Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze48.0ms (0.3%)

Memory

-19.3MiB live, 62.9MiB allocated

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)

sample9.7s (61.8%)

Memory

110.2MiB live, 10 441.4MiB allocated

Samples

3.9s	25 655×	0	invalid
3.1s	5 677×	2	valid
697.0ms	2 440×	1	valid
26.0ms	139×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.1s

ival-cos: 2.7s (43.4% of total)

const: 790.0ms (12.9% of total)

ival-sub: 431.0ms (7% of total)

adjust: 404.0ms (6.6% of total)

ival-<: 397.0ms (6.5% of total)

ival-mult: 379.0ms (6.2% of total)

ival-<=: 336.0ms (5.5% of total)

ival-fabs: 288.0ms (4.7% of total)

ival-add: 265.0ms (4.3% of total)

ival-and: 108.0ms (1.8% of total)

exact: 48.0ms (0.8% of total)

ival-assert: 14.0ms (0.2% of total)

Bogosity

explain270.0ms (1.7%)

Memory

-5.3MiB live, 109.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
140	2	(2.4819280137201468e-155 4.273606060750313e-169)	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
1	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	142	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	140	0
-	2	114

Precision

0.9859154929577465

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	140	0	0
-	2	0	114

Precision?

0.9859154929577465

Recall?

1.0

Freqs

test

number	freq
0	114
1	141
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

181.0ms	344×	2	valid
21.0ms	164×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 151.0ms

ival-cos: 123.0ms (81.2% of total)

adjust: 18.0ms (11.9% of total)

ival-sub: 6.0ms (4% of total)

ival-add: 3.0ms (2% of total)

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

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

preprocess54.0ms (0.3%)

Memory

-23.2MiB live, 20.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify7.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

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	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

Stop Event

1×	iter limit
1×	saturated
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 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
x
eps
(cos.f64 x)

localize102.0ms (0.7%)

Memory

27.0MiB live, 65.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.045893016315378836	(cos.f64 (+.f64 x eps))
accuracy	32.135994912270064	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

84.0ms	172×	2	valid
11.0ms	82×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 82.0ms

ival-cos: 67.0ms (81.4% of total)

adjust: 10.0ms (12.1% of total)

ival-sub: 3.0ms (3.6% of total)

ival-add: 2.0ms (2.4% of total)

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

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

series6.0ms (0%)

Memory

6.5MiB live, 6.5MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify242.0ms (1.5%)

Memory

-43.8MiB live, 103.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	498
1	277	495
2	607	495
3	2403	494
4	7855	494
0	8007	474

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

Inputs
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
x
(+ eps x)
(+ eps x)
(+ eps x)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(cos x)
(cos x)
(cos x)
(cos x)
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(cos x)
(cos x)
(cos x)
(cos x)

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

rewrite243.0ms (1.5%)

Memory

17.8MiB live, 177.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16

Stop Event

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

Counts

4 → 228

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
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eval52.0ms (0.3%)

Memory: -9.8MiB live, 28.8MiB allocated
Compiler: Compiled 7 285 to 896 computations (87.7% saved)

prune42.0ms (0.3%)

Memory

-19.9MiB live, 19.9MiB allocated

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	297	9	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	297	10	307

Accuracy

99.8%

Counts

307 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.8%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
	49.8%	(-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (cos.f64 x))
✓	49.7%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	49.3%	(-.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))))
	49.3%	(-.f64 (cos.f64 (+.f64 x eps)) #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))))
	49.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	48.9%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
▶	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 285 to 212 computations (25.6% saved)

simplify158.0ms (1%)

Memory

28.2MiB live, 180.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(cos.f64 x)
cost-diff	6272	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
cost-diff	0	#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)))
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 (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))))
cost-diff	0	(sin.f64 x)
cost-diff	0	(neg.f64 eps)
cost-diff	0	(*.f64 (neg.f64 eps) (sin.f64 x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
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 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	241
0	74	231
1	131	231
2	244	227
3	457	227
4	1348	227
5	3503	227
6	3979	227
7	4345	227
8	5433	227
0	8072	223

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
eps
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
(+.f64 #s(literal 0 binary64) eps)
#s(literal 0 binary64)
#s(literal -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)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
eps
(sin.f64 x)
x
(-.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))))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
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)))
(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))
(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))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 x x)
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
(cos.f64 x)
x
(cos.f64 eps)
eps
(neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))
(sin.f64 eps)
(sin.f64 x)

Outputs
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 eps #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(fma.f64 x #s(literal 2 binary64) eps)
#s(literal 2 binary64)
x
eps
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
eps
#s(literal 0 binary64)
#s(literal -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)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (sin.f64 x) (neg.f64 eps)))
(*.f64 (sin.f64 x) (neg.f64 eps))
(neg.f64 eps)
eps
(sin.f64 x)
x
(-.f64 (cos.f64 (+.f64 eps x)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(cos.f64 (+.f64 eps x))
(+.f64 eps x)
x
eps
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #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 -1/720 binary64) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 x x)
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 eps)) (cos.f64 x) (*.f64 (sin.f64 eps) (sin.f64 x))))
(cos.f64 x)
x
(cos.f64 eps)
eps
(neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))
(sin.f64 eps)
(sin.f64 x)

localize435.0ms (2.8%)

Memory

-11.8MiB live, 671.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 x)
accuracy	0	(cos.f64 eps)
accuracy	0.00390625	(fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))
accuracy	32.13609207514977	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
accuracy	0.00390625	(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	0.045893016315378836	(cos.f64 (+.f64 x eps))
accuracy	0.41589847005492536	#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)))
accuracy	32.135994912270064	(-.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))))
accuracy	0	(*.f64 (neg.f64 eps) (sin.f64 x))
accuracy	0	(sin.f64 x)
accuracy	0	(neg.f64 eps)
accuracy	12.72701463768964	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
accuracy	0	(cos.f64 eps)
accuracy	31.97037739172395	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	32.198699648653644	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.0078125	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
accuracy	0.05807530757699087	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.14453125	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))

