Metrics for 2cos (problem 3.3.5)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze41.0ms (0.3%)

Memory

21.1MiB live, 58.9MiB 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)

sample10.2s (65.2%)

Memory

-91.1MiB live, 10 122.8MiB allocated

Samples

3.9s	26 069×	0	invalid
3.7s	5 690×	2	valid
550.0ms	2 428×	1	valid
17.0ms	138×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.4s

ival-cos: 2.8s (44% of total)

const: 816.0ms (12.7% of total)

adjust: 754.0ms (11.7% of total)

ival-add: 374.0ms (5.8% of total)

ival-mult: 374.0ms (5.8% of total)

ival-<=: 321.0ms (5% of total)

ival-sub: 306.0ms (4.7% of total)

ival-fabs: 287.0ms (4.5% of total)

ival-<: 221.0ms (3.4% of total)

ival-and: 105.0ms (1.6% of total)

exact: 43.0ms (0.7% of total)

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

Bogosity

explain205.0ms (1.3%)

Memory

9.1MiB live, 447.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
140	1	(-8.221018175746746e-160 7.148497068513278e-164)	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
2	0	-	-	`(cos.f64 (+.f64 x eps))`
0	0	-	-	`eps`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	141	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	140	0
-	1	115

Precision

0.9929078014184397

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	140	0	0
-	1	0	115

Precision?

0.9929078014184397

Recall?

1.0

Freqs

test

number	freq
0	115
1	139
2	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

137.0ms	346×	2	valid
20.0ms	162×	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: 127.0ms

ival-cos: 98.0ms (77.1% of total)

adjust: 18.0ms (14.2% of total)

ival-sub: 6.0ms (4.7% of total)

ival-add: 3.0ms (2.4% of total)

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

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

preprocess28.0ms (0.2%)

Memory

6.7MiB live, 44.7MiB 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: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.5%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify8.0ms (0.1%)

Memory

-25.5MiB live, 13.6MiB 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)

localize84.0ms (0.5%)

Memory

6.0MiB live, 168.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(cos.f64 x)
accuracy	0.05975959538661774	(cos.f64 (+.f64 x eps))
accuracy	31.633005745537808	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

64.0ms	173×	2	valid
13.0ms	81×	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: 58.0ms

ival-cos: 44.0ms (75.4% of total)

adjust: 9.0ms (15.4% of total)

ival-sub: 3.0ms (5.1% of total)

ival-add: 2.0ms (3.4% of total)

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

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

series5.0ms (0%)

Memory

5.7MiB live, 5.7MiB 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	@	-inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms	eps	@	0	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
0.0ms	x	@	-inf	((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))

simplify139.0ms (0.9%)

Memory

-6.1MiB live, 150.2MiB 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)

rewrite157.0ms (1%)

Memory

25.1MiB live, 187.4MiB 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
#<batchref>
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eval49.0ms (0.3%)

Memory: -24.0MiB live, 59.8MiB allocated
Compiler: Compiled 7 285 to 896 computations (87.7% saved)

prune10.0ms (0.1%)

Memory

-16.6MiB live, 23.2MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	299	7	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	299	8	307

Accuracy

99.8%

Counts

307 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.6%	(fma.f64 (+.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))) #s(literal 1/2 binary64) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
	80.4%	(-.f64 (fma.f64 #s(literal -1 binary64) (cos.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (sin.f64 eps) (sin.f64 x)))
✓	50.5%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	49.8%	(-.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))
▶	49.7%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
▶	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
▶	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))

Compiler

Compiled 213 to 168 computations (21.1% saved)

simplify411.0ms (2.6%)

Memory

15.0MiB live, 133.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
cost-diff	0	(-.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x))
cost-diff	0	(.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
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	#s(approx (cos 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) #s(literal 1 binary64)))
cost-diff	0	(cos.f64 eps)
cost-diff	0	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
cost-diff	0	(.f64 (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	37	190
0	60	180
1	103	180
2	195	176
3	318	176
4	459	176
5	671	176
6	1183	176
7	1793	176
8	2368	176
9	2810	176
10	2998	176
11	3081	176
12	3146	176
13	3148	176
14	3148	176
15	3210	176
16	3234	176
17	3234	176
18	3234	176
19	3234	176
20	5425	176
21	5977	176
22	6645	176
23	6821	176
24	6821	176
25	6821	176
26	6975	176
27	7019	176
28	7019	176
29	7019	176
0	11810	172

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

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

localize232.0ms (1.5%)

Memory

-4.6MiB live, 152.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(-.f64 (.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x))
accuracy	0.01953125	(.f64 (.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
accuracy	0.10546875	(.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps)
accuracy	0.25595782087737773	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
accuracy	0	(sin.f64 x)
accuracy	0	(neg.f64 eps)
accuracy	0.01171875	(*.f64 (neg.f64 eps) (sin.f64 x))
accuracy	12.818616679951244	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
accuracy	0	(+.f64 x eps)
accuracy	0.05975959538661774	(cos.f64 (+.f64 x eps))
accuracy	1.217113782465589	#s(approx (cos x) #s(literal 1 binary64))
accuracy	31.633005745537808	(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0	(cos.f64 eps)
accuracy	30.999486598156047	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	31.435871949333066	#s(approx (- (cos (+ x eps)) (cos x)) (-.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	0.06981466660419622	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.10546875	(.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

160.0ms	179×	2	valid
36.0ms	75×	1	valid
1.0ms	2×	0	valid

Compiler

Compiled 360 to 69 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 144.0ms

ival-cos: 66.0ms (45.8% of total)

adjust: 32.0ms (22.2% of total)

ival-mult: 26.0ms (18% of total)

ival-sub: 9.0ms (6.2% of total)

ival-sin: 6.0ms (4.2% of total)

ival-add: 4.0ms (2.8% of total)

exact: 1.0ms (0.7% of total)

ival-neg: 1.0ms (0.7% of total)

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

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

series32.0ms (0.2%)

Memory

-3.8MiB live, 34.5MiB allocated

Counts

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

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

Calls

6 calls:

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

simplify174.0ms (1.1%)

Memory

15.9MiB live, 53.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	366	3590
1	1106	3431
2	2906	3382
3	6717	3382
0	8399	3187

