Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze41.0ms (0.3%)

Memory

14.3MiB live, 52.9MiB 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)

sample6.7s (53%)

Memory

-190.0MiB live, 6 696.4MiB allocated

Samples

3.6s	26 264×	0	invalid
647.0ms	5 429×	0	valid
433.0ms	2 827×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.6s

const: 896.0ms (25.2% of total)

ival-sin: 742.0ms (20.9% of total)

ival-mult: 528.0ms (14.9% of total)

ival-add: 284.0ms (8% of total)

ival-<=: 258.0ms (7.3% of total)

ival-sub: 216.0ms (6.1% of total)

ival-fabs: 213.0ms (6% of total)

ival-<: 175.0ms (4.9% of total)

ival-and: 109.0ms (3.1% of total)

adjust: 73.0ms (2.1% of total)

exact: 47.0ms (1.3% of total)

ival-assert: 13.0ms (0.4% of total)

Bogosity

explain100.0ms (0.8%)

Memory

24.5MiB live, 145.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
223	5	(1.8108691400316763e-249 9.814208414101727e-252)	2	(2.683220340783668e-194 3.703869171771409e-196)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
0	1	(-632.8079536509733 4.428062031802412e-12)	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	226	9
`sin.f64`	`(sin.f64 (+.f64 x eps))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	221	2
-	5	28

Precision

0.9778761061946902

Recall

0.9910313901345291

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	221	2	0
-	5	7	21

Precision?

0.948936170212766

Recall?

1.0

Freqs

test

number	freq
0	30
1	225
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

37.0ms	168×	1	valid
16.0ms	340×	0	valid
1.0ms	4×	3	valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-sin: 30.0ms (75.7% of total)

adjust: 3.0ms (7.6% of total)

ival-add: 3.0ms (7.6% of total)

ival-sub: 3.0ms (7.6% of total)

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

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

preprocess35.0ms (0.3%)

Memory

-9.4MiB live, 29.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	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 (sin.f64 (+.f64 x eps)) (sin.f64 x))

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Memory

9.3MiB live, 9.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

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

localize30.0ms (0.2%)

Memory

-19.8MiB live, 55.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	(sin.f64 x)
accuracy	0.04363251953688403	(sin.f64 (+.f64 x eps))
accuracy	23.540467793007167	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

13.0ms	84×	1	valid
8.0ms	170×	0	valid
1.0ms	2×	3	valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-sin: 8.0ms (55.3% of total)

adjust: 3.0ms (20.7% of total)

ival-add: 2.0ms (13.8% of total)

ival-sub: 2.0ms (13.8% of total)

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

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

series5.0ms (0%)

Memory

10.2MiB live, 10.1MiB allocated

Counts

4 → 84

Calls

Call 1

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

Outputs
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (cos x))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (taylor 0 eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- x (* -1 eps))) (sin x)) (taylor -inf eps) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- x (* -1 eps))) (taylor -inf eps) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (sin eps) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (cos eps) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) (taylor 0 x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin eps) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (cos eps))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) (taylor 0 x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/6 (pow x 2)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (taylor 0 x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (+ eps x)) (sin x)) (taylor inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (+ eps x)) (taylor inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (sin (- eps (* -1 x))) (taylor -inf x) (#s(alt (sin.f64 (+.f64 x eps)) (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())
#s(alt (sin x) (taylor -inf x) (#s(alt (sin.f64 x) (patch (sin.f64 x) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify170.0ms (1.4%)

Memory

-3.9MiB live, 207.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	496
1	314	496
2	775	489
3	2829	489
4	6198	489
0	8141	458

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 77

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
x
(+ eps x)
(+ eps x)
(+ eps x)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(sin x)
(sin x)
(sin x)
(sin x)
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(sin x)
(sin x)
(sin x)
(sin x)

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

rewrite150.0ms (1.2%)

Memory

5.7MiB live, 200.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16

Stop Event

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

Counts

4 → 214

Calls

Call 1

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

Outputs
#<batchref>
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eval36.0ms (0.3%)

Memory: -12.5MiB live, 63.7MiB allocated
Compiler: Compiled 6 625 to 852 computations (87.1% saved)

prune8.0ms (0.1%)

Memory

24.9MiB live, 24.9MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	286	5	291
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	286	6	292

Accuracy

100.0%

Counts

292 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	63.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	99.9%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
▶	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
▶	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 111 to 94 computations (15.3% saved)

simplify233.0ms (1.8%)

Memory

6.3MiB live, 88.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
cost-diff	0	(fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
cost-diff	0	(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
cost-diff	0	(cos.f64 x)
cost-diff	0	(*.f64 (cos.f64 x) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff	0	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff	128	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
cost-diff	192	(+.f64 #s(literal 0 binary64) eps)
cost-diff	576	(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	221
0	56	211
1	89	211
2	190	211
3	451	211
4	625	211
5	738	211
6	817	211
7	851	211
8	986	211
9	1021	211
10	1248	211
11	1600	211
12	1939	211
13	2675	211
14	3213	211
15	3371	208
16	3488	208
17	3609	208
18	3945	208
19	4892	208
20	5975	208
21	6213	208
22	6429	208
23	6507	208
24	6531	208
25	6585	208
26	7631	208
0	8011	206

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

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

localize156.0ms (1.2%)

Memory

-0.2MiB live, 154.8MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
accuracy	0.01171875	(*.f64 (cos.f64 x) eps)
accuracy	0.015625	(fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
accuracy	0.10474212647000496	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
accuracy	0	(cos.f64 x)
accuracy	0.0078125	(.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)
accuracy	0.01171875	(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x))
accuracy	0.3561300526783626	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
accuracy	0	(cos.f64 x)
accuracy	0.01171875	(*.f64 (cos.f64 x) eps)
accuracy	0.9397492705821587	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
accuracy	0	(sin.f64 eps)
accuracy	2.043753361807231	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))
accuracy	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)))
accuracy	0.00390625	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64))
accuracy	0.04644337485707608	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Samples