Samples

285.0ms	172×	2	valid
61.0ms	81×	1	valid
4.0ms	1×	3	valid
1.0ms	2×	0	valid

Compiler

Compiled 454 to 85 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 303.0ms

ival-cos: 108.0ms (35.7% of total)

ival-mult: 84.0ms (27.7% of total)

adjust: 36.0ms (11.9% of total)

ival-add: 27.0ms (8.9% of total)

ival-sin: 22.0ms (7.3% of total)

const: 13.0ms (4.3% of total)

ival-sub: 7.0ms (2.3% of total)

ival-neg: 4.0ms (1.3% of total)

exact: 1.0ms (0.3% of total)

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

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

series44.0ms (0.3%)

Memory

2.1MiB live, 122.6MiB allocated

Counts

22 → 420

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (cos.f64 eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (neg.f64 eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.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)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch #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))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (neg.f64 eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (neg.f64 eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (neg.f64 eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (neg.f64 eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.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)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.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)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.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)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.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)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (neg.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.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)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.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)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.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)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.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)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #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))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #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))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #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))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #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))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (cos x) (cos eps)) (neg (+ (* (sin eps) (sin x)) (cos x)))) (cos x) (neg (+ (* (sin eps) (sin x)) (cos x))) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* -1/720 (* x x)) 1/24) (+ (* (sin eps) (sin x)) (cos x)))
6.0ms	x	@	inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (cos x) (cos eps)) (neg (+ (* (sin eps) (sin x)) (cos x)))) (cos x) (neg (+ (* (sin eps) (sin x)) (cos x))) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* -1/720 (* x x)) 1/24) (+ (* (sin eps) (sin x)) (cos x)))
5.0ms	x	@	-inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (cos x) (cos eps)) (neg (+ (* (sin eps) (sin x)) (cos x)))) (cos x) (neg (+ (* (sin eps) (sin x)) (cos x))) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* -1/720 (* x x)) 1/24) (+ (* (sin eps) (sin x)) (cos x)))
4.0ms	eps	@	0	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (cos x) (cos eps)) (neg (+ (* (sin eps) (sin x)) (cos x)))) (cos x) (neg (+ (* (sin eps) (sin x)) (cos x))) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* -1/720 (* x x)) 1/24) (+ (* (sin eps) (sin x)) (cos x)))
3.0ms	eps	@	-inf	((* 1/2 (+ (* 2 x) eps)) (+ 0 eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x) (+ (* (cos x) (cos eps)) (neg (+ (* (sin eps) (sin x)) (cos x)))) (cos x) (neg (+ (* (sin eps) (sin x)) (cos x))) (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps))) (+ (* -1/720 (* x x)) 1/24) (+ (* (sin eps) (sin x)) (cos x)))

simplify179.0ms (1.1%)

Memory

-7.2MiB live, 308.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	370	3611
1	1105	3460
2	2841	3407
3	6514	3407
0	8114	3167

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 398

Calls

Call 1

Inputs
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
x
(+ eps x)
(+ eps x)
(+ eps x)
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (cos x))
(- (* -1 (* eps (sin x))) (cos x))
(- (* eps (- (* 1/6 (* (pow eps 2) (sin x))) (sin x))) (cos x))
(- (* eps (- (* (pow eps 2) (- (* -1/120 (* (pow eps 2) (sin x))) (* -1/6 (sin x)))) (sin x))) (cos x))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(cos x)
(+ (cos x) (* eps (sin x)))
(+ (cos x) (* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x))))))
(+ (cos x) (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x))))))))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
eps
eps
eps
eps
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
-1
(- (* -1 (* x (sin eps))) 1)
(- (* x (- (* 1/2 x) (sin eps))) 1)
(- (* x (- (* x (+ 1/2 (* 1/6 (* x (sin eps))))) (sin eps))) 1)
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
1/24
(+ 1/24 (* -1/720 (pow x 2)))
(+ 1/24 (* -1/720 (pow x 2)))
(+ 1/24 (* -1/720 (pow x 2)))
1
(+ 1 (* x (sin eps)))
(+ 1 (* x (+ (sin eps) (* -1/2 x))))
(+ 1 (* x (+ (sin eps) (* x (- (* -1/6 (* x (sin eps))) 1/2)))))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(sin x)
(sin x)
(sin x)
(sin x)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(cos x)
(cos x)
(cos x)
(cos x)
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(cos x)
(cos x)
(cos x)
(cos x)
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(sin x)
(sin x)
(sin x)
(sin x)
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(cos x)
(cos x)
(cos x)
(cos x)
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(cos x)
(cos x)
(cos x)
(cos x)
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(* -1 (+ (cos x) (* (sin eps) (sin x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))
(+ (cos x) (* (sin eps) (sin x)))

