) -1/2) #s(hole binary64 (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sin (+ (* (PI) 1/2) x)) #s(hole binary64 (sin (+ x (* 1/2 (PI))))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- eps (* -1 x))) (cos x))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/6 (* 1/4 (/ eps x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ eps x)) 1) x)) (* -1/4 eps)) x)))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos (- eps (* -1 x))) (sin (- (* 1/2 (PI)) (* -1 x))))))
#s(approx (sin (+ (/ (PI) 2) x)) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/36 (* 1/48 (/ eps x)))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/36 (* -1 (/ (+ (* -1/48 eps) (* 1/6 (/ 1 x))) x)))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* -1 (* (pow x 3) (+ 1/36 (* -1 (/ (+ (* -1 (/ (- (* -1/24 (/ eps x)) 1/6) x)) (* -1/48 eps)) x)))))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1 (* x (+ 1/6 (* 1/4 (/ eps x)))))))
#s(approx (sin (+ (* (PI) 1/2) x)) #s(hole binary64 (sin (- (* 1/2 (PI)) (* -1 x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* -1/2 (* eps (cos x))) (sin x))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1/2 (* eps (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))))
#s(approx (- (cos eps) 1) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))))
#s(approx (* (* eps eps) -1/2) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1 (* eps (sin x)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (sin x)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (+ (* eps (+ 1/2 (* -1/4 (pow x 2)))) (* x (+ 1 (* -1/6 (pow x 2)))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos x)))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* -1 (* eps (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))))
#s(approx (cos (+ x eps)) #s(hole binary64 (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos x) (sin (+ x (* 1/2 (PI)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos x) (* -1 (* eps (sin x)))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/6 (sin x))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* x (+ 1/6 (* -1/36 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (+ (* eps (+ 1/24 (* -1/48 (pow x 2)))) (* x (+ 1/6 (* -1/36 (pow x 2)))))))
#s(approx (* -1/48 eps) #s(hole binary64 (* -1/48 eps)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* 1/24 (* (pow eps 4) (cos x)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* 1/24 (* (pow eps 3) (cos x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))))
#s(approx (- (cos eps) 1) #s(hole binary64 (- (cos eps) 1)))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* -1/2 (* (pow eps 2) (cos x)))))
#s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* 1/2 (* eps (cos x)))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* -1/4 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (+ (* -1/4 (pow x 2)) (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* 1/24 (* eps (cos x)))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* eps (+ 1/24 (* -1/48 (pow x 2))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* eps (+ 1/24 (+ (* -1/48 (pow x 2)) (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps))))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* eps (- (* -1/6 (/ x eps)) 1/4))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos (- x (* -1 eps))) (cos x))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* eps (- (* 1/4 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* eps (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2)))))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos (- x (* -1 eps))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* -1 (* eps (- (* 1/48 (pow x 2)) 1/24)))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* -1 (* eps (- (+ (* -1 (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)) (* 1/48 (pow x 2))) 1/24)))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1 (* eps (+ 1/4 (* 1/6 (/ x eps)))))))