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)))
(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 (* 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)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* 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))))))))
(* 1/2 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))))
(* 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))
(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 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))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos 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))
(* 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))
(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 (- 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))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos 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))
(* 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)
(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 (* 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)
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 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)))))))))
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))
(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 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))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos 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
(* -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))
(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 (* -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))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos 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
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 (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 (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 (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 (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)
(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 (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 (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 (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))
(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 (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 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(neg.f64 (sin.f64 x))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) 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 (.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)
(*.f64 #s(literal 1/2 binary64) 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 (/.f64 x eps) #s(literal -1/2 binary64)) eps)
eps
eps
eps
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 (.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 eps) #s(literal 1 binary64))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
(cos.f64 eps)
(cos.f64 eps)
(cos.f64 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))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 eps x))
(cos.f64 (+.f64 eps x))
eps
(fma.f64 (/.f64 x eps) eps eps)
(fma.f64 (/.f64 x eps) eps eps)
(fma.f64 (/.f64 x eps) eps 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 (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 (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 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) eps)
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) eps)
(.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) 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))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) 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 (/.f64 x eps) #s(literal -1/2 binary64)) eps)
eps
eps
eps
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)))
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(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)
(-.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))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) 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))

rewrite142.0ms (0.9%)

Memory

12.3MiB live, 59.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	157
0	60	149
1	201	149
2	1495	149
0	8551	149

Stop Event

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

Counts

21 → 506

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

Outputs
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eval99.0ms (0.6%)

Memory: 4.7MiB live, 79.0MiB allocated
Compiler: Compiled 23 768 to 2 556 computations (89.2% saved)

prune45.0ms (0.3%)

Memory

-37.9MiB live, 48.7MiB allocated

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	902	14	916
Fresh	0	2	2
Picked	3	2	5
Done	1	0	1
Total	906	18	924

Accuracy

100.0%

Counts

924 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.6%	(fma.f64 (+.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))) #s(literal 1/2 binary64) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
▶	80.4%	(-.f64 (fma.f64 #s(literal -1 binary64) (cos.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (sin.f64 eps) (sin.f64 x)))
▶	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))
	41.7%	(.f64 (.f64 (/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (-.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 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))
	99.4%	(.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))
▶	49.7%	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
✓	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
▶	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps))
✓	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
▶	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (neg.f64 eps)) x))))
	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
	79.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

Compiler

Compiled 972 to 616 computations (36.6% saved)

simplify201.0ms (1.3%)

Memory

12.9MiB live, 12.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (cos.f64 eps) (cos.f64 x))
cost-diff	0	(cos.f64 x)
cost-diff	0	(-.f64 (fma.f64 #s(literal -1 binary64) (cos.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (sin.f64 eps) (sin.f64 x)))
cost-diff	6592	(fma.f64 #s(literal -1 binary64) (cos.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x)))
cost-diff	0	#s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps))
cost-diff	0	(-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x))
cost-diff	0	(.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps))
cost-diff	0	(fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))
cost-diff	0	#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))
cost-diff	0	(.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) 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	54	357
0	89	323
1	156	323
2	299	323
3	584	323
4	1067	323
5	1674	323
6	2424	323
7	3122	323
8	3792	323
9	4029	323
10	4107	323
11	4192	323
12	4787	323
13	5019	323
14	5019	323
15	5019	323
16	5021	323
17	5021	323
18	5021	323
19	5021	323
20	5033	323
0	5033	323

Stop Event

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

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

localize324.0ms (2.1%)

Memory

5.7MiB live, 82.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(*.f64 (cos.f64 eps) (cos.f64 x))
accuracy	0.0234375	(*.f64 (sin.f64 eps) (sin.f64 x))
accuracy	0.1015625	(-.f64 (fma.f64 #s(literal -1 binary64) (cos.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (sin.f64 eps) (sin.f64 x)))
accuracy	30.969814656422248	(fma.f64 #s(literal -1 binary64) (cos.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x)))
accuracy	0.0078125	(-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x))
accuracy	0.10546875	(.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps)
accuracy	0.25595782087737773	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps))
accuracy	1.1985842521937684	#s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps))
accuracy	0.0078125	(fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))
accuracy	0.10546875	(.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)
accuracy	0.25595782087737773	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps))
accuracy	1.271136140284924	#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)))
accuracy	0.2719575799604339	#s(approx (cos eps) #s(literal 1 binary64))
accuracy	30.999486598156047	(-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64))
accuracy	31.435871949333066	#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) #s(literal 1 binary64)) #s(literal 1 binary64)))
accuracy	0.00390625	(.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x)))
accuracy	0.0078125	(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	0.10546875	(.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

235.0ms	172×	2	valid
48.0ms	82×	1	valid
1.0ms	2×	0	valid

Compiler

Compiled 640 to 104 computations (83.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 239.0ms

ival-cos: 115.0ms (48.2% of total)

adjust: 48.0ms (20.1% of total)

ival-mult: 40.0ms (16.7% of total)

ival-sub: 12.0ms (5% of total)

ival-sin: 12.0ms (5% of total)

ival-add: 9.0ms (3.8% 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)

series36.0ms (0.2%)