85.0ms	173×	0	valid
47.0ms	83×	1	valid

Compiler

Compiled 391 to 65 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 102.0ms

ival-mult: 65.0ms (63.8% of total)

ival-add: 12.0ms (11.8% of total)

ival-sin: 7.0ms (6.9% of total)

adjust: 5.0ms (4.9% of total)

ival-cos: 4.0ms (3.9% of total)

const: 4.0ms (3.9% of total)

ival-div: 2.0ms (2% of total)

ival-sub: 1.0ms (1% of total)

exact: 1.0ms (1% of total)

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

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

series66.0ms (0.5%)

Memory

-14.9MiB live, 59.6MiB allocated

Counts

20 → 396

Calls

Call 1

Inputs
#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())
#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())
#s(alt (sin.f64 eps) (patch (sin.f64 eps) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (cos.f64 x) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (cos.f64 x) eps)) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 x) eps) (patch (.f64 (cos.f64 x) eps) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) (patch (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (patch (.f64 (sin.f64 x) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) (patch (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) #<representation binary64>) () ())

Outputs
#s(alt (* -1 x) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 x) (* -1/2 eps)) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 x) (* -1/2 eps)) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 x) (* -1/2 eps)) (taylor 0 eps) (#s(alt (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 #s(literal 0 binary64) eps) (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (cos (* -1 x)) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) (taylor 0 eps) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) (patch (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) (patch (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) (patch (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) (patch (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (patch (.f64 (sin.f64 x) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (patch (.f64 (sin.f64 x) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (patch (.f64 (sin.f64 x) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sin x)) (taylor -inf x) (#s(alt (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (patch (.f64 (sin.f64 x) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) (patch (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) (patch (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
29.0ms	eps	@	inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)))
4.0ms	x	@	0	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)))
4.0ms	eps	@	0	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)))
4.0ms	eps	@	-inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)))
4.0ms	x	@	inf	((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* 1/2 (+ 0 eps)))

simplify236.0ms (1.9%)

Memory

1.0MiB live, 182.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	386	3975
1	1177	3719
2	3278	3637
3	7926	3637
0	8160	3377

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 380

Calls

Call 1

Inputs
(* -1 x)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
eps
eps
eps
eps
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* -1/2 (sin x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 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)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1/2 eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
eps
eps
eps
eps
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* eps (cos x)))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
eps
eps
eps
eps
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* -1/6 (* eps (cos x)))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))

Outputs
(* -1 x)
(neg.f64 x)
(+ (* -1 x) (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
(+ (* -1 x) (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
(+ (* -1 x) (* -1/2 eps))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
eps
eps
eps
eps
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (.f64 (cos.f64 x) #s(literal -1/8 binary64)) eps)) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) (.f64 (*.f64 (cos.f64 x) #s(literal -1/8 binary64)) eps)) eps (cos.f64 x))
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(.f64 (fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) (.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
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(*.f64 #s(literal -1/6 binary64) eps)
(+ (* -1/2 x) (* -1/6 eps))
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))
(* -1 x)
(neg.f64 x)
(* x (- (* -1/2 (/ eps x)) 1))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x)
(* x (- (* -1/2 (/ eps x)) 1))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x)
(* x (- (* -1/2 (/ eps x)) 1))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x)
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(* -1/2 (sin x))
(*.f64 (sin.f64 x) #s(literal -1/2 binary64))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))

rewrite197.0ms (1.6%)

Memory

-12.2MiB live, 226.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	185
0	56	175
1	188	175
2	1555	175
0	8255	175

Stop Event

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

Counts

20 → 632

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval148.0ms (1.2%)

Memory: 12.9MiB live, 292.8MiB allocated
Compiler: Compiled 28 458 to 3 057 computations (89.3% saved)

prune86.0ms (0.7%)

Memory

8.4MiB live, 85.0MiB allocated

Pruning

23 alts after pruning (20 fresh and 3 done)

	Pruned	Kept	Total
New	1 115	20	1 135
Fresh	0	0	0
Picked	2	3	5
Done	1	0	1
Total	1 118	23	1 141

Accuracy

100.0%

Counts

1 141 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.9%	(.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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.8%	(.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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	47.4%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
✓	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
▶	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
▶	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps x) eps)))
▶	99.9%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))

Compiler

Compiled 661 to 500 computations (24.4% saved)

simplify112.0ms (0.9%)

Memory

-5.2MiB live, 78.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(neg.f64 (*.f64 eps eps))
cost-diff	0	(.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
cost-diff	1280	(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))
cost-diff	0	#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
cost-diff	384	(fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64)))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) x)
cost-diff	0	(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
cost-diff	0	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
cost-diff	0	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
cost-diff	0	(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
cost-diff	0	(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
cost-diff	128	(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	440
0	95	438
1	178	438
2	474	434
3	1392	426
4	2966	416
5	4658	416
6	7934	416
0	8358	396

Stop Event

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

Calls

Call 1

Inputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
eps
#s(literal -1/2 binary64)
(neg.f64 x)
x
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(*.f64 eps (+.f64 eps x))
eps
(+.f64 eps x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64)))
(fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
(*.f64 eps (+.f64 eps x))
eps
(+.f64 eps x)
x
#s(literal 1/12 binary64)
#s(literal -1/2 binary64)
(*.f64 eps #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(*.f64 eps eps)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))
(.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x))
(neg.f64 (*.f64 eps eps))
(*.f64 eps eps)
eps
(cos.f64 x)
x
(neg.f64 eps)