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (cos eps) 1)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(hole binary64 (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) x) eps (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) #s(hole binary64 (+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (* eps (- (* 1/24 (pow eps 2)) 1/2))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)))
#s(approx (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) #s(hole binary64 (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))))
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#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/24 binary64) (cos.f64 x)))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))))
#s(approx (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (sin.f64 x))) (neg.f64 eps)))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* eps (- (* 1/4 (pow x 2)) 1/2)))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 eps)))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) #s(hole binary64 (* -1 (* eps (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2)))))
#s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) eps) #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64))) (neg.f64 eps)))
#s(approx (cos (+ x eps)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (cos (+ x eps)) (cos.f64 (+.f64 eps x)))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ x eps) (*.f64 (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1 binary64)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) #s(hole binary64 (- (cos (- x (* -1 eps))) (sin (+ x (* 1/2 (PI)))))))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (-.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(hole binary64 (* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (.f64 (fma.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/24 binary64) (cos.f64 x))) (neg.f64 eps)))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* -1 (* eps (- (* 1/48 (pow x 2)) 1/24)))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) (.f64 (-.f64 (.f64 #s(literal 1/48 binary64) (*.f64 x x)) #s(literal 1/24 binary64)) (neg.f64 eps)))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) #s(hole binary64 (* -1 (* eps (- (+ (* -1 (/ (* x (+ 1/6 (* -1/36 (pow x 2)))) eps)) (* 1/48 (pow x 2))) 1/24)))))
#s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) (.f64 (fma.f64 (neg.f64 x) (/.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) x) x #s(literal 1/6 binary64)) eps) (-.f64 (.f64 #s(literal 1/48 binary64) (.f64 x x)) #s(literal 1/24 binary64))) (neg.f64 eps)))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) #s(hole binary64 (* -1 (* eps (+ 1/4 (* 1/6 (/ x eps)))))))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)) (neg.f64 eps)))

rewrite139.0ms (0.9%)

Memory

-35.0MiB live, 67.3MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	451
0	112	443
1	460	443
0	3791	430

Stop Event

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

Counts

26 → 178

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(-.f64 (.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 eps eps)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
(.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps))
#s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps)))
(fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
#s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
#s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))
(*.f64 #s(literal -1/48 binary64) eps)
#s(approx (+ (* -1/6 x) (* -1/4 eps)) (*.f64 #s(literal -1/6 binary64) x))
(*.f64 #s(literal -1/6 binary64) x)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(PI.f64)
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))

Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(.f64 eps (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64))))
(/.f64 (.f64 eps (-.f64 (pow.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (fma.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
(/.f64 (.f64 eps (-.f64 (pow.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(approx (+ ( (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
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(-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal -1/24 binary64) eps))) (/.f64 (.f64 #s(literal 1/576 binary64) (.f64 eps eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal -1/24 binary64) eps))))
(-.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x) (*.f64 (neg.f64 eps) #s(literal 1/24 binary64)))
(-.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x) (*.f64 #s(literal -1/24 binary64) eps))
(-.f64 (.f64 #s(literal 1/24 binary64) eps) (.f64 (neg.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (*.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64))) x))
(-.f64 (.f64 #s(literal 1/24 binary64) eps) (.f64 (neg.f64 x) (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (*.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x) #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) (-.f64 (.f64 #s(literal 1/24 binary64) eps) (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x)) (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal 1/13824 binary64) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) (-.f64 (.f64 #s(literal 1/24 binary64) eps) (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x)) (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (*.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x) #s(literal 2 binary64)))))
(+.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x) (*.f64 #s(literal 1/24 binary64) eps))
(+.f64 (.f64 #s(literal 1/24 binary64) eps) (.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (*.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x))
(*.f64 #s(literal -1/48 binary64) eps)
(*.f64 eps #s(literal -1/48 binary64))
#s(approx (+ (* -1/6 x) (* -1/4 eps)) (*.f64 #s(literal -1/6 binary64) x))
(*.f64 #s(literal -1/6 binary64) x)
(*.f64 x #s(literal -1/6 binary64))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal -1/8 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (*.f64 x x) #s(literal -1/48 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(/.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (.f64 (*.f64 x x) #s(literal -1/48 binary64)))))
(/.f64 (fma.f64 #s(literal 1/13824 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (*.f64 x x) #s(literal -1/48 binary64))))
(fma.f64 (*.f64 #s(literal 1/24 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal -1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/24 binary64) (neg.f64 x)) (neg.f64 x) #s(literal -1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 x (*.f64 #s(literal 1/24 binary64) x) #s(literal -1/2 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))
(-.f64 #s(literal -1/2 binary64) (.f64 (neg.f64 (.f64 #s(literal 1/24 binary64) x)) x))
(-.f64 #s(literal -1/2 binary64) (.f64 (neg.f64 (.f64 x x)) #s(literal 1/24 binary64)))
(-.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/48 binary64)))) (/.f64 #s(literal -1/8 binary64) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))
(+.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
(PI.f64)
(/.f64 (-.f64 (.f64 (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 x))) (.f64 (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 x)))) (-.f64 (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 x))))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 x)) (-.f64 (.f64 (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 x))) (.f64 (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 x))))))
(fma.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 x) (.f64 (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 x)))
(fma.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 x)))
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))
(-.f64 (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (neg.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 x)) (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 x)))
(+.f64 (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (cos.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 x)))