Memory

19.4MiB live, 19.4MiB allocated

Counts

22 → 468

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 #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 #s(literal -1 binary64) (cos.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 (fma.f64 #s(literal -1 binary64) (cos.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (sin.f64 eps) (sin.f64 x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (cos.f64 eps) (cos.f64 x)) #<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 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) (sin.f64 x)) #<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>) () ())) ())
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#s(alt #<batchref> (taylor -inf x) (#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 -inf x) (#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 -inf x) (#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 -inf x) (#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 -inf x) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (* (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal -1 binary64) (cos.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal -1 binary64) (cos.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal -1 binary64) (cos.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal -1 binary64) (cos.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (fma.f64 #s(literal -1 binary64) (cos.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (sin.f64 eps) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (fma.f64 #s(literal -1 binary64) (cos.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (sin.f64 eps) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (fma.f64 #s(literal -1 binary64) (cos.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (sin.f64 eps) (sin.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 (*.f64 (cos.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (cos.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (cos.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (cos.f64 eps) (cos.f64 x)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf x) (#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> (taylor -inf x) (#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> (taylor -inf x) (#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> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	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) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (+ (* -1 (cos x)) (* (cos eps) (cos x))) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (cos x) (* (cos eps) (cos x)) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (* (cos (* eps 1/2)) (sin (* 1 x))) (* (sin eps) (sin x)))
4.0ms	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) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (+ (* -1 (cos x)) (* (cos eps) (cos x))) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (cos x) (* (cos eps) (cos x)) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (* (cos (* eps 1/2)) (sin (* 1 x))) (* (sin eps) (sin x)))
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) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (+ (* -1 (cos x)) (* (cos eps) (cos x))) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (cos x) (* (cos eps) (cos x)) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (* (cos (* eps 1/2)) (sin (* 1 x))) (* (sin eps) (sin x)))
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) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (+ (* -1 (cos x)) (* (cos eps) (cos x))) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (cos x) (* (cos eps) (cos x)) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (* (cos (* eps 1/2)) (sin (* 1 x))) (* (sin eps) (sin x)))
3.0ms	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) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (* (* (cos x) -1/2) eps) (+ (* -1 (cos x)) (* (cos eps) (cos x))) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (cos x) (* (cos eps) (cos x)) (+ (* (sin (* eps 1/2)) (cos (* 1 x))) (* (cos (* eps 1/2)) (sin (* 1 x)))) (* (cos (* eps 1/2)) (sin (* 1 x))) (* (sin eps) (sin x)))

simplify181.0ms (1.2%)

Memory

-19.1MiB live, 60.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	424	5004
1	1356	4853
2	4111	4803
0	8381	4579

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 444

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 (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)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1 x)
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) x)
(- (* eps (- (* 1/4 (pow x 2)) 1/2)) 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)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(+ (cos x) (* -1 (cos x)))
(+ (cos x) (+ (* -1 (cos x)) (* -1/2 (* (pow eps 2) (cos x)))))
(+ (cos x) (+ (* -1 (cos x)) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x)))))))
(+ (cos x) (+ (* -1 (cos x)) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x))))))))
(+ (cos x) (* -1 (cos x)))
(+ (cos x) (+ (* -1 (cos x)) (* -1 (* eps (sin x)))))
(+ (cos x) (+ (* -1 (cos x)) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
(+ (cos x) (+ (* -1 (cos x)) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (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))))))))
(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)))))))
(* eps (sin x))
(* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin 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)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* eps (- (+ (* -1 (/ x eps)) (* 1/4 (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))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos 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 (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin 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)
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ x eps))))
(* -1 (* eps (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ 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))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos 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 (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
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)
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 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)
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(- (cos eps) 1)
(- (+ (cos eps) (* (pow x 2) (+ 1/2 (* -1/2 (cos eps))))) 1)
(- (+ (cos eps) (* (pow x 2) (+ 1/2 (+ (* -1/2 (cos eps)) (* (pow x 2) (- (* 1/24 (cos eps)) 1/24)))))) 1)
(- (+ (cos eps) (* (pow x 2) (+ 1/2 (+ (* -1/2 (cos eps)) (* (pow x 2) (- (+ (* 1/24 (cos eps)) (* (pow x 2) (+ 1/720 (* -1/720 (cos eps))))) 1/24)))))) 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
(+ 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)
(+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos 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 (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 (sin eps))
(* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin 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))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 eps)) (/ 1 x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(cos x)
(cos x)
(cos x)
(cos x)
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos 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 (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin 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))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (- (* 1/4 eps) (/ 1 x)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(* (pow x 2) (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(cos x)
(cos x)
(cos x)
(cos x)
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos 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 (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (cos (* 1/2 eps)) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))

Outputs
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 (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 #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 #s(literal 1/4 binary64) (cos.f64 x) (.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 x)) eps)) eps (.f64 #s(literal 1/2 binary64) (sin.f64 x))) 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 #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 (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 (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 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(neg.f64 (sin.f64 x))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(neg.f64 x)
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.f64 x))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps (neg.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 (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 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(neg.f64 (sin.f64 x))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
#s(literal 0 binary64)
(.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)
(.f64 (.f64 (.f64 (cos.f64 x) eps) eps) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))
(.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))
#s(literal 0 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)
(cos.f64 x)
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) (cos.f64 x))
(fma.f64 (.f64 (.f64 (cos.f64 x) eps) eps) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (cos.f64 x))
(fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64)) (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 (.f64 #s(literal -1/8 binary64) eps) (sin.f64 x) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 #s(literal -1/48 binary64) eps) #s(literal 1/2 binary64)))) eps (sin.f64 x))
(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 (sin.f64 x) eps)
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (*.f64 (sin.f64 x) eps))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64))) (*.f64 (sin.f64 x) eps))
(.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (sin.f64 x) (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64))) (.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 x))) eps)
eps
eps
eps
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(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x))
(*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x))
(*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x))
(*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x))
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x)))
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x)))
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x)))
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x)))
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(cos.f64 x)
(*.f64 (cos.f64 eps) (cos.f64 x))
(*.f64 (cos.f64 eps) (cos.f64 x))
(*.f64 (cos.f64 eps) (cos.f64 x))
(*.f64 (cos.f64 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)))
(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)))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))
(*.f64 (sin.f64 eps) (sin.f64 x))
(*.f64 (sin.f64 eps) (sin.f64 x))
(*.f64 (sin.f64 eps) (sin.f64 x))
(*.f64 (sin.f64 eps) (sin.f64 x))

rewrite147.0ms (0.9%)

Memory

-10.8MiB live, 64.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	288
0	89	257
1	314	232
2	2446	232
0	9096	229

Stop Event

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

Counts

22 → 539

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

Outputs
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eval119.0ms (0.8%)

Memory: 9.8MiB live, 90.9MiB allocated
Compiler: Compiled 36 298 to 2 832 computations (92.2% saved)

prune30.0ms (0.2%)

Memory

13.1MiB live, 52.6MiB allocated

Pruning

22 alts after pruning (18 fresh and 4 done)