Outputs
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
eps
#s(literal -1/2 binary64)
(neg.f64 x)
x
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (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)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 (+.f64 x eps) eps) (.f64 x #s(literal -1/2 binary64)) eps)))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 (+.f64 x eps) eps) (.f64 x #s(literal -1/2 binary64)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
(fma.f64 (.f64 (+.f64 x eps) eps) (.f64 x #s(literal -1/2 binary64)) eps)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
x
(*.f64 eps (+.f64 eps x))
(*.f64 (+.f64 x eps) eps)
eps
(+.f64 eps x)
(+.f64 x eps)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x) (+.f64 x eps) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
(.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x) (+.f64 x eps) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x) (+.f64 x eps) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) x) (+.f64 x eps) (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64)))
(.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) x) eps #s(literal -1/2 binary64)) (+.f64 x eps))
(fma.f64 (*.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/12 binary64) (*.f64 (+.f64 x eps) eps) #s(literal -1/2 binary64))
(*.f64 eps (+.f64 eps x))
(*.f64 (+.f64 x eps) eps)
eps
(+.f64 eps x)
(+.f64 x eps)
x
#s(literal 1/12 binary64)
#s(literal -1/2 binary64)
(*.f64 eps #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) eps)
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
(*.f64 eps eps)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))
(*.f64 (cos.f64 x) eps)
(.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x))
(.f64 (neg.f64 eps) (.f64 (cos.f64 x) eps))
(neg.f64 (*.f64 eps eps))
(*.f64 (neg.f64 eps) eps)
(*.f64 eps eps)
eps
(cos.f64 x)
x
(neg.f64 eps)

localize177.0ms (1.4%)

Memory

-20.4MiB live, 170.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(cos.f64 x)
accuracy	0.0078125	(.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x))
accuracy	0.9397492705821587	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
accuracy	32.7288630672104	(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))
accuracy	0.02734375	(fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64)))
accuracy	0.1015625	(*.f64 eps (+.f64 eps x))
accuracy	0.10474212647000496	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
accuracy	1.4561210438859844	#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
accuracy	0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0.1015625	(*.f64 eps (+.f64 eps x))
accuracy	0.3561300526783626	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
accuracy	1.4368172811726831	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))
accuracy	0.0078125	(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
accuracy	0.3561300526783626	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
accuracy	2.0650079917750532	#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
accuracy	0	(neg.f64 x)
accuracy	0	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
accuracy	0.00390625	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
accuracy	0.04644337485707608	(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))

Samples

73.0ms	169×	0	valid
63.0ms	85×	1	valid
2.0ms	2×	3	valid

Compiler

Compiled 590 to 102 computations (82.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 111.0ms

ival-mult: 40.0ms (36.2% of total)

ival-add: 18.0ms (16.3% of total)

adjust: 14.0ms (12.7% of total)

ival-cos: 13.0ms (11.8% of total)

const: 8.0ms (7.2% of total)

ival-sin: 7.0ms (6.3% of total)

ival-div: 4.0ms (3.6% of total)

ival-neg: 3.0ms (2.7% of total)

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

exact: 1.0ms (0.9% of total)

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

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

series49.0ms (0.4%)

Memory

15.8MiB live, 53.3MiB allocated

Counts

23 → 492

Calls

Call 1

Inputs
#s(alt (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (patch (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (patch #s(approx ( (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (patch (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)) (patch (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (patch (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))) #<representation binary64>) () ())
#s(alt #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)) (patch #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/2 binary64) x) (patch (.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) (patch (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) (patch (.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (patch #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)) (patch (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (patch (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) #<representation binary64>) () ())
#s(alt (neg.f64 (.f64 eps eps)) (patch (neg.f64 (.f64 eps eps)) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (patch (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (.f64 eps (+.f64 eps x)) (patch (.f64 eps (+.f64 eps x)) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())

Outputs
#s(alt (cos (neg x)) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (patch (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (patch (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x)))))) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (patch (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x)))))) (taylor 0 eps) (#s(alt (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (patch (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos (* -1 x))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (patch #s(approx ( (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (patch #s(approx ( (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (patch #s(approx ( (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) (taylor 0 eps) (#s(alt #s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (patch #s(approx ( (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos (neg x))) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (patch (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (patch (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (patch (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))) (taylor 0 eps) (#s(alt (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (patch (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 eps) (#s(alt (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)) (patch (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 eps) x) (taylor 0 eps) (#s(alt (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)) (patch (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 eps) x) (taylor 0 eps) (#s(alt (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)) (patch (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 eps) x) (taylor 0 eps) (#s(alt (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)) (patch (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (patch (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (patch (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (patch (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) (patch (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor 0 eps) (#s(alt #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor 0 eps) (#s(alt #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor 0 eps) (#s(alt #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* -1/2 (* eps (sin x)))) (taylor 0 eps) (#s(alt #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) (taylor 0 eps) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor 0 eps) (#s(alt #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)) (patch #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)) (patch #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)) (patch #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* -1/2 (* eps (sin x))))) (taylor 0 eps) (#s(alt #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)) (patch #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* -1/2 (pow x 2)))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps) #<representation binary64>) () ())) ())
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#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (.f64 #s(literal -1/2 binary64) x) (patch (.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/12 (* eps (pow x 2))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) (patch (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) (patch (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) (patch (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) (patch (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) (patch (.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) (patch (.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) (patch (.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) (patch (.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (patch #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (patch #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (patch #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (patch #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor -inf x) (#s(alt (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)) (patch (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor -inf x) (#s(alt (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)) (patch (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor -inf x) (#s(alt (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)) (patch (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (cos x)) (taylor -inf x) (#s(alt (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)) (patch (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 2) (cos x))) (taylor -inf x) (#s(alt (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (patch (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 2) (cos x))) (taylor -inf x) (#s(alt (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (patch (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 2) (cos x))) (taylor -inf x) (#s(alt (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (patch (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow eps 2) (cos x))) (taylor -inf x) (#s(alt (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (patch (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* eps x) (taylor -inf x) (#s(alt (.f64 eps (+.f64 eps x)) (patch (.f64 eps (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (.f64 eps (+.f64 eps x)) (patch (.f64 eps (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (.f64 eps (+.f64 eps x)) (patch (.f64 eps (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (.f64 eps (+.f64 eps x)) (patch (.f64 eps (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (cos x)) (neg (* eps eps)) (* (sin (* 1/2 eps)) 2) (neg x) (* eps (+ eps x)) (cos x))
5.0ms	eps	@	inf	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (cos x)) (neg (* eps eps)) (* (sin (* 1/2 eps)) 2) (neg x) (* eps (+ eps x)) (cos x))
4.0ms	eps	@	-inf	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (cos x)) (neg (* eps eps)) (* (sin (* 1/2 eps)) 2) (neg x) (* eps (+ eps x)) (cos x))
4.0ms	x	@	-inf	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (cos x)) (neg (* eps eps)) (* (sin (* 1/2 eps)) 2) (neg x) (* eps (+ eps x)) (cos x))
4.0ms	x	@	inf	((cos (+ (* eps -1/2) (neg x))) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (cos (+ (* eps -1/2) (neg x))) (* (sin (* 1/2 eps)) 2)) (+ (* eps -1/2) (neg x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (- (sin (+ x eps)) (sin x)) (* (neg (* eps eps)) (cos x)) (neg (* eps eps)) (* (sin (* 1/2 eps)) 2) (neg x) (* eps (+ eps x)) (cos x))