Outputs
x
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 #s(literal 1/2 binary64) eps x)
eps
eps
eps
eps
(*.f64 (neg.f64 eps) (sin.f64 x))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/6 binary64) eps) #s(literal -1 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) eps)
(.f64 (fma.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 (neg.f64 (sin.f64 x))) eps)
(.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps)) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(*.f64 (neg.f64 eps) (sin.f64 x))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/6 binary64) eps) #s(literal -1 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) eps)
(.f64 (fma.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 (neg.f64 (sin.f64 x))) eps)
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
#s(literal 1 binary64)
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(*.f64 (neg.f64 eps) (sin.f64 x))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/6 binary64) eps) #s(literal -1 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) eps)
(.f64 (fma.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 (neg.f64 (sin.f64 x))) eps)
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
(neg.f64 eps)
(neg.f64 eps)
(neg.f64 eps)
(*.f64 (neg.f64 eps) (sin.f64 x))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/6 binary64) eps) #s(literal -1 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) eps)
(.f64 (fma.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 (neg.f64 (sin.f64 x))) eps)
(cos.f64 x)
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps (cos.f64 x))
(fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/6 binary64) eps) #s(literal -1 binary64)) (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) eps (cos.f64 x))
x
(+.f64 eps x)
(+.f64 eps x)
(+.f64 eps x)
(*.f64 (neg.f64 eps) (sin.f64 x))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal 1/6 binary64) eps) #s(literal -1 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) eps)
(.f64 (fma.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 (neg.f64 (sin.f64 x))) eps)
(neg.f64 (cos.f64 x))
(neg.f64 (fma.f64 (sin.f64 x) eps (cos.f64 x)))
(-.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/6 binary64) eps) #s(literal -1 binary64))) eps) (cos.f64 x))
(fma.f64 (-.f64 (.f64 (.f64 (sin.f64 x) (fma.f64 (.f64 #s(literal -1/120 binary64) eps) eps #s(literal 1/6 binary64))) (.f64 eps eps)) (sin.f64 x)) eps (neg.f64 (cos.f64 x)))
(sin.f64 x)
(fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps (.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x))
(fma.f64 (fma.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) (.f64 (*.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps)) eps (sin.f64 x))
(*.f64 #s(literal 1/2 binary64) eps)
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(cos.f64 x)
(fma.f64 (sin.f64 x) eps (cos.f64 x))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (.f64 (sin.f64 x) eps) (cos.f64 x))
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(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(sin.f64 x)
(sin.f64 x)
(sin.f64 x)
(sin.f64 x)
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 eps x))
x
(fma.f64 (/.f64 eps x) x x)
(fma.f64 (/.f64 eps x) x x)
(fma.f64 (/.f64 eps x) x x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
(fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
(fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
(fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) x) x)
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) x) x)
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) x) x)
(fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))
(fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))
(fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))
(fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))
x
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(sin.f64 x)
(sin.f64 x)
(sin.f64 x)
(sin.f64 x)
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 eps x))
x
(fma.f64 (/.f64 eps x) x x)
(fma.f64 (/.f64 eps x) x x)
(fma.f64 (/.f64 eps x) x x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
(fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
(fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
(fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64))))
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) x) x)
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) x) x)
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) x) x)
(fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))
(fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))
(fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))
(fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))

rewrite163.0ms (1%)

Memory

28.6MiB live, 337.3MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	178
0	74	170
1	284	164
2	2177	164
0	8651	164

Stop Event

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

Counts

22 → 498

Calls

Call 1

Inputs
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
(+.f64 #s(literal 0 binary64) eps)
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
#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)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
(sin.f64 x)
(-.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))))
(cos.f64 (+.f64 x eps))
(+.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)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
(cos.f64 x)
(neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))

Outputs
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eval168.0ms (1.1%)

Memory: -7.3MiB live, 394.5MiB allocated
Compiler: Compiled 27 970 to 2 375 computations (91.5% saved)

prune122.0ms (0.8%)

Memory

11.7MiB live, 130.1MiB allocated

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	921	22	943
Fresh	3	1	4
Picked	4	1	5
Done	1	0	1
Total	929	24	953

Accuracy

100.0%

Counts

953 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	49.8%	(fma.f64 (cos.f64 x) #s(approx (cos eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
	49.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	99.8%	(.f64 (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	42.1%	(.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	35.4%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))))))) #s(literal -2 binary64))
	35.0%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64)))))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	99.6%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	48.9%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
▶	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
✓	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	50.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
	79.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
	80.4%	#s(approx (+ (* (cos x) (cos eps)) (neg (+ (* (sin eps) (sin x)) (cos x)))) (fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
	99.1%	#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 #s(literal 1/3 binary64) x))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) x)) x (.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))))
	98.5%	#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))))

Compiler

Compiled 1 127 to 838 computations (25.6% saved)

simplify213.0ms (1.4%)

Memory

0.2MiB live, 123.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 eps eps)))))
cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))))) #s(literal -2 binary64))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
cost-diff	7488	(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))
cost-diff	0	(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
cost-diff	0	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	832	(*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps)
cost-diff	0	(*.f64 eps eps)
cost-diff	0	(.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
cost-diff	1024	(/.f64 (*.f64 eps 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 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
cost-diff	0	(.f64 (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	320	(*.f64 #s(literal 1 binary64) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	390
0	90	329
1	155	322
2	311	302
3	708	290
4	1566	290
5	3428	290
6	4257	290
7	6170	290
0	8240	277

Stop Event

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

Calls

Call 1

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

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

localize372.0ms (2.4%)

Memory

-10.1MiB live, 482.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))))) #s(literal -2 binary64))
accuracy	0.05026280757699087	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.140625	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 eps eps)))))
accuracy	40.8042951510716	(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))
accuracy	0.01953125	(-.f64 (/.f64 x eps) #s(literal -1/2 binary64))
accuracy	0.05026280757699087	(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps)))
accuracy	0.140625	(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
accuracy	0.26953125	(*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps)
accuracy	0	(sin.f64 x)
accuracy	0	(neg.f64 eps)
accuracy	12.525995470374044	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
accuracy	27.229544013166443	(/.f64 (*.f64 eps eps) (neg.f64 eps))
accuracy	0.2006670094101592	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	31.74131835841842	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
accuracy	31.973599062929416	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	0	(cos.f64 (*.f64 #s(literal 1 binary64) x))
accuracy	0.00390625	(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x))))
accuracy	0.0078125	(.f64 (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
accuracy	0.140625	(.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))

Samples

230.0ms	173×	2	valid
52.0ms	80×	1	valid
8.0ms	2×	5	exit
0.0ms	1×	0	valid

Compiler

Compiled 745 to 108 computations (85.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 226.0ms

ival-cos: 78.0ms (34.5% of total)

ival-mult: 54.0ms (23.9% of total)

adjust: 44.0ms (19.5% of total)

ival-sin: 19.0ms (8.4% of total)

ival-div: 9.0ms (4% of total)

ival-sub: 9.0ms (4% of total)

ival-pow: 6.0ms (2.7% of total)

ival-add: 6.0ms (2.7% of total)

exact: 1.0ms (0.4% of total)

ival-neg: 1.0ms (0.4% of total)

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

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

series44.0ms (0.3%)