	Pruned	Kept	Total
New	991	10	1 001
Fresh	3	8	11
Picked	3	2	5
Done	0	2	2
Total	997	22	1 019

Accuracy

100.0%

Counts

1 019 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	80.4%	(fma.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
▶	99.8%	(-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) (*.f64 (sin.f64 eps) (sin.f64 x)))
	99.8%	(-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (.f64 (.f64 (cos.f64 x) eps) eps) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (*.f64 (sin.f64 eps) (sin.f64 x)))
	98.7%	(.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 (neg.f64 (.f64 eps eps)) (pow.f64 (neg.f64 eps) #s(literal -1 binary64)))))) #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))
	99.4%	(.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))
▶	49.7%	#s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64))
✓	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
✓	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps))
✓	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
▶	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
✓	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
	50.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps))) eps))
	97.7%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps))
	79.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x)) (.f64 x x)))) eps))
	50.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 (*.f64 eps x) x) #s(literal 1/4 binary64)))) eps))
	79.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x))) eps))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (neg.f64 eps)) x))))
▶	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))

Compiler

Compiled 1 221 to 838 computations (31.4% saved)

simplify114.0ms (0.7%)

Memory

-6.0MiB live, 31.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
cost-diff	0	(.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)))
cost-diff	0	(.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))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
cost-diff	0	#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps)))
cost-diff	0	(.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps)
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
cost-diff	0	(fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))
cost-diff	0	(.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)))
cost-diff	0	#s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))
cost-diff	0	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
cost-diff	0	#s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))
cost-diff	0	#s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps)))
cost-diff	0	(-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) (*.f64 (sin.f64 eps) (sin.f64 x)))
cost-diff	6720	(fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	464
0	107	449
1	204	441
2	501	437
3	1240	437
4	2863	434
5	4138	434
6	5632	434
0	8020	426

Stop Event

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

Calls

Call 1

Inputs
(-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) (*.f64 (sin.f64 eps) (sin.f64 x)))
#s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps)))
(.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))
(fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)))
(cos.f64 x)
x
(fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 eps eps)
eps
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
(*.f64 (sin.f64 eps) (sin.f64 x))
(sin.f64 eps)
(sin.f64 x)
#s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
#s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))
(.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)
(.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)))
eps
(fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))
(*.f64 #s(literal 1/6 binary64) x)
#s(literal 1/6 binary64)
x
#s(literal -1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
(.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps)
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64))
(fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))
#s(literal 1/6 binary64)
x
(*.f64 #s(literal 1/4 binary64) eps)
#s(literal 1/4 binary64)
eps
#s(literal -1 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
(.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 (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)))
(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
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))
(*.f64 eps eps)
#s(literal -1/48 binary64)
#s(literal -2 binary64)

Outputs
(fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps) (cos.f64 x))))
#s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps) (cos.f64 x)))
(.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps) (cos.f64 x))
(.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (cos.f64 x))
(cos.f64 x)
x
(fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
#s(literal -1/720 binary64)
(*.f64 eps eps)
eps
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
#s(literal -1/2 binary64)
(*.f64 (sin.f64 x) (sin.f64 eps))
(sin.f64 eps)
(sin.f64 x)
#s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)) eps)))
#s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)) eps))
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)) eps)
(.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) eps)
eps
(fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))
(*.f64 #s(literal 1/6 binary64) x)
#s(literal 1/6 binary64)
x
#s(literal -1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
(.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps)
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(fma.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64))
(fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))
#s(literal 1/6 binary64)
x
(*.f64 #s(literal 1/4 binary64) eps)
#s(literal 1/4 binary64)
eps
#s(literal -1 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #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))
(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
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
(*.f64 eps eps)
#s(literal -1/48 binary64)
#s(literal -2 binary64)

localize408.0ms (2.6%)

Memory

-16.6MiB live, 106.3MiB allocated

Localize:

Found 17 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))) #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))
accuracy	0.056126445480057324	#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))
accuracy	0.06981466660419622	(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
accuracy	0.10546875	(.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)))
accuracy	0.10546875	(.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps)
accuracy	0.25595782087737773	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
accuracy	0.3662300293053261	(fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps))
accuracy	0.8024194371448311	#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps)))
accuracy	0.00390625	(.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)
accuracy	0.3828125	(*.f64 #s(literal 1/6 binary64) x)
accuracy	0.8027586967302975	#s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))
accuracy	12.627770488345202	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
accuracy	31.944982706897928	#s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64))
accuracy	0.0234375	(*.f64 (sin.f64 eps) (sin.f64 x))
accuracy	0.0234375	(.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)))
accuracy	0.0390625	(.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))
accuracy	0.1015625	(-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) (*.f64 (sin.f64 eps) (sin.f64 x)))

Samples

277.0ms	172×	2	valid
77.0ms	81×	1	valid
2.0ms	1×	5	exit
1.0ms	2×	0	valid

Compiler

Compiled 794 to 137 computations (82.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 288.0ms

ival-cos: 112.0ms (38.9% of total)

ival-mult: 70.0ms (24.3% of total)

adjust: 46.0ms (16% of total)

const: 20.0ms (6.9% of total)

ival-add: 20.0ms (6.9% of total)

ival-sin: 10.0ms (3.5% of total)

ival-sub: 8.0ms (2.8% of total)

exact: 1.0ms (0.3% of total)

ival-neg: 1.0ms (0.3% of total)

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

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

series41.0ms (0.3%)