simplify166.0ms (1.3%)

Memory

19.6MiB live, 168.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	469	5214
1	1521	5010
2	4035	4939
0	8315	4552

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 487

Calls

Call 1

Inputs
(cos (neg x))
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x))))))
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (cos (neg x)))
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))))
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))))
(* -1 x)
(- (* -1/2 eps) x)
(- (* -1/2 eps) x)
(- (* -1/2 eps) x)
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* -1/2 x)
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2)))
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* eps x)
(* eps (+ eps x))
(* eps (+ eps x))
(* eps (+ eps x))
(cos (neg (+ x (* 1/2 eps))))
(cos (neg (+ x (* 1/2 eps))))
(cos (neg (+ x (* 1/2 eps))))
(cos (neg (+ x (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (neg (+ x (* 1/2 eps)))) (sin (* 1/2 eps))))
(* -1/2 eps)
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* 1/12 (* (pow eps 2) x))
(* (pow eps 2) (- (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/12 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(pow eps 2)
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* 1/12 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* -1/12 (pow x 2))) eps)) (* 1/12 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/12 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/12 x)))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* -1 (pow eps 2))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(pow eps 2)
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* -1/2 eps))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))
(+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* -1 (pow eps 2))
(+ (* -1 (pow eps 2)) (* 1/2 (* (pow eps 2) (pow x 2))))
(+ (* -1 (pow eps 2)) (* (pow x 2) (+ (* -1/24 (* (pow eps 2) (pow x 2))) (* 1/2 (pow eps 2)))))
(+ (* -1 (pow eps 2)) (* (pow x 2) (+ (* 1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/24 (pow eps 2)) (* 1/720 (* (pow eps 2) (pow x 2))))))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(pow eps 2)
(+ (* eps x) (pow eps 2))
(+ (* eps x) (pow eps 2))
(+ (* eps x) (pow eps 2))
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 (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(cos (- (* -1/2 eps) x))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* -1/2 eps) x)) (sin (* 1/2 eps))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(* x (- (* -1/2 (/ eps x)) 1))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x)))) (* 1/2 (/ 1 x))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos (+ (* -1 x) (* -1/2 eps)))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos (+ (* -1 x) (* -1/2 eps)))
(cos (+ (* -1 x) (* -1/2 eps)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* 1/12 (* eps (pow x 2)))
(* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 (* (pow eps 2) (cos x)))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* eps x)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(cos x)
(cos x)
(cos x)
(cos x)

Outputs
(cos (neg x))
(cos.f64 x)
(+ (cos (neg x)) (* 1/2 (* eps (sin (neg x)))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos (neg x)) (* eps (- (* -1/8 (* eps (cos (neg x)))) (* -1/2 (sin (neg x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal -1/8 binary64) eps) (cos.f64 x))) eps (cos.f64 x))
(+ (cos (neg x)) (* eps (- (* eps (+ (* -1/8 (cos (neg x))) (* -1/48 (* eps (sin (neg x)))))) (* -1/2 (sin (neg x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (.f64 #s(literal -1/48 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 x) #s(literal -1/8 binary64))) eps)) eps (cos.f64 x))
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps)) eps (cos.f64 x)) eps)
(* eps (cos (neg x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (neg x)) (* 1/2 (* eps (sin (neg x))))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* 2 (* eps (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x))))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos (neg x)) (* eps (+ (* 1/2 (sin (neg x))) (* eps (+ (* -1/24 (* eps (sin (neg x)))) (* 2 (+ (* -1/16 (cos (neg x))) (* -1/48 (cos (neg x)))))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 (.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps)) eps (cos.f64 x)) eps)
(* -1 x)
(neg.f64 x)
(- (* -1/2 eps) x)
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(- (* -1/2 eps) x)
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(- (* -1/2 eps) x)
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps)) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps)) eps (cos.f64 x)) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ 1 (* -1/2 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x))
(+ (* -1/2 x) (* eps (- (+ (* 1/12 (* eps x)) (* 1/12 (pow x 2))) 1/2)))
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(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ (* -1 x) (* -1/2 eps))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x)
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64)) x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* -1/2 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(.f64 (.f64 (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)) (*.f64 x x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) (/.f64 eps x)) x)) x) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) (/.f64 eps x)) x)) x) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* 1/12 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 eps x) x) #s(literal 1/12 binary64))
(* (pow x 2) (- (+ (* 1/12 eps) (* 1/12 (/ (pow eps 2) x))) (* 1/2 (/ 1 x))))
(.f64 (fma.f64 (fma.f64 eps (/.f64 eps x) eps) #s(literal 1/12 binary64) (/.f64 #s(literal -1/2 binary64) x)) (.f64 x x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) (fma.f64 #s(literal -1/12 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 x))) x) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))) x)) (* 1/12 eps)))
(.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) (fma.f64 #s(literal -1/12 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 x))) x) x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x))) eps (cos.f64 x)) eps)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (sin.f64 x) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x))) eps (cos.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* -1 (* (pow eps 2) (cos x)))
(.f64 (neg.f64 eps) (.f64 (cos.f64 x) eps))
(* -1 (* (pow eps 2) (cos x)))
(.f64 (neg.f64 eps) (.f64 (cos.f64 x) eps))
(* -1 (* (pow eps 2) (cos x)))
(.f64 (neg.f64 eps) (.f64 (cos.f64 x) eps))
(* -1 (* (pow eps 2) (cos x)))
(.f64 (neg.f64 eps) (.f64 (cos.f64 x) eps))
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* eps x)
(*.f64 eps x)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 eps (/.f64 eps x) eps) x)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 eps (/.f64 eps x) eps) x)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 eps (/.f64 eps x) eps) x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)