Memory

-8.1MiB live, 72.4MiB allocated

Counts

25 → 480

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (*.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (cos eps) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (*.f64 eps eps) (neg.f64 eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 eps eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 eps eps))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (cos.f64 (*.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (neg.f64 eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (cos eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (cos eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (cos eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (cos eps) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (*.f64 eps eps) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (*.f64 eps eps) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (*.f64 eps eps) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (*.f64 eps eps) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)) #<representation binary64>) () ())) ())
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Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	inf	((* 1 x) (+ 0 eps) (* (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (/ (* eps eps) (neg eps)) (- (cos (+ x eps)) (cos x)) (* (/ (* eps eps) (neg eps)) (sin x)) (* eps eps) (* (- (/ x eps) -1/2) eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (/ (pow eps 3) (* eps eps)) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (/ (pow eps 3) (* eps eps))))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (/ (pow eps 3) (* eps eps))))) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (cos (* 1 x)) (neg eps) (sin x) (sin (* 1/2 (+ (* 2 x) eps))) (- (/ x eps) -1/2) (sin (* 1/2 (+ (* 2 x) eps))))
4.0ms	eps	@	-inf	((* 1 x) (+ 0 eps) (* (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (/ (* eps eps) (neg eps)) (- (cos (+ x eps)) (cos x)) (* (/ (* eps eps) (neg eps)) (sin x)) (* eps eps) (* (- (/ x eps) -1/2) eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (/ (pow eps 3) (* eps eps)) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (/ (pow eps 3) (* eps eps))))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (/ (pow eps 3) (* eps eps))))) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (cos (* 1 x)) (neg eps) (sin x) (sin (* 1/2 (+ (* 2 x) eps))) (- (/ x eps) -1/2) (sin (* 1/2 (+ (* 2 x) eps))))
3.0ms	x	@	inf	((* 1 x) (+ 0 eps) (* (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (/ (* eps eps) (neg eps)) (- (cos (+ x eps)) (cos x)) (* (/ (* eps eps) (neg eps)) (sin x)) (* eps eps) (* (- (/ x eps) -1/2) eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (/ (pow eps 3) (* eps eps)) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (/ (pow eps 3) (* eps eps))))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (/ (pow eps 3) (* eps eps))))) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (cos (* 1 x)) (neg eps) (sin x) (sin (* 1/2 (+ (* 2 x) eps))) (- (/ x eps) -1/2) (sin (* 1/2 (+ (* 2 x) eps))))
3.0ms	x	@	-inf	((* 1 x) (+ 0 eps) (* (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (/ (* eps eps) (neg eps)) (- (cos (+ x eps)) (cos x)) (* (/ (* eps eps) (neg eps)) (sin x)) (* eps eps) (* (- (/ x eps) -1/2) eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (/ (pow eps 3) (* eps eps)) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (/ (pow eps 3) (* eps eps))))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (/ (pow eps 3) (* eps eps))))) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (cos (* 1 x)) (neg eps) (sin x) (sin (* 1/2 (+ (* 2 x) eps))) (- (/ x eps) -1/2) (sin (* 1/2 (+ (* 2 x) eps))))
2.0ms	eps	@	0	((* 1 x) (+ 0 eps) (* (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) -2) (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (/ (* eps eps) (neg eps)) (- (cos (+ x eps)) (cos x)) (* (/ (* eps eps) (neg eps)) (sin x)) (* eps eps) (* (- (/ x eps) -1/2) eps) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (/ (pow eps 3) (* eps eps)) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (/ (pow eps 3) (* eps eps))))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (/ (pow eps 3) (* eps eps))))) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (cos (* 1 x)) (neg eps) (sin x) (sin (* 1/2 (+ (* 2 x) eps))) (- (/ x eps) -1/2) (sin (* 1/2 (+ (* 2 x) eps))))

simplify185.0ms (1.2%)

Memory

17.6MiB live, 290.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	286	4725
1	866	4474
2	2296	4396
3	5258	4396
0	8374	4070

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 437

Calls

Call 1

Inputs
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
eps
eps
eps
eps
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(/ x eps)
(/ (+ x (* 1/2 eps)) eps)
(/ (+ x (* 1/2 eps)) eps)
(/ (+ x (* 1/2 eps)) eps)
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
eps
eps
eps
eps
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
eps
eps
eps
eps
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
eps
eps
eps
eps
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
eps
eps
eps
eps
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
x
x
x
x
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
1/2
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(+ 1/2 (/ x eps))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
x
x
x
x
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(cos x)
(cos x)
(cos x)
(cos x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(/ x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
x
x
x
x
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(cos x)
(cos x)
(cos x)
(cos x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(/ x eps)
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(* x (+ (/ 1 eps) (* 1/2 (/ 1 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))

Outputs
eps
eps
eps
eps
(*.f64 (neg.f64 eps) (sin.f64 x))
(.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x))) eps)
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.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 (neg.f64 (sin.f64 x))) eps)
(.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps)) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(*.f64 (neg.f64 eps) (sin.f64 x))
(.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x))) eps)
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.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 (neg.f64 (sin.f64 x))) eps)
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) eps)
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
#s(literal 1 binary64)
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(neg.f64 eps)
(neg.f64 eps)
(neg.f64 eps)
(neg.f64 eps)
(*.f64 (neg.f64 eps) (sin.f64 x))
(.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x))) eps)
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.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 (neg.f64 (sin.f64 x))) eps)
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 eps eps)
(*.f64 eps eps)
(*.f64 eps eps)
(*.f64 eps eps)
x
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 #s(literal 1/2 binary64) eps x)
(*.f64 (neg.f64 eps) (sin.f64 x))
(.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x))) eps)
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.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 (neg.f64 (sin.f64 x))) eps)
(.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps)) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
eps
eps
eps
eps
x
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 #s(literal 1/2 binary64) eps x)
(*.f64 (neg.f64 eps) (sin.f64 x))
(.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x))) eps)
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.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 (neg.f64 (sin.f64 x))) eps)
(.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps)) eps (.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/12 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (*.f64 (sin.f64 x) #s(literal 1/2 binary64))) eps)
(sin.f64 x)
(fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps (.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x))
(fma.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal -1/48 binary64) eps) #s(literal 1/2 binary64)) (.f64 (*.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps)) eps (sin.f64 x))
(neg.f64 eps)
(neg.f64 eps)
(neg.f64 eps)
(neg.f64 eps)
(sin.f64 x)
(fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps (sin.f64 x))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps (.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x))
(fma.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal -1/48 binary64) eps) #s(literal 1/2 binary64)) (.f64 (*.f64 #s(literal -1/8 binary64) (sin.f64 x)) eps)) eps (sin.f64 x))
(/.f64 x eps)
(/.f64 (fma.f64 #s(literal 1/2 binary64) eps x) eps)
(/.f64 (fma.f64 #s(literal 1/2 binary64) eps x) eps)
(/.f64 (fma.f64 #s(literal 1/2 binary64) eps x) eps)
(sin.f64 x)
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(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(sin.f64 x)
(sin.f64 x)
(sin.f64 x)
(sin.f64 x)
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(/.f64 x eps)
(-.f64 (/.f64 x eps) #s(literal -1/2 binary64))
(-.f64 (/.f64 x eps) #s(literal -1/2 binary64))
(-.f64 (/.f64 x eps) #s(literal -1/2 binary64))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite167.0ms (1.1%)