Memory

25.7MiB live, 25.7MiB allocated

Counts

23 → 516

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) (*.f64 (sin.f64 eps) (sin.f64 x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) #<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))) #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)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.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))) #<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 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) (sin.f64 x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) (*.f64 (sin.f64 eps) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) (*.f64 (sin.f64 eps) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) (*.f64 (sin.f64 eps) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) (*.f64 (sin.f64 eps) (sin.f64 x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #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 x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.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 (*.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 (*.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 (*.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 (.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)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.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)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.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)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.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)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.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))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.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))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.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))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.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))) #<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 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/6 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) eps)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	((+ (* (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* eps eps)) (* -1/2 (cos x))) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (+ (* (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* eps eps)) (* -1/2 (cos x))) (* eps eps)) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* eps (+ (* (* 1/6 x) x) -1)) (+ (* (* 1/6 x) x) -1) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* (+ (* (+ (* 1/6 x) (* 1/4 eps)) x) -1) x) (* -1/2 eps)) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* (sin eps) (sin x)) (* 1/6 x) (* (* eps (+ (* (* 1/6 x) x) -1)) x) (+ (* 1/6 x) (* 1/4 eps)) (sin (* 1/2 (+ 0 eps))))
5.0ms	x	@	-inf	((+ (* (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* eps eps)) (* -1/2 (cos x))) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (+ (* (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* eps eps)) (* -1/2 (cos x))) (* eps eps)) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* eps (+ (* (* 1/6 x) x) -1)) (+ (* (* 1/6 x) x) -1) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* (+ (* (+ (* 1/6 x) (* 1/4 eps)) x) -1) x) (* -1/2 eps)) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* (sin eps) (sin x)) (* 1/6 x) (* (* eps (+ (* (* 1/6 x) x) -1)) x) (+ (* 1/6 x) (* 1/4 eps)) (sin (* 1/2 (+ 0 eps))))
5.0ms	eps	@	inf	((+ (* (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* eps eps)) (* -1/2 (cos x))) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (+ (* (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* eps eps)) (* -1/2 (cos x))) (* eps eps)) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* eps (+ (* (* 1/6 x) x) -1)) (+ (* (* 1/6 x) x) -1) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* (+ (* (+ (* 1/6 x) (* 1/4 eps)) x) -1) x) (* -1/2 eps)) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* (sin eps) (sin x)) (* 1/6 x) (* (* eps (+ (* (* 1/6 x) x) -1)) x) (+ (* 1/6 x) (* 1/4 eps)) (sin (* 1/2 (+ 0 eps))))
4.0ms	eps	@	0	((+ (* (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* eps eps)) (* -1/2 (cos x))) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (+ (* (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* eps eps)) (* -1/2 (cos x))) (* eps eps)) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* eps (+ (* (* 1/6 x) x) -1)) (+ (* (* 1/6 x) x) -1) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* (+ (* (+ (* 1/6 x) (* 1/4 eps)) x) -1) x) (* -1/2 eps)) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* (sin eps) (sin x)) (* 1/6 x) (* (* eps (+ (* (* 1/6 x) x) -1)) x) (+ (* 1/6 x) (* 1/4 eps)) (sin (* 1/2 (+ 0 eps))))
4.0ms	eps	@	-inf	((+ (* (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* eps eps)) (* -1/2 (cos x))) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (+ (* (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* eps eps)) (* -1/2 (cos x))) (* eps eps)) (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* eps (+ (* (* 1/6 x) x) -1)) (+ (* (* 1/6 x) x) -1) (- (cos (+ x eps)) (cos x)) (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (- (* (* (cos x) -1/2) eps) (sin x)) (+ (* (+ (* (+ (* 1/6 x) (* 1/4 eps)) x) -1) x) (* -1/2 eps)) (* 1/2 (+ (* 2 x) eps)) (* (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) -2) (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 (+ 0 eps)))) (sin (* 1/2 (+ (* 2 x) eps))) (* (cos x) (+ (* -1/720 (* eps eps)) 1/24)) (* (sin eps) (sin x)) (* 1/6 x) (* (* eps (+ (* (* 1/6 x) x) -1)) x) (+ (* 1/6 x) (* 1/4 eps)) (sin (* 1/2 (+ 0 eps))))

simplify141.0ms (0.9%)

Memory

15.8MiB live, 52.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	533	6103
1	1756	5855
2	5581	5817
0	8543	5445