eval43.0ms (0.3%)

Memory: 35.1MiB live, 35.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 15 955 to 1 828 computations (88.5% saved)

prune40.0ms (0.3%)

Memory

7.8MiB live, 53.0MiB allocated; 4ms collecting garbage

Pruning

32 alts after pruning (26 fresh and 6 done)

	Pruned	Kept	Total
New	376	8	384
Fresh	6	18	24
Picked	2	3	5
Done	1	3	4
Total	385	32	417

Accuracy

100.0%

Counts

417 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.8%	(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
	53.8%	(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
✓	53.6%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	52.4%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
✓	53.6%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
✓	52.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
	83.6%	(.f64 (.f64 (sin.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))
	10.9%	(.f64 #s(literal 2 binary64) #s(approx ( (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) (.f64 (sin.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))))))
	76.5%	#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (*.f64 (neg.f64 eps) (sin.f64 x)))
	51.3%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
✓	51.2%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	98.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/720 binary64) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
	98.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) (.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) x) x #s(literal 1/6 binary64)) x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	98.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(approx (+ (* 1/24 eps) (* 1/6 x)) (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
	98.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) (sin.f64 x)) eps))
	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
	97.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
✓	97.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
	97.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x))) (neg.f64 eps)))
	97.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
	97.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
	52.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
	52.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
	23.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (+.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 4 binary64)))))
	97.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))

Compiler

Compiled 3 289 to 1 142 computations (65.3% saved)

regimes48.0ms (0.3%)

Memory

-45.4MiB live, 52.3MiB allocated; 10ms collecting garbage

Counts

60 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (.f64 eps x) #s(literal 1/6 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.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 eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/720 binary64) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
(.f64 #s(literal 2 binary64) #s(approx ( (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) (.f64 (sin.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(approx (+ (* 1/24 eps) (* 1/6 x)) (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) (.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) x) x #s(literal 1/6 binary64)) x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 (.f64 (sin.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))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (.f64 (.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (.f64 (+.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) eps) (.f64 #s(literal 1/24 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))

Outputs

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

Calls

3 calls:

14.0ms	eps
13.0ms	x
10.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
99.1%	1	`x`
99.1%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes40.0ms (0.3%)

Memory

22.1MiB live, 22.1MiB allocated; 0ms collecting garbage

Counts

56 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (.f64 eps x) #s(literal 1/6 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.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 eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/720 binary64) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
(.f64 #s(literal 2 binary64) #s(approx ( (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) (.f64 (sin.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(approx (+ (* 1/24 eps) (* 1/6 x)) (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) (.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) x) x #s(literal 1/6 binary64)) x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 (.f64 (sin.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))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))

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

Calls

3 calls:

13.0ms	eps
12.0ms	x
9.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes37.0ms (0.2%)

Memory

20.0MiB live, 20.0MiB allocated; 0ms collecting garbage

Counts

55 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (.f64 eps x) #s(literal 1/6 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.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 eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/720 binary64) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
(.f64 #s(literal 2 binary64) #s(approx ( (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) (.f64 (sin.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(approx (+ (* 1/24 eps) (* 1/6 x)) (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 #s(literal 1/24 binary64) eps (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(approx (+ (* (+ (* (+ (* -1/36 x) (* -1/48 eps)) x) 1/6) x) (* 1/24 eps)) (.f64 (fma.f64 (.f64 #s(literal -1/36 binary64) x) x #s(literal 1/6 binary64)) x))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 (.f64 (sin.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))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) x (.f64 #s(literal -1/48 binary64) eps)) x #s(literal 1/6 binary64)) x (.f64 #s(literal 1/24 binary64) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))