Memory

-25.5MiB live, 248.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	274
0	90	247
1	296	187
2	2132	187
0	8905	177

Stop Event

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

Counts

25 → 589

Calls

Call 1

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

Outputs
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eval149.0ms (0.9%)

Memory: 14.3MiB live, 200.4MiB allocated
Compiler: Compiled 33 502 to 3 101 computations (90.7% saved)

prune85.0ms (0.5%)

Memory

-18.9MiB live, 161.6MiB allocated

Pruning

33 alts after pruning (31 fresh and 2 done)

	Pruned	Kept	Total
New	1 162	21	1 183
Fresh	8	10	18
Picked	4	1	5
Done	0	1	1
Total	1 174	33	1 207

Accuracy

100.0%

Counts

1 207 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	49.8%	(fma.f64 (cos.f64 x) #s(approx (cos eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
	49.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
▶	100.0%	(.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) eps)))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) eps)))))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
	35.0%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64)))))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 eps #s(literal -1/2 binary64)))))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (neg.f64 eps) eps) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
	95.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (exp.f64 (log.f64 eps))))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps)))) #s(literal -2 binary64))
▶	99.4%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	53.7%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 x (.f64 (neg.f64 eps) eps)) (neg.f64 eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
▶	99.6%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (neg.f64 eps) eps) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
	99.8%	(.f64 #s(approx ( (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) (.f64 (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
▶	69.6%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps))
	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
✓	48.9%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
	69.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (neg.f64 eps))))
✓	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	50.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
	79.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
▶	79.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps)))
	80.4%	#s(approx (+ (* (cos x) (cos eps)) (neg (+ (* (sin eps) (sin x)) (cos x)))) (fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
	98.5%	#s(approx (* (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))))

Compiler

Compiled 1 535 to 1 129 computations (26.4% saved)

simplify75.0ms (0.5%)

Memory

18.5MiB live, 18.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	448	(/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps))
cost-diff	832	(.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps))
cost-diff	0	(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
cost-diff	0	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	1024	(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
cost-diff	0	(*.f64 (neg.f64 eps) eps)
cost-diff	0	(.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps))
cost-diff	1024	(/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps)
cost-diff	0	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) eps)
cost-diff	0	#s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps)))
cost-diff	0	(sin.f64 x)
cost-diff	0	(.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
cost-diff	0	(.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
cost-diff	7040	(fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	462
0	91	434
1	171	434
2	409	382
3	1126	372
4	3757	355
5	5692	354
0	8238	339

Stop Event

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

Calls

Call 1

Inputs
(.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin.f64 x)
x
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(cos.f64 x)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps))
(*.f64 (neg.f64 x) eps)
(neg.f64 x)
x
eps
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps))
(/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps)
(.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x))
(*.f64 (neg.f64 eps) eps)
(neg.f64 eps)
eps
(sin.f64 x)
x
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)))
#s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64))
(/.f64 eps x)
eps
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
(+.f64 #s(literal 0 binary64) eps)
#s(literal 0 binary64)
#s(literal -2 binary64)
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps))))
#s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))
(/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps))
(.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps))
(-.f64 (/.f64 x eps) #s(literal -1/2 binary64))
(/.f64 x eps)
x
eps
#s(literal -1/2 binary64)
(*.f64 (neg.f64 eps) eps)
(neg.f64 eps)
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
#s(literal 1/2 binary64)
(+.f64 #s(literal 0 binary64) eps)
#s(literal 0 binary64)
#s(literal -2 binary64)

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

localize257.0ms (1.6%)

Memory

3.4MiB live, 81.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.05026280757699087	(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps))))
accuracy	0.140625	(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
accuracy	0.2624279116392061	(.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps))
accuracy	27.186405892990997	(/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps))
accuracy	0.0078125	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
accuracy	0.05026280757699087	(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)))
accuracy	0.140625	(.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))))
accuracy	0.234375	(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
accuracy	0	(neg.f64 eps)
accuracy	0.08984375	(.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x))
accuracy	10.693453449161511	(/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps)
accuracy	12.525995470374044	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps))
accuracy	0	(*.f64 (neg.f64 x) eps)
accuracy	0	(neg.f64 x)
accuracy	0.834438751617371	#s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps))
accuracy	12.525995470374044	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps)))
accuracy	0.00390625	(.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
accuracy	0.0078125	(.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
accuracy	0.0078125	(.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
accuracy	0.015625	(fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))

Samples

163.0ms	168×	2	valid
48.0ms	84×	1	valid
5.0ms	2×	5	exit
1.0ms	2×	0	valid

Compiler

Compiled 808 to 108 computations (86.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 169.0ms

ival-cos: 49.0ms (29.1% of total)

ival-mult: 40.0ms (23.7% of total)

adjust: 31.0ms (18.4% of total)

ival-sin: 19.0ms (11.3% of total)

ival-div: 13.0ms (7.7% of total)

ival-add: 9.0ms (5.3% of total)

ival-sub: 5.0ms (3% of total)

ival-neg: 2.0ms (1.2% of total)

exact: 1.0ms (0.6% of total)

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

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

series56.0ms (0.4%)

Memory

-8.9MiB live, 28.7MiB allocated

Counts

25 → 540

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (neg.f64 x) eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (neg.f64 eps) eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (neg.f64 eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (neg.f64 eps) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (neg.f64 eps) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (neg.f64 eps) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (neg.f64 eps) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify150.0ms (1%)