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 513

Calls

Call 1

Inputs
(* -1/2 (cos x))
(+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))
(+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))
(+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))
(+ (cos x) (* -1 (cos x)))
(+ (cos x) (+ (* -1 (cos x)) (* -1 (* eps (sin x)))))
(+ (cos x) (+ (* -1 (cos x)) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
(+ (cos x) (+ (* -1 (cos x)) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))))
(+ (cos x) (* -1 (cos x)))
(+ (cos x) (+ (* -1 (cos x)) (* -1/2 (* (pow eps 2) (cos x)))))
(+ (cos x) (+ (* -1 (cos x)) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x)))))))
(+ (cos x) (+ (* -1 (cos x)) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x))))))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x)))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x))))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x))))))
(+ (cos x) (* -1 (cos x)))
(+ (cos x) (+ (* -1 (cos x)) (* -1 (* eps (sin x)))))
(+ (cos x) (+ (* -1 (cos x)) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))))
(+ (cos x) (+ (* -1 (cos x)) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (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)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* -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)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* x (- (* 1/6 (pow x 2)) 1))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
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))))))))
(* 1/24 (cos x))
(+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))
(+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))
(+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))
(* eps (sin x))
(* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(* 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))))
(* -1/720 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2)))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 4))) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2))))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 4))) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2))))))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(* -1/720 (* (pow eps 6) (cos x)))
(* (pow eps 6) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2)))))
(* (pow eps 6) (+ (* -1/2 (/ (cos x) (pow eps 4))) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2))))))
(* (pow eps 6) (+ (* -1/2 (/ (cos x) (pow eps 4))) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2))))))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin 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)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) 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))))))
(* (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))))
(* -1/720 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2)))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* 1/4 eps)
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* -1/720 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2)))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 4))) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2))))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 4))) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2))))))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(* -1/720 (* (pow eps 6) (cos x)))
(* (pow eps 6) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2)))))
(* (pow eps 6) (+ (* -1/2 (/ (cos x) (pow eps 4))) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2))))))
(* (pow eps 6) (+ (* -1/2 (/ (cos x) (pow eps 4))) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2))))))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin 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)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (* 1/6 (pow x 2)) 1))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))
(* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))
(* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))
(* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 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)))))
(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))))
(* -1/720 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/720 (cos x)) (* 1/24 (/ (cos x) (pow eps 2)))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* 1/4 eps)
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)
(- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/4 (* -1/2 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) 1/2)
(- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/4 (+ (* -1/2 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (- (* 1/24 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/48)))))) 1/2)
(- (+ (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ 1/4 (+ (* -1/2 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (- (+ (* 1/24 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* (pow x 2) (+ 1/1440 (* -1/720 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) 1/48)))))) 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)
(- (cos eps) 1)
(- (+ (cos eps) (* (pow x 2) (+ 1/2 (* -1/2 (cos eps))))) 1)
(- (+ (cos eps) (* (pow x 2) (+ 1/2 (+ (* -1/2 (cos eps)) (* (pow x 2) (- (* 1/24 (cos eps)) 1/24)))))) 1)
(- (+ (cos eps) (* (pow x 2) (+ 1/2 (+ (* -1/2 (cos eps)) (* (pow x 2) (- (+ (* 1/24 (cos eps)) (* (pow x 2) (+ 1/720 (* -1/720 (cos eps))))) 1/24)))))) 1)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(+ (* (pow eps 2) (* (pow x 2) (+ 1/4 (* -1/2 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* (pow eps 2) (* (pow x 2) (- (* 1/24 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/48))) (* (pow eps 2) (+ 1/4 (* -1/2 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))))))))
(+ (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) (* (pow x 2) (+ (* (pow eps 2) (+ 1/4 (* -1/2 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))))) (* (pow x 2) (+ (* (pow eps 2) (* (pow x 2) (+ 1/1440 (* -1/720 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2))))) 1/48)))))))
(- (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 eps)
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
(+ (* -1 eps) (* 1/6 (* eps (pow x 2))))
-1
(- (* 1/6 (pow x 2)) 1)
(- (* 1/6 (pow x 2)) 1)
(- (* 1/6 (pow x 2)) 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)
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* 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)))))))))
(+ 1/24 (* -1/720 (pow eps 2)))
(+ 1/24 (+ (* -1/2 (* (pow x 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* -1/720 (pow eps 2))))
(+ 1/24 (+ (* -1/720 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1/24 (* -1/720 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1/24 (* -1/720 (pow eps 2)))))))))
(+ 1/24 (+ (* -1/720 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1/24 (* -1/720 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1/24 (* -1/720 (pow eps 2))))) (* 1/24 (+ 1/24 (* -1/720 (pow eps 2))))))))))
(* x (sin eps))
(* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* 1/4 eps)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2))))))
(+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2))))))
(+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2))))))
(+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2))))))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin 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)))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/4 (/ eps x))))
(* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 3))) (* 1/4 (/ eps x)))) (/ 1 (pow x 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)))))
(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) (+ 1/24 (* -1/720 (pow eps 2))))
(* (cos x) (+ 1/24 (* -1/720 (pow eps 2))))
(* (cos x) (+ 1/24 (* -1/720 (pow eps 2))))
(* (cos x) (+ 1/24 (* -1/720 (pow eps 2))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* 1/6 x)
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2))))))
(+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2))))))
(+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2))))))
(+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2))))))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(+ (* -1 (cos x)) (* (cos eps) (cos x)))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (* (cos x) (+ 1/24 (* -1/720 (pow eps 2)))))))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x)))
(- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin 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 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* 1/6 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 2) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)) 1/6)))
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)))))
(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) (+ 1/24 (* -1/720 (pow eps 2))))
(* (cos x) (+ 1/24 (* -1/720 (pow eps 2))))
(* (cos x) (+ 1/24 (* -1/720 (pow eps 2))))
(* (cos x) (+ 1/24 (* -1/720 (pow eps 2))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* 1/6 x)
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))

Outputs
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(.f64 (cos.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))
(fma.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64)) (cos.f64 x) (.f64 (cos.f64 x) (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64))))
(fma.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64)) (cos.f64 x) (.f64 (cos.f64 x) (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64))))
#s(literal 0 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 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
#s(literal 0 binary64)
(.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) eps)
(.f64 (.f64 (cos.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64))) (.f64 eps eps))
(.f64 (fma.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64)) (cos.f64 x) (.f64 (cos.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))) (*.f64 eps eps))
(.f64 (.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) eps)
(.f64 (.f64 (cos.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64))) (.f64 eps eps))
(.f64 (fma.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64)) (cos.f64 x) (.f64 (cos.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))) (*.f64 eps eps))
(.f64 (fma.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64)) (cos.f64 x) (.f64 (cos.f64 x) (fma.f64 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))) (*.f64 eps eps))
#s(literal 0 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 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (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 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (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 (.f64 #s(literal 1/24 binary64) eps) 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 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 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 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (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 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))) eps (neg.f64 (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 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(neg.f64 (sin.f64 x))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x)))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x))
(fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)))
(fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)))
(fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)))
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 (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (cos.f64 x) (neg.f64 (sin.f64 x))) eps)
(.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (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 (.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))) eps (neg.f64 (sin.f64 x))) eps)
(.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 (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 #s(literal 1/2 binary64) (sin.f64 x))) 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 (fma.f64 #s(literal -1/8 binary64) (sin.f64 x) (.f64 #s(literal -1/48 binary64) (.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x))
(*.f64 #s(literal 1/24 binary64) (cos.f64 x))
(.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (cos.f64 x))
(.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (cos.f64 x))
(.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
(.f64 (.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) (sin.f64 x)) eps)
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 (sin.f64 x) (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64))) (*.f64 (sin.f64 x) eps))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) (sin.f64 x) (.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (sin.f64 x) (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64))))) eps)
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)) eps)
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)) eps)
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)) eps)
(*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64) (neg.f64 x)) eps)
(*.f64 #s(literal 1/6 binary64) x)
(fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))
(fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))
(fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))
(*.f64 #s(literal 1/2 binary64) eps)
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #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)
(.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/720 binary64)) (cos.f64 x))
(.f64 (fma.f64 (/.f64 #s(literal 1/24 binary64) eps) (/.f64 (cos.f64 x) eps) (.f64 #s(literal -1/720 binary64) (cos.f64 x))) (pow.f64 eps #s(literal 4 binary64)))
(.f64 (fma.f64 (cos.f64 x) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/24 binary64) eps) (/.f64 (cos.f64 x) eps) (.f64 #s(literal -1/720 binary64) (cos.f64 x)))) (pow.f64 eps #s(literal 4 binary64)))
(.f64 (fma.f64 (cos.f64 x) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/24 binary64) eps) (/.f64 (cos.f64 x) eps) (.f64 #s(literal -1/720 binary64) (cos.f64 x)))) (pow.f64 eps #s(literal 4 binary64)))
(fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x)))
(fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x)))
(fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x)))
(fma.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x) (*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x)))
(*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x))
(*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x))
(*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x))
(*.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (cos.f64 x))
(.f64 (.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/720 binary64)) (cos.f64 x))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (fma.f64 (/.f64 #s(literal 1/24 binary64) eps) (/.f64 (cos.f64 x) eps) (.f64 #s(literal -1/720 binary64) (cos.f64 x))))
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(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
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(.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))
(.f64 (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)) (.f64 x x))
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x
(fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x) x)
(fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x) x)
(fma.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (neg.f64 x) x)
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(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))
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(.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)) (cos.f64 x))
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(*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/6 binary64) eps (/.f64 (/.f64 (neg.f64 eps) x) x)))
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/4 binary64) #s(literal -1/6 binary64)) (neg.f64 x))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/4 binary64) #s(literal -1/6 binary64)) (neg.f64 x))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/4 binary64) #s(literal -1/6 binary64)) (neg.f64 x))