rewrite202.0ms (1.6%)

Memory

10.8MiB live, 209.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	358
0	95	356
1	367	344
2	3137	344
0	8618	332

Stop Event

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

Counts

23 → 562

Calls

Call 1

Inputs
(cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
(.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)
(*.f64 #s(literal -1/2 binary64) x)
(fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
(.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x))
(neg.f64 (*.f64 eps eps))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(neg.f64 x)
(*.f64 eps (+.f64 eps x))
(cos.f64 x)

Outputs
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eval209.0ms (1.7%)

Memory: 4.7MiB live, 241.5MiB allocated
Compiler: Compiled 29 438 to 4 132 computations (86% saved)

prune55.0ms (0.4%)

Memory

-10.1MiB live, 111.9MiB allocated

Pruning

30 alts after pruning (23 fresh and 7 done)

	Pruned	Kept	Total
New	1 211	10	1 221
Fresh	2	13	15
Picked	1	4	5
Done	0	3	3
Total	1 214	30	1 244

Accuracy

100.0%

Counts

1 244 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.9%	(.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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.8%	(.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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
✓	47.4%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
	46.9%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 eps)))
	46.9%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 (.f64 (.f64 eps x) x) eps) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) x) x (.f64 (.f64 eps #s(literal 1/2 binary64)) eps)) (.f64 x x) (.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
✓	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
▶	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
▶	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (* eps (+ eps x)) (.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (.f64 (.f64 (.f64 eps x) x) #s(literal 1/12 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
✓	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
▶	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
✓	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x (/.f64 x eps) x) (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
▶	5.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
	99.8%	#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #s(approx ( (sin (* 1/2 eps)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps))))

Compiler

Compiled 914 to 671 computations (26.6% saved)

simplify156.0ms (1.2%)

Memory

-1.6MiB live, 108.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)))
cost-diff	0	(fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
cost-diff	0	#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
cost-diff	0	(.f64 (.f64 eps x) x)
cost-diff	0	#s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
cost-diff	320	(fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) eps))
cost-diff	0	(.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64))
cost-diff	0	#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64))))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
cost-diff	0	(.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)
cost-diff	0	#s(approx (sin (* 1/2 (+ 0 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))
cost-diff	0	(.f64 #s(approx (sin ( 1/2 (+ 0 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)) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	661
0	117	655
1	219	655
2	621	647
3	1871	639
4	3593	639
5	5525	639
0	8691	620

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx (sin ( 1/2 (+ 0 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)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 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 (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)
(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))
(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))
(fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64))
#s(literal -1/645120 binary64)
(*.f64 eps eps)
eps
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
x
#s(literal -2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64))))
#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))
(.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64))
(.f64 (.f64 eps x) x)
(*.f64 eps x)
eps
x
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
(fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
(fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) eps))
(.f64 (.f64 eps x) x)
(*.f64 eps x)
eps
x
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
(*.f64 x x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
#s(literal 1/12 binary64)
#s(literal -1/2 binary64)
x
(*.f64 #s(literal -1/2 binary64) eps)
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x))
#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)))
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
#s(literal -1/6 binary64)
eps
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(cos.f64 x)

Outputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) (.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #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 (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)) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) #s(approx (sin ( 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
#s(approx (sin (* 1/2 (+ 0 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))
#s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #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 (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(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))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64))
(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))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64))
(fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64))
#s(literal -1/645120 binary64)
(*.f64 eps eps)
eps
#s(literal 1/3840 binary64)
#s(literal -1/48 binary64)
#s(literal 1/2 binary64)
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal -2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x eps) x)))))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64))))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x eps) x))))
#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x eps) x)))
(.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x eps) x))
(.f64 (.f64 eps x) x)
(.f64 (.f64 x eps) x)
(*.f64 eps x)
(*.f64 x eps)
eps
x
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (.f64 eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))))
#s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (.f64 eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))
(fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
(.f64 eps (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))))
(fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) eps))
(.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) eps)
(.f64 (.f64 eps x) x)
(.f64 (.f64 x eps) x)
(*.f64 eps x)
(*.f64 x eps)
eps
x
#s(literal 1/24 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
(*.f64 x x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
(.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(fma.f64 (*.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
#s(literal 1/12 binary64)
#s(literal -1/2 binary64)
x
(*.f64 #s(literal -1/2 binary64) eps)
(fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64))
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x))
#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)))
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
#s(literal -1/6 binary64)
eps
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
(cos.f64 x)

localize268.0ms (2.1%)