Memory

23.3MiB live, 58.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	385	5752
1	1262	5397
2	3744	5228
0	8109	4918

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 521

Calls

Call 1

Inputs
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(sin x)
(+ (sin x) (* -1/8 (* (pow eps 2) (sin x))))
(+ (sin x) (* (pow eps 2) (+ (* -1/8 (sin x)) (* 1/384 (* (pow eps 2) (sin x))))))
(+ (sin x) (* (pow eps 2) (+ (* -1/8 (sin x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (sin x))) (* 1/384 (sin x)))))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* eps (+ (* -1 x) (* -1/2 eps)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))
(* 1/4 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/4 (cos x))))
(* (pow eps 2) (+ (* 1/4 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/1440 (* (pow eps 2) (cos x)))))))
(* (pow eps 2) (+ (* 1/4 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/80640 (* (pow eps 2) (cos x))) (* 1/1440 (cos x))))))))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
eps
eps
eps
eps
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1 (/ x eps)) 1/2))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* x (cos (* 1/2 eps)))
(* x (+ (cos (* 1/2 eps)) (* -1/6 (* (pow x 2) (cos (* 1/2 eps))))))
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* 1/120 (* (pow x 2) (cos (* 1/2 eps))))))))
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/120 (cos (* 1/2 eps)))))))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1 (* (pow eps 2) x))
(* x (+ (* -1 (pow eps 2)) (* 1/6 (* (pow eps 2) (pow x 2)))))
(* x (+ (* -1 (pow eps 2)) (* (pow x 2) (+ (* -1/120 (* (pow eps 2) (pow x 2))) (* 1/6 (pow eps 2))))))
(* x (+ (* -1 (pow eps 2)) (* (pow x 2) (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/120 (pow eps 2)) (* 1/5040 (* (pow eps 2) (pow x 2)))))))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* -1/2 (* (pow x 2) (pow (sin (* 1/2 eps)) 2))) (pow (sin (* 1/2 eps)) 2))
(+ (* (pow x 2) (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* 1/24 (* (pow x 2) (pow (sin (* 1/2 eps)) 2))))) (pow (sin (* 1/2 eps)) 2))
(+ (* (pow x 2) (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (pow (sin (* 1/2 eps)) 2))) (* 1/24 (pow (sin (* 1/2 eps)) 2)))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(sin x)
(sin x)
(sin x)
(sin x)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* -1/2 (/ (pow eps 2) x))))
(* x (+ (* -1 eps) (* -1/2 (/ (pow eps 2) x))))
(* x (+ (* -1 eps) (* -1/2 (/ (pow eps 2) x))))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* -2 (+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(sin x)
(sin x)
(sin x)
(sin x)
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 (* eps x))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
(* -1 (* (pow eps 2) (sin x)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* -1 (* eps x))
(* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ eps (* 1/2 (/ (pow eps 2) x)))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(* (cos x) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))

Outputs
(.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 x)) eps)
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (cos.f64 x)) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps (.f64 #s(literal 1/4 binary64) (cos.f64 x))) eps (.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal -1/48 binary64) eps) #s(literal 1/4 binary64)))) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x))) eps)
(*.f64 (neg.f64 eps) (sin.f64 x))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)))) eps (neg.f64 (sin.f64 x))) eps)
(sin.f64 x)
(.f64 (fma.f64 eps (.f64 #s(literal -1/8 binary64) eps) #s(literal 1 binary64)) (sin.f64 x))
(fma.f64 (.f64 (sin.f64 x) (fma.f64 #s(literal 1/384 binary64) (.f64 eps eps) #s(literal -1/8 binary64))) (*.f64 eps eps) (sin.f64 x))
(fma.f64 (fma.f64 eps (.f64 #s(literal -1/8 binary64) eps) #s(literal 1 binary64)) (sin.f64 x) (.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (sin.f64 x) (fma.f64 #s(literal -1/46080 binary64) (.f64 eps eps) #s(literal 1/384 binary64)))))
(*.f64 (neg.f64 eps) (sin.f64 x))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)))) eps (neg.f64 (sin.f64 x))) eps)
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) x)
(*.f64 (neg.f64 eps) x)
(*.f64 (neg.f64 eps) x)
(*.f64 (neg.f64 eps) x)
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(*.f64 (neg.f64 eps) (sin.f64 x))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) (sin.f64 x)) eps (.f64 (cos.f64 x) (fma.f64 eps (.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)))) eps (neg.f64 (sin.f64 x))) eps)
(.f64 (neg.f64 eps) (.f64 (sin.f64 x) eps))
(.f64 (neg.f64 eps) (.f64 (sin.f64 x) eps))
(.f64 (neg.f64 eps) (.f64 (sin.f64 x) eps))
(.f64 (neg.f64 eps) (.f64 (sin.f64 x) eps))
(*.f64 (neg.f64 eps) eps)
(*.f64 (neg.f64 eps) eps)
(*.f64 (neg.f64 eps) eps)
(*.f64 (neg.f64 eps) eps)
x
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 #s(literal 1/2 binary64) eps x)
(fma.f64 #s(literal 1/2 binary64) eps x)
eps
eps
eps
eps
(*.f64 (neg.f64 eps) (sin.f64 x))
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x
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(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(.f64 (neg.f64 eps) (.f64 (sin.f64 x) eps))
(.f64 (neg.f64 eps) (.f64 (sin.f64 x) eps))
(.f64 (neg.f64 eps) (.f64 (sin.f64 x) eps))
(.f64 (neg.f64 eps) (.f64 (sin.f64 x) eps))
x
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(fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x) x)
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
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x
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(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
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(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite173.0ms (1.1%)

Memory

-16.1MiB live, 65.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	342
0	91	324
1	312	263
2	2251	263
0	9516	255

Stop Event

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

Counts

25 → 529

Calls

Call 1

Inputs
(fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps))
(*.f64 (neg.f64 x) eps)
(neg.f64 x)
(/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps)
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps))
(.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x))
(*.f64 (neg.f64 eps) eps)
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(+.f64 #s(literal 0 binary64) eps)
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
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(sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps))))