Outputs

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

Calls

3 calls:

13.0ms	eps
12.0ms	x
9.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes34.0ms (0.2%)

Memory

-6.3MiB live, 39.8MiB allocated; 2ms collecting garbage

Counts

49 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (.f64 eps x) #s(literal 1/6 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.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 eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/720 binary64) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
(.f64 #s(literal 2 binary64) #s(approx ( (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) (.f64 (sin.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (fma.f64 #s(approx (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) #s(approx (+ (* 1/24 eps) (* 1/6 x)) (.f64 #s(literal 1/6 binary64) x))) eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))

Outputs

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

Calls

3 calls:

13.0ms	eps
11.0ms	x
8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.5%	1	`x`
98.5%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes34.0ms (0.2%)

Memory

-3.7MiB live, 42.0MiB allocated; 3ms collecting garbage

Counts

48 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (.f64 eps x) #s(literal 1/6 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.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 eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/720 binary64) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
(.f64 #s(literal 2 binary64) #s(approx ( (sin (/ (- (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2)) (cos (/ (+ (+ (neg (+ eps x)) (/ (PI) 2)) (+ (/ (PI) 2) x)) 2))) (.f64 (sin.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)) (neg.f64 eps)))

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

Calls

3 calls:

13.0ms	eps
11.0ms	x
8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.4%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.4%	1	`x`
98.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes33.0ms (0.2%)

Memory

-7.9MiB live, 37.6MiB allocated; 3ms collecting garbage

Counts

44 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (.f64 eps x) #s(literal 1/6 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.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 eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x (.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/720 binary64) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))))

Outputs

#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/4 binary64)) x (*.f64 #s(literal 1/6 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))

Calls

3 calls:

13.0ms	x
10.0ms	eps
8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes41.0ms (0.3%)

Memory

-16.2MiB live, 36.1MiB allocated; 16ms collecting garbage

Counts

40 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (.f64 eps x) #s(literal 1/6 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.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 eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (fma.f64 (.f64 eps x) #s(literal 1/6 binary64) (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (sin (+ (/ (PI) 2) x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))

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

Calls

3 calls:

21.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
9.0ms	x
9.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.2%)

Memory

0.7MiB live, 47.9MiB allocated; 2ms collecting garbage

Counts

35 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (.f64 eps x) #s(literal 1/6 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))

Outputs

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

Calls

3 calls:

8.0ms	eps
8.0ms	x
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.1%)

Memory

23.3MiB live, 23.3MiB allocated; 0ms collecting garbage

Counts

32 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (.f64 eps x) #s(literal 1/6 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 #s(approx ( (cos x) eps) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))

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

Calls

3 calls:

7.0ms	eps
7.0ms	x
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes21.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated; 0ms collecting garbage

Counts

30 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 eps eps) (.f64 (.f64 eps x) #s(literal 1/6 binary64))) x (neg.f64 eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) x) eps (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (.f64 (-.f64 (.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64)) x (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps)) x (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* -1/2 (cos x))) eps) (sin x)) eps) (fma.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps (.f64 (fma.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal -1/36 binary64) (.f64 eps eps) #s(literal 1/6 binary64))) x (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/4 binary64)) eps) eps)) x (.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (sin (+ (/ (PI) 2) x))) (*.f64 (neg.f64 eps) (sin.f64 x)))

Outputs

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

Calls

3 calls:

7.0ms	eps
7.0ms	x
5.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes32.0ms (0.2%)