Memory

-4.7MiB live, 314.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)
accuracy	0.0078125	(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
accuracy	0.10474212647000496	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
accuracy	1.946389431846776	#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)))
accuracy	0.00390625	(.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
accuracy	0.01953125	(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
accuracy	0.10474212647000496	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
accuracy	1.4538298367106193	#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
accuracy	0.01297628162065376	(fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) eps))
accuracy	0.0859375	(.f64 (.f64 eps x) x)
accuracy	0.9397492705821587	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
accuracy	1.1405394195200003	#s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
accuracy	0.0859375	(.f64 (.f64 eps x) x)
accuracy	0.3561300526783626	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
accuracy	1.4368172811726831	#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64))))
accuracy	60.37375830649558	#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))
accuracy	0.00390625	(.f64 #s(approx (sin ( 1/2 (+ 0 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)) #s(literal 2 binary64))
accuracy	0.0078125	(.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)
accuracy	0.01171875	(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))
accuracy	0.04644337485707608	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Samples

107.0ms	170×	0	valid
95.0ms	84×	1	valid
3.0ms	2×	3	valid

Compiler

Compiled 853 to 126 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 155.0ms

ival-mult: 57.0ms (36.8% of total)

adjust: 33.0ms (21.3% of total)

ival-add: 24.0ms (15.5% of total)

const: 19.0ms (12.3% of total)

ival-sin: 6.0ms (3.9% of total)

ival-div: 4.0ms (2.6% of total)

ival-cos: 4.0ms (2.6% of total)

ival-neg: 4.0ms (2.6% of total)

ival-sub: 2.0ms (1.3% of total)

exact: 1.0ms (0.6% of total)

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

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

series58.0ms (0.5%)

Memory

0.0MiB live, 120.8MiB allocated

Counts

24 → 528

Calls

Call 1

Inputs
#s(alt (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (sin ( 1/2 (+ 0 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)) #s(literal 2 binary64)) (patch (.f64 #s(approx (sin ( 1/2 (+ 0 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)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sin (* 1/2 (+ 0 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)) (patch #s(approx (sin (* 1/2 (+ 0 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)) #<representation binary64>) () ())
#s(alt (.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) (patch (.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) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (.f64 eps x) x) #s(literal -1/2 binary64))))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx ( (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (.f64 eps x) x) #s(literal -1/2 binary64)))) (patch #s(approx ( (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (.f64 eps x) x) #s(literal -1/2 binary64))) (patch #s(approx (+ ( (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 eps x) x) #s(literal -1/2 binary64)) (patch (.f64 (.f64 (.f64 eps x) x) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (patch (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))) (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))) #<representation binary64>) () ())
#s(alt #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) (patch #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 eps x) x) (patch (.f64 (.f64 eps x) x) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) (patch (.f64 #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (patch #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (patch (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps) #<representation binary64>) () ())
#s(alt (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) (patch (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())
#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (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)) (patch (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)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) (patch (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) (patch (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())

Outputs
#s(alt (* eps (cos (* -1 x))) (taylor 0 eps) (#s(alt (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) (taylor 0 eps) (#s(alt (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) (taylor 0 eps) (#s(alt (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) (taylor 0 eps) (#s(alt (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (patch (.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (.f64 #s(approx (sin ( 1/2 (+ 0 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)) #s(literal 2 binary64)) (patch (.f64 #s(approx (sin ( 1/2 (+ 0 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)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) (patch #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (patch (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (patch (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (patch (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) (patch (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (- (sin (- eps (* -1 x))) (sin x)) (taylor -inf x) (#s(alt #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)) (patch #s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps) (patch (.f64 (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) (patch (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) (patch (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) (patch (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))) (taylor -inf x) (#s(alt (fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) (patch (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor -inf x) (#s(alt #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor -inf x) (#s(alt #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor -inf x) (#s(alt #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))) (taylor -inf x) (#s(alt #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (cos (* -1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* -1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* -1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (cos (* -1/2 (- eps (* -2 x)))) (taylor -inf x) (#s(alt (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (* 1/12 (pow eps 2)) 1/2)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) (patch (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) (patch (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) (patch (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) (patch (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) (patch (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1/2 (* 1/6 (/ eps x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) (patch (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1/2 (* 1/6 (/ eps x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) (patch (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1/2 (* 1/6 (/ eps x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) (patch (fma.f64 #s(literal -1/6 binary64) eps (.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	eps	@	-inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* (* (* eps x) x) -1/2) (+ (* (* (* eps x) x) 1/24) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (* (* eps x) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (cos (/ (+ (* 2 x) eps) -2)) (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (+ (* -1/6 eps) (* -1/2 x)))
5.0ms	eps	@	inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* (* (* eps x) x) -1/2) (+ (* (* (* eps x) x) 1/24) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (* (* eps x) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (cos (/ (+ (* 2 x) eps) -2)) (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (+ (* -1/6 eps) (* -1/2 x)))
4.0ms	eps	@	0	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* (* (* eps x) x) -1/2) (+ (* (* (* eps x) x) 1/24) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (* (* eps x) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (cos (/ (+ (* 2 x) eps) -2)) (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (+ (* -1/6 eps) (* -1/2 x)))
4.0ms	x	@	inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* (* (* eps x) x) -1/2) (+ (* (* (* eps x) x) 1/24) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (* (* eps x) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (cos (/ (+ (* 2 x) eps) -2)) (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (+ (* -1/6 eps) (* -1/2 x)))
4.0ms	x	@	-inf	((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* (* (* eps x) x) -1/2) (+ (* (* (* eps x) x) 1/24) (* -1/2 eps)) (- (sin (+ x eps)) (sin x)) (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (* (* eps x) x) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (- (sin (+ x eps)) (sin x)) (* (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) eps) (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (cos (/ (+ (* 2 x) eps) -2)) (+ (* (+ (* -1/645120 (* eps eps)) 1/3840) (* eps eps)) -1/48) (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (+ (* -1/6 eps) (* -1/2 x)))

simplify231.0ms (1.8%)