Outputs
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eval154.0ms (1%)

Memory: 3.6MiB live, 122.1MiB allocated
Compiler: Compiled 43 197 to 4 120 computations (90.5% saved)

prune55.0ms (0.4%)

Memory

1.7MiB live, 79.0MiB allocated

Pruning

37 alts after pruning (34 fresh and 3 done)

	Pruned	Kept	Total
New	1 314	13	1 327
Fresh	5	21	26
Picked	4	1	5
Done	0	2	2
Total	1 323	37	1 360

Accuracy

100.0%

Counts

1 360 → 37

Alt Table

Click to see full alt table

Status	Accuracy	Program
	49.8%	(fma.f64 (cos.f64 x) #s(approx (cos eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
	49.0%	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
	99.8%	(.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(approx (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (.f64 (.f64 (*.f64 (cos.f64 x) eps) eps) #s(literal 1/4 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps)))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) eps)))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) eps)))))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
	35.0%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64)))))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 eps #s(literal -1/2 binary64)))))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (neg.f64 eps) eps) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
	95.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (exp.f64 (log.f64 eps))))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
	53.7%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 x (.f64 (neg.f64 eps) eps)) (neg.f64 eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (neg.f64 eps) eps) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
	99.8%	(.f64 #s(approx (+ ( (* (sin x) (cos (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))) #s(literal -2 binary64))
	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
	69.2%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps))
	69.1%	#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (neg.f64 eps) x) eps)) eps))
✓	48.9%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
	99.5%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (sin.f64 x) eps) (.f64 (neg.f64 eps) eps)))
	69.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (.f64 eps (/.f64 (sin.f64 x) eps))))
✓	80.1%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	79.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ (* (* (neg eps) eps) (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
	50.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (- (cos eps) 1) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
	18.2%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 x)) (.f64 eps eps))))
	69.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (neg.f64 x)) (neg.f64 eps))))
	79.8%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
	79.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
✓	79.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.f64 x) eps)))
	80.4%	#s(approx (+ (* (cos x) (cos eps)) (neg (+ (* (sin eps) (sin x)) (cos x)))) (fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))

Compiler

Compiled 2 457 to 1 022 computations (58.4% saved)

regimes47.0ms (0.3%)

Memory

-16.4MiB live, 22.9MiB allocated

Counts

66 → 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 (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.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 (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ (* (* (neg eps) eps) (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (neg.f64 eps) x) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (neg.f64 x)) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps))
#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)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (.f64 eps (/.f64 (sin.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (sin.f64 x) eps) (.f64 (neg.f64 eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #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))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.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 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 x (.f64 (neg.f64 eps) eps)) (neg.f64 eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (neg.f64 eps) eps) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (neg.f64 eps) eps) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) eps)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))))) #s(literal -2 binary64))
#s(approx (+ (* (cos x) (cos eps)) (neg (+ (* (sin eps) (sin x)) (cos x)))) (fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (exp.f64 (log.f64 eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 eps #s(literal -1/2 binary64)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64)))))) #s(literal -2 binary64))
(fma.f64 (cos.f64 x) #s(approx (cos eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
(.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(approx (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (.f64 (.f64 (*.f64 (cos.f64 x) eps) eps) #s(literal 1/4 binary64)))) #s(literal -2 binary64))
#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
(-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (cos.f64 x))
(.f64 #s(approx ( (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) (.f64 (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 #s(approx (+ ( (* (sin x) (cos (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))) #s(literal -2 binary64))
(.f64 (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 #s(literal 1/3 binary64) x))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) x)) x (.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))))

Outputs

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

Calls

3 calls:

16.0ms	x
15.0ms	eps
12.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes44.0ms (0.3%)

Memory

22.4MiB live, 22.4MiB allocated

Counts

64 → 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 (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.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 (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ (* (* (neg eps) eps) (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (neg.f64 eps) x) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (neg.f64 x)) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps))
#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)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (.f64 eps (/.f64 (sin.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (sin.f64 x) eps) (.f64 (neg.f64 eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #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))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.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 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 x (.f64 (neg.f64 eps) eps)) (neg.f64 eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (neg.f64 eps) eps) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (neg.f64 eps) eps) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) eps)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))))) #s(literal -2 binary64))
#s(approx (+ (* (cos x) (cos eps)) (neg (+ (* (sin eps) (sin x)) (cos x)))) (fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (exp.f64 (log.f64 eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 eps #s(literal -1/2 binary64)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64)))))) #s(literal -2 binary64))
(fma.f64 (cos.f64 x) #s(approx (cos eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
(.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(approx (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (.f64 (.f64 (*.f64 (cos.f64 x) eps) eps) #s(literal 1/4 binary64)))) #s(literal -2 binary64))
#s(approx (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))))
#s(approx (* (* (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) -2) (fma.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64)) (.f64 (.f64 (.f64 #s(literal -2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(.f64 (.f64 (sin.f64 (/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
(-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (cos.f64 x))
(.f64 #s(approx ( (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (sin (* 1/2 (+ 0 eps)))) (.f64 (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 #s(approx (+ ( (* (sin x) (cos (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))) #s(literal -2 binary64))
(.f64 (.f64 (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1 binary64) x)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1 binary64) x)))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

15.0ms	x
15.0ms	eps
12.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes44.0ms (0.3%)

Memory

-33.4MiB live, 20.0MiB allocated

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 (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.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 (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ (* (* (neg eps) eps) (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (neg.f64 eps) x) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (neg.f64 x)) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps))
#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)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (.f64 eps (/.f64 (sin.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (sin.f64 x) eps) (.f64 (neg.f64 eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #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))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.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 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 #s(approx ( 1/2 (+ (* 2 x) eps)) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (fma.f64 (/.f64 x (.f64 (neg.f64 eps) eps)) (neg.f64 eps) #s(literal 1/2 binary64)) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (neg.f64 eps) eps) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (neg.f64 eps) eps) (/.f64 #s(literal -1 binary64) eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (/.f64 (.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (.f64 (neg.f64 eps) eps)) (neg.f64 eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (neg.f64 (*.f64 eps eps))))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) eps)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))))) #s(literal -2 binary64))
#s(approx (+ (* (cos x) (cos eps)) (neg (+ (* (sin eps) (sin x)) (cos x)))) (fma.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps) (*.f64 (cos.f64 x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (exp.f64 (log.f64 eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 eps #s(literal -1/2 binary64)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64)))))) #s(literal -2 binary64))
(fma.f64 (cos.f64 x) #s(approx (cos eps) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))