Memory

-37.6MiB live, 10.0MiB allocated; 0ms collecting garbage

Counts

16 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

23.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms	eps
4.0ms	x

Results

Accuracy	Segments	Branch
97.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
97.5%	1	`x`
97.5%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes11.0ms (0.1%)

Memory

15.1MiB live, 15.1MiB allocated; 0ms collecting garbage

Counts

14 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 eps #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x))) (neg.f64 eps)))

Outputs

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

Calls

3 calls:

4.0ms	eps
4.0ms	x
3.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
97.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
97.5%	1	`x`
97.5%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory

13.2MiB live, 13.2MiB allocated; 0ms collecting garbage

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* -1/6 x) (* -1/4 eps)) (.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))

Outputs

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

Calls

3 calls:

4.0ms	eps
4.0ms	x
3.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
97.4%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
97.4%	1	`x`
97.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated; 0ms collecting garbage

Counts

11 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 #s(literal -1/2 binary64) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) #s(approx (+ (* (+ (* (+ (* -1/6 x) (* -1/4 eps)) x) 1) x) (* 1/2 eps)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (+.f64 x (.f64 (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (+ ( (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 eps x) #s(literal 1 binary64)) x (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory

-35.8MiB live, 10.3MiB allocated; 2ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	x
2.0ms	eps
2.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
97.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
97.1%	1	`x`
97.1%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory

10.1MiB live, 10.1MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	eps
2.0ms	x
1.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
52.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
52.5%	1	`x`
52.5%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory

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

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
51.2%	1	`x`
51.2%	1	`eps`
51.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify51.0ms (0.3%)

Memory

23.0MiB live, 23.0MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	542
1	227	542
2	398	542
3	817	540
4	1636	540
5	3464	540

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations1.3s (8.4%)

Memory

-22.4MiB live, 407.9MiB allocated; 36ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 542 to 151 computations (72.1% saved)

preprocess75.0ms (0.5%)

Memory: 20.0MiB live, 65.6MiB allocated; 5ms collecting garbage
Compiler: Compiled 1 132 to 344 computations (69.6% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze892.0ms (5.8%)

sample8.2s (52.8%)

explain472.0ms (3.1%)

preprocess265.0ms (1.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify191.0ms (1.2%)

localize143.0ms (0.9%)

series4.0ms (0%)

simplify146.0ms (0.9%)

rewrite142.0ms (0.9%)

eval21.0ms (0.1%)

prune11.0ms (0.1%)

simplify124.0ms (0.8%)

localize411.0ms (2.7%)

series33.0ms (0.2%)

simplify145.0ms (0.9%)

rewrite105.0ms (0.7%)

eval84.0ms (0.5%)

prune34.0ms (0.2%)

simplify125.0ms (0.8%)

localize560.0ms (3.6%)

series22.0ms (0.1%)

simplify166.0ms (1.1%)

rewrite97.0ms (0.6%)

eval47.0ms (0.3%)

prune64.0ms (0.4%)

simplify122.0ms (0.8%)

localize643.0ms (4.2%)

series25.0ms (0.2%)

simplify154.0ms (1%)

rewrite139.0ms (0.9%)

eval43.0ms (0.3%)

prune40.0ms (0.3%)

regimes48.0ms (0.3%)

regimes40.0ms (0.3%)

regimes37.0ms (0.2%)

regimes34.0ms (0.2%)

regimes34.0ms (0.2%)

regimes33.0ms (0.2%)

regimes41.0ms (0.3%)

regimes25.0ms (0.2%)

regimes22.0ms (0.1%)

regimes21.0ms (0.1%)

regimes32.0ms (0.2%)

regimes11.0ms (0.1%)

regimes10.0ms (0.1%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

regimes5.0ms (0%)

regimes3.0ms (0%)

simplify51.0ms (0.3%)

derivations1.3s (8.4%)

preprocess75.0ms (0.5%)

end0.0ms (0%)

Profiling