Memory

-7.1MiB live, 254.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	478	6299
1	1449	5996
2	4208	5913
0	8794	5456

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 524

Calls

Call 1

Inputs
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
eps
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 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 (* -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))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* -1/2 (sin x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
-1/48
(- (* 1/3840 (pow eps 2)) 1/48)
(- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)
(- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)
(* -1/2 x)
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))
(* -1/2 x)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/2 x) (* -1/6 eps))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* -1/645120 (pow eps 7))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(* eps (- (* 1/24 (pow x 2)) 1/2))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2)))))
(* -1/6 (* eps (cos x)))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* eps (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* 1/12 (* (pow eps 2) x))
(* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1/2 (/ x (pow eps 2))) (* 1/12 x)) (* 1/2 (/ 1 eps))))
(* -1/6 eps)
(* eps (- (* -1/2 (/ x eps)) 1/6))
(* eps (- (* -1/2 (/ x eps)) 1/6))
(* eps (- (* -1/2 (/ x eps)) 1/6))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* -1/645120 (pow eps 7))
(* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1 (* eps (+ 1/2 (* -1/24 (pow x 2)))))
(* -1 (* eps (+ 1/2 (* -1/24 (pow x 2)))))
(* -1 (* eps (+ 1/2 (* -1/24 (pow x 2)))))
(* -1 (* eps (+ 1/2 (* -1/24 (pow x 2)))))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(* -1/6 (* (pow eps 3) (cos x)))
(* -1 (* (pow eps 3) (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x)))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))))
(* -1/6 (* eps (cos x)))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(* -1 (* eps (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps)))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* 1/12 (* (pow eps 2) x))
(* (pow eps 2) (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* 1/2 (/ x eps))) eps)) (* 1/12 x)))
(* -1/6 eps)
(* -1 (* eps (+ 1/6 (* 1/2 (/ x eps)))))
(* -1 (* eps (+ 1/6 (* 1/2 (/ x eps)))))
(* -1 (* eps (+ 1/6 (* 1/2 (/ x eps)))))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/12 (* (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2)))))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (+ (* 1/12 (* eps x)) (* 1/12 (pow eps 2))) 1/2))))))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/6 eps) (* x (- (* 1/12 (* eps x)) 1/2)))
(+ (* -1/6 eps) (* x (- (* x (+ (* 1/12 eps) (* 1/12 x))) 1/2)))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))
(* -1/6 eps)
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/2 x) (* -1/6 eps))
(+ (* -1/2 x) (* -1/6 eps))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* 1/24 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* x (- (* 1/12 (pow eps 2)) 1/2))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* -1/2 x)
(* x (- (* -1/6 (/ eps x)) 1/2))
(* x (- (* -1/6 (/ eps x)) 1/2))
(* x (- (* -1/6 (/ eps x)) 1/2))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* 1/24 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(* x (- (* 1/12 (pow eps 2)) 1/2))
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(* -1/2 x)
(* -1 (* x (+ 1/2 (* 1/6 (/ eps x)))))
(* -1 (* x (+ 1/2 (* 1/6 (/ eps x)))))
(* -1 (* x (+ 1/2 (* 1/6 (/ eps x)))))

Outputs
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
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(* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) x)
(* x (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* -1/6 (/ eps x)) 1/2))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/6 binary64) #s(literal -1/2 binary64)) x)
(* x (- (* -1/6 (/ eps x)) 1/2))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/6 binary64) #s(literal -1/2 binary64)) x)
(* x (- (* -1/6 (/ eps x)) 1/2))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/6 binary64) #s(literal -1/2 binary64)) x)
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* -1/2 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(.f64 (.f64 (fma.f64 eps (/.f64 eps x) eps) #s(literal -1/2 binary64)) (*.f64 x x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) eps) #s(literal -1 binary64) (/.f64 eps x)) x)) x) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) eps) #s(literal -1 binary64) (/.f64 eps x)) x)) x) x)
(* -1/2 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64))
(* -1/2 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64))
(* -1/2 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64))
(* -1/2 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x eps) x) #s(literal -1/2 binary64))
(* 1/24 (* eps (pow x 2)))
(.f64 (.f64 (*.f64 x x) #s(literal 1/24 binary64)) eps)
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(.f64 (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) eps)) x) x)
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(.f64 (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) eps)) x) x)
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(.f64 (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) eps)) x) x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (pow x 2))
(.f64 (.f64 x eps) x)
(* eps (pow x 2))
(.f64 (.f64 x eps) x)
(* eps (pow x 2))
(.f64 (.f64 x eps) x)
(* eps (pow x 2))
(.f64 (.f64 x eps) x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)) x) x)
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/12 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) x) x)
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) x)) x)) #s(literal 1/2 binary64)) (.f64 x x))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) eps) eps (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) x)) x)) #s(literal 1/2 binary64)) (.f64 x x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))
(fma.f64 (.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (.f64 (sin.f64 x) #s(literal -1/2 binary64)))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))
(* x (- (* 1/12 (pow eps 2)) 1/2))
(.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x)
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(.f64 (neg.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) (fma.f64 #s(literal -1/12 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) x)
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(.f64 (neg.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) (fma.f64 #s(literal -1/12 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) x)
(* -1 (* x (+ (* -1 (- (* 1/12 (pow eps 2)) 1/2)) (* 1/2 (/ eps x)))))
(.f64 (neg.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) (fma.f64 #s(literal -1/12 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))) x)
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* -1 (* x (+ 1/2 (* 1/6 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (neg.f64 x))
(* -1 (* x (+ 1/2 (* 1/6 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (neg.f64 x))
(* -1 (* x (+ 1/2 (* 1/6 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (neg.f64 x))

rewrite210.0ms (1.7%)