rewrite170.0ms (1.1%)

Memory

-21.4MiB live, 61.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	387
0	107	367
1	398	358
2	3363	358
0	9092	354

Stop Event

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

Counts

23 → 412

Calls

Call 1

Inputs
(fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) (*.f64 (sin.f64 eps) (sin.f64 x)))
#s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps)))
(.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))
#s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
#s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x))
(.f64 eps (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)))
(fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
(.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps)
#s(approx (- (* (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps))
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(.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)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64)))
(*.f64 (sin.f64 eps) (sin.f64 x))
(*.f64 #s(literal 1/6 binary64) x)
(.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)
(fma.f64 #s(literal 1/6 binary64) x (*.f64 #s(literal 1/4 binary64) 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))

Outputs
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eval98.0ms (0.6%)

Memory: 9.2MiB live, 83.4MiB allocated
Compiler: Compiled 37 854 to 2 899 computations (92.3% saved)

prune32.0ms (0.2%)

Memory

12.7MiB live, 50.5MiB allocated

Pruning

23 alts after pruning (17 fresh and 6 done)

	Pruned	Kept	Total
New	916	9	925
Fresh	5	8	13
Picked	3	2	5
Done	0	4	4
Total	924	23	947

Accuracy

100.0%

Counts

947 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (.f64 (cos.f64 x) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64))) (*.f64 eps eps))))
	99.8%	(-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (.f64 (.f64 (cos.f64 x) eps) eps) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (*.f64 (sin.f64 eps) (sin.f64 x)))
	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))
	99.4%	(.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))
	99.7%	(.f64 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))) #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))
✓	49.7%	#s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64))
✓	99.4%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 (.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps) (sin.f64 x)) eps))
✓	99.3%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps))
✓	80.0%	#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/6 x) (* 1/4 eps)) (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
✓	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps))
	97.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
	50.9%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* 1/6 x) (* 1/4 eps)) x) -1) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps))) eps))
	79.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x)) (.f64 x x)))) eps))
	50.1%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 (*.f64 eps x) x) #s(literal 1/4 binary64)))) eps))
	79.0%	#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x))) eps))
	98.6%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (neg.f64 eps)) x))))
	98.0%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (*.f64 eps x))))
	22.1%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (fma.f64 (neg.f64 (.f64 eps eps)) (neg.f64 eps) (.f64 eps (.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) (neg.f64 (.f64 eps eps))))) (.f64 eps (neg.f64 eps))) x)))
	78.7%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 eps)) x)))
✓	79.3%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
	49.5%	#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx ( eps (+ (* (* 1/6 x) x) -1)) (.f64 (.f64 (*.f64 eps x) x) #s(literal 1/6 binary64))) x)))

Compiler

Compiled 1 884 to 768 computations (59.2% saved)

regimes33.0ms (0.2%)

Memory

-33.5MiB live, 15.7MiB allocated

Counts

41 → 1

Calls

Call 1

Inputs
#s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64))
#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)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx ( eps (+ (* (* 1/6 x) x) -1)) (.f64 (.f64 (*.f64 eps x) x) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 (*.f64 eps x) x) #s(literal 1/4 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (*.f64 eps x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* 1/6 x) (* 1/4 eps)) x) -1) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/6 x) (* 1/4 eps)) (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x)) (.f64 x x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (fma.f64 (neg.f64 (.f64 eps eps)) (neg.f64 eps) (.f64 eps (.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) (neg.f64 (.f64 eps eps))))) (.f64 eps (neg.f64 eps))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) 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 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))) #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 (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 (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))
(.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 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (.f64 (.f64 (cos.f64 x) eps) eps) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (*.f64 (sin.f64 eps) (sin.f64 x)))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (.f64 (cos.f64 x) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64))) (*.f64 eps eps))))
(fma.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (sin.f64 x)))
(-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (.f64 eps eps))) (*.f64 (sin.f64 eps) (sin.f64 x)))
(-.f64 (fma.f64 #s(literal -1 binary64) (cos.f64 x) (.f64 (cos.f64 eps) (cos.f64 x))) (.f64 (sin.f64 eps) (sin.f64 x)))
(fma.f64 (+.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))) #s(literal 1/2 binary64) (neg.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))))
(.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 (.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 (neg.f64 (.f64 eps eps)) (pow.f64 (neg.f64 eps) #s(literal -1 binary64)))))) #s(literal -2 binary64))
(.f64 (.f64 (/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (-.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1 binary64) x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

10.0ms	eps
10.0ms	x
8.0ms	(-.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)

regimes24.0ms (0.2%)