Outputs

(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))

Calls

3 calls:

18.0ms	x
13.0ms	eps
10.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes21.0ms (0.1%)

Memory

12.0MiB live, 12.0MiB allocated

Counts

27 → 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 (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.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 (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ (* (* (neg eps) eps) (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (neg.f64 eps) x) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (neg.f64 x)) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps))
#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)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (.f64 eps (/.f64 (sin.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (sin.f64 x) eps) (.f64 (neg.f64 eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #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))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.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))))

Outputs

(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes19.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

25 → 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 (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.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 (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ (* (* (neg eps) eps) (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (neg.f64 eps) x) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (neg.f64 x)) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps))
#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)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (.f64 eps (/.f64 (sin.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (sin.f64 x) eps) (.f64 (neg.f64 eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #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))))

Outputs
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -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
99.5%	1	`x`
99.5%	1	`eps`
99.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated

Counts

23 → 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 (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.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 (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ (* (* (neg eps) eps) (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (neg.f64 eps) x) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (neg.f64 x)) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps))
#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)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (neg.f64 eps) (.f64 eps (/.f64 (sin.f64 x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 eps eps) (/.f64 (sin.f64 x) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (sin.f64 x) eps) (.f64 (neg.f64 eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (/.f64 (.f64 eps eps) (neg.f64 eps)) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 x)) (.f64 eps eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (.f64 (sin.f64 x) (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
80.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
80.1%	1	`x`
80.1%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory

-31.3MiB live, 8.4MiB allocated

Counts

15 → 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 (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.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 (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ (* (* (neg eps) eps) (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (neg.f64 eps) x) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (neg.f64 x)) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps))
#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)))

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

Calls

3 calls:

5.0ms	x
4.0ms	eps
3.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
80.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
80.1%	1	`eps`
80.1%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated

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 (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.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 (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ (* (* (neg eps) eps) (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (neg.f64 eps) x) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (neg.f64 x)) (neg.f64 eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)) eps))
#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)))

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
79.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
79.8%	1	`eps`
79.8%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

Counts

10 → 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 (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (*.f64 (neg.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 (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (/ (* (* (neg eps) eps) (sin x)) eps) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 #s(approx (* (* (neg eps) eps) (sin x)) (.f64 (.f64 (neg.f64 eps) x) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 #s(literal 0 binary64) x)) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (neg.f64 x)) (neg.f64 eps))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
79.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
79.7%	1	`eps`
79.7%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

5.0MiB live, 5.0MiB allocated

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
79.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
79.6%	1	`eps`
79.6%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

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

Results

Accuracy	Segments	Branch
48.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
48.9%	1	`eps`
48.9%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify24.0ms (0.2%)

Memory

-20.6MiB live, 19.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	253
1	126	253
2	144	253
3	161	253
4	165	253
5	166	253

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(.f64 (fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(approx (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (.f64 (.f64 (*.f64 (cos.f64 x) eps) eps) #s(literal 1/4 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))) #s(approx (sin ( 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))

Outputs
(.f64 #s(literal -2 binary64) (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(.f64 (fma.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(approx (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (.f64 #s(literal 1/4 binary64) (.f64 (*.f64 (cos.f64 x) eps) eps)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (sin.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (sin.f64 x) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (/ (* eps eps) (neg eps)) (sin x)) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)) eps) (.f64 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))

soundness1.1s (7%)

Memory

17.2MiB live, 17.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	178
0	74	170
1	284	164
2	2177	164
0	8651	164
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	370	3611
1	1105	3460
2	2841	3407
3	6514	3407
0	8114	3167
0	286	4725
1	866	4474
2	2296	4396
3	5258	4396
0	8374	4070
0	385	5752
1	1262	5397
2	3744	5228
0	8109	4918
0	55	274
0	90	247
1	296	187
2	2132	187
0	8905	177
0	105	498
1	277	495
2	607	495
3	2403	494
4	7855	494
0	8007	474

Stop Event

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

Compiler

Compiled 533 to 321 computations (39.8% saved)

preprocess150.0ms (1%)

Memory: -20.7MiB live, 58.5MiB allocated
Compiler: Compiled 554 to 224 computations (59.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18

start0.0ms (0%)

analyze48.0ms (0.3%)

sample9.7s (61.8%)

explain270.0ms (1.7%)

preprocess54.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify7.0ms (0%)

localize102.0ms (0.7%)

series6.0ms (0%)

simplify242.0ms (1.5%)

rewrite243.0ms (1.5%)

eval52.0ms (0.3%)

prune42.0ms (0.3%)

simplify158.0ms (1%)

localize435.0ms (2.8%)

series44.0ms (0.3%)

simplify179.0ms (1.1%)

rewrite163.0ms (1%)

eval168.0ms (1.1%)

prune122.0ms (0.8%)

simplify213.0ms (1.4%)

localize372.0ms (2.4%)

series44.0ms (0.3%)

simplify185.0ms (1.2%)

rewrite167.0ms (1.1%)

eval149.0ms (0.9%)

prune85.0ms (0.5%)

simplify75.0ms (0.5%)

localize257.0ms (1.6%)

series56.0ms (0.4%)

simplify150.0ms (1%)

rewrite173.0ms (1.1%)

eval154.0ms (1%)

prune55.0ms (0.4%)

regimes47.0ms (0.3%)

regimes44.0ms (0.3%)

regimes44.0ms (0.3%)

regimes21.0ms (0.1%)

regimes19.0ms (0.1%)

regimes18.0ms (0.1%)

regimes13.0ms (0.1%)

regimes12.0ms (0.1%)

regimes9.0ms (0.1%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify24.0ms (0.2%)

soundness1.1s (7%)

preprocess150.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	107	18
8	151	18
9	166	18
10	174	18
0	174	18