Memory

13.3MiB live, 13.3MiB allocated

Counts

33 → 1

Calls

Call 1

Inputs
#s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64))
#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)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 #s(approx ( eps (+ (* (* 1/6 x) x) -1)) (.f64 (.f64 (*.f64 eps x) x) #s(literal 1/6 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (.f64 (*.f64 eps x) x) #s(literal 1/4 binary64)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (.f64 eps (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (*.f64 eps x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* (+ (* (+ (* 1/6 x) (* 1/4 eps)) x) -1) x) (* -1/2 eps)) (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1/2 binary64)) (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/6 x) (* 1/4 eps)) (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (.f64 (fma.f64 #s(literal 1/4 binary64) eps (/.f64 #s(literal -1 binary64) x)) (.f64 x x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) #s(approx (+ (* eps (+ (* (* x x) 1/4) -1/2)) (neg x)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) eps)) #s(literal -1/2 binary64)) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (fma.f64 (.f64 (.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (neg.f64 (.f64 eps eps))) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (.f64 (/.f64 (fma.f64 (neg.f64 (.f64 eps eps)) (neg.f64 eps) (.f64 eps (.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) (neg.f64 (.f64 eps eps))))) (.f64 eps (neg.f64 eps))) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) 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 (.f64 (sin.f64 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))) #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 (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 (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))
(.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 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (.f64 (.f64 (cos.f64 x) eps) eps) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (*.f64 (sin.f64 eps) (sin.f64 x)))

Outputs

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

Calls

3 calls:

8.0ms	eps
8.0ms	x
7.0ms	(-.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)

regimes24.0ms (0.2%)

Memory

13.3MiB live, 13.3MiB allocated

Counts

32 → 1

Calls

Call 1

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

Outputs
(.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))

Calls

3 calls:

8.0ms	eps
8.0ms	x
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)

regimes24.0ms (0.2%)

Memory

-26.4MiB live, 12.9MiB allocated

Counts

31 → 1

Calls

Call 1

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

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:

8.0ms	eps
8.0ms	x
7.0ms	(-.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

11.8MiB live, 11.8MiB allocated

Counts

28 → 1

Calls

Call 1

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

Outputs

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

regimes20.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

26 → 1

Calls

Call 1

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

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
99.4%	1	`x`
99.4%	1	`eps`
99.4%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.1%)

Memory

-28.4MiB live, 11.2MiB allocated

Counts

25 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes19.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated

Counts

24 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Counts

18 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.1%)

Memory

7.6MiB live, 7.6MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.0%	1	`x`
98.0%	1	`eps`
98.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory

-34.8MiB live, 5.0MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
79.0%	1	`x`
79.0%	1	`eps`
79.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs

#s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64))

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

Outputs
#s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 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
49.7%	1	`x`
49.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
49.7%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify25.0ms (0.2%)

Memory

19.4MiB live, 19.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	351
1	163	351
2	187	351
3	202	351
4	208	351

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (.f64 (cos.f64 x) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64))) (*.f64 eps eps))))
(-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (.f64 (.f64 (cos.f64 x) eps) eps) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)))) (*.f64 (sin.f64 eps) (sin.f64 x)))
(.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) (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 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x))) #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 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 eps (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps))) x (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/6 x) (* 1/4 eps)) (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (neg.f64 x) eps (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64))

Outputs
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (cos.f64 x)) (*.f64 eps eps))))
(-.f64 #s(approx (+ (* -1 (cos x)) (* (cos eps) (cos x))) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) eps) eps))) (*.f64 (sin.f64 eps) (sin.f64 x)))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 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 #s(approx (* 1/2 (+ (* 2 x) eps)) (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 #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))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 (-.f64 #s(approx ( (* (cos x) -1/2) eps) (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) eps (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x (.f64 #s(literal 1/4 binary64) eps)) eps) x (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/6 x) (* 1/4 eps)) (.f64 #s(literal 1/6 binary64) x)) x #s(literal -1 binary64)) x (.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (* (cos x) -1/2) eps) (sin x)) eps) (fma.f64 (neg.f64 x) eps (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))
#s(approx (- (cos (+ x eps)) (cos x)) (.f64 #s(approx (- ( (* (cos x) -1/2) eps) (sin x)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (+ (* -1 (cos x)) (* (cos eps) (cos x))) (* (sin eps) (sin x))) #s(literal 0 binary64))

soundness1.2s (7.9%)

Memory

-22.4MiB live, 18.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	387
0	107	367
1	398	358
2	3363	358
0	9092	354
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	533	6103
1	1756	5855
2	5581	5817
0	8543	5445
0	366	3590
1	1106	3431
2	2906	3382
3	6717	3382
0	8399	3187
0	424	5004
1	1356	4853
2	4111	4803
0	8381	4579
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×	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 659 to 347 computations (47.3% saved)

preprocess74.0ms (0.5%)

Memory: 25.4MiB live, 64.3MiB allocated
Compiler: Compiled 750 to 290 computations (61.3% 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%)

analyze41.0ms (0.3%)

sample10.2s (65.2%)

explain205.0ms (1.3%)

preprocess28.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify8.0ms (0.1%)

localize84.0ms (0.5%)

series5.0ms (0%)

simplify139.0ms (0.9%)

rewrite157.0ms (1%)

eval49.0ms (0.3%)

prune10.0ms (0.1%)

simplify411.0ms (2.6%)

localize232.0ms (1.5%)

series32.0ms (0.2%)

simplify174.0ms (1.1%)

rewrite142.0ms (0.9%)

eval99.0ms (0.6%)

prune45.0ms (0.3%)

simplify201.0ms (1.3%)

localize324.0ms (2.1%)

series36.0ms (0.2%)

simplify181.0ms (1.2%)

rewrite147.0ms (0.9%)

eval119.0ms (0.8%)

prune30.0ms (0.2%)

simplify114.0ms (0.7%)

localize408.0ms (2.6%)

series41.0ms (0.3%)

simplify141.0ms (0.9%)

rewrite170.0ms (1.1%)

eval98.0ms (0.6%)

prune32.0ms (0.2%)

regimes33.0ms (0.2%)

regimes24.0ms (0.2%)

regimes24.0ms (0.2%)

regimes24.0ms (0.2%)

regimes21.0ms (0.1%)

regimes20.0ms (0.1%)

regimes20.0ms (0.1%)

regimes19.0ms (0.1%)

regimes15.0ms (0.1%)

regimes12.0ms (0.1%)

regimes6.0ms (0%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify25.0ms (0.2%)

soundness1.2s (7.9%)

preprocess74.0ms (0.5%)

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