Memory

11.4MiB live, 238.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	546
0	117	540
1	474	528
2	4250	528
0	10641	513

Stop Event

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

Counts

24 → 389

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 #s(approx (sin ( 1/2 (+ 0 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)) #s(literal 2 binary64))
#s(approx (sin (* 1/2 (+ 0 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 (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)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64))))
#s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))
(.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64))
(fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
(.f64 (.f64 eps x) x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
(.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
(.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps)
(fma.f64 #s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x))
#s(approx (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x)))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(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))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps))
(fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))

Outputs
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eval155.0ms (1.2%)

Memory: 6.8MiB live, 201.8MiB allocated
Compiler: Compiled 26 057 to 2 697 computations (89.6% saved)

prune44.0ms (0.4%)

Memory

8.6MiB live, 91.7MiB allocated

Pruning

29 alts after pruning (20 fresh and 9 done)

	Pruned	Kept	Total
New	935	8	943
Fresh	6	12	18
Picked	2	3	5
Done	1	6	7
Total	944	29	973

Accuracy

100.0%

Counts

973 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps) eps (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.9%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
	99.9%	(.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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.8%	(.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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.5%	(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
✓	47.4%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
	46.9%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 eps)))
	46.9%	#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 (.f64 (.f64 eps x) x) eps) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) x) x (.f64 (.f64 eps #s(literal 1/2 binary64)) eps)) (.f64 x x) (.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
✓	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
✓	99.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
	99.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
✓	98.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) #s(approx (+ (* -1/6 eps) (* -1/2 x)) (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
	98.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
✓	98.5%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
	97.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (* eps (+ eps x)) (.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
	95.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 x eps) (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps))) (.f64 eps eps))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
✓	96.8%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
✓	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
	97.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps)))
✓	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
	97.6%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
	97.4%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x (/.f64 x eps) x) (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
✓	5.5%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))

Compiler

Compiled 1 238 to 625 computations (49.5% saved)

regimes61.0ms (0.5%)

Memory

-27.3MiB live, 46.8MiB allocated

Counts

44 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (.f64 (.f64 (.f64 eps x) x) #s(literal 1/12 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x (/.f64 x eps) x) (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (* eps (+ eps x)) (.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 x eps) (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps))) (.f64 eps eps))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 (.f64 (.f64 eps x) x) eps) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) x) x (.f64 (.f64 eps #s(literal 1/2 binary64)) eps)) (.f64 x x) (.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) #s(approx (+ (* -1/6 eps) (* -1/2 x)) (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps) eps (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) #s(approx ( (sin (* 1/2 eps)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps))))
#s(approx (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (cos.f64 (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))

Outputs

(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) eps) eps) eps (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Calls

3 calls:

31.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
17.0ms	x
11.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes31.0ms (0.2%)

Memory

19.1MiB live, 19.1MiB allocated

Counts

37 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (.f64 (.f64 (.f64 eps x) x) #s(literal 1/12 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x (/.f64 x eps) x) (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (* eps (+ eps x)) (.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 x eps) (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps))) (.f64 eps eps))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 (.f64 (.f64 eps x) x) eps) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) x) x (.f64 (.f64 eps #s(literal 1/2 binary64)) eps)) (.f64 x x) (.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) #s(approx (+ (* -1/6 eps) (* -1/2 x)) (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes73.0ms (0.6%)

Memory

-37.9MiB live, 18.3MiB allocated

Counts

35 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (.f64 (.f64 (.f64 eps x) x) #s(literal 1/12 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x (/.f64 x eps) x) (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (* eps (+ eps x)) (.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 x eps) (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps))) (.f64 eps eps))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 (.f64 (.f64 eps x) x) eps) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) x) x (.f64 (.f64 eps #s(literal 1/2 binary64)) eps)) (.f64 x x) (.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) #s(approx (+ (* -1/6 eps) (* -1/2 x)) (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes54.0ms (0.4%)

Memory

37.5MiB live, 37.5MiB allocated

Counts

34 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (.f64 (.f64 (.f64 eps x) x) #s(literal 1/12 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x (/.f64 x eps) x) (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (* eps (+ eps x)) (.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 x eps) (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps))) (.f64 eps eps))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 (.f64 (.f64 eps x) x) eps) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) x) x (.f64 (.f64 eps #s(literal 1/2 binary64)) eps)) (.f64 x x) (.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) #s(approx (+ (* -1/6 eps) (* -1/2 x)) (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
(.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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes51.0ms (0.4%)

Memory

-0.7MiB live, 36.3MiB allocated

Counts

33 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (.f64 (.f64 (.f64 eps x) x) #s(literal 1/12 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x (/.f64 x eps) x) (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (* eps (+ eps x)) (.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 x eps) (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps))) (.f64 eps eps))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 (.f64 (.f64 eps x) x) eps) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) x) x (.f64 (.f64 eps #s(literal 1/2 binary64)) eps)) (.f64 x x) (.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) #s(approx (+ (* -1/6 eps) (* -1/2 x)) (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 #s(literal 1/12 binary64) (+.f64 eps x)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 (fma.f64 (.f64 (+.f64 x eps) #s(literal 1/12 binary64)) x #s(literal -1/2 binary64)) x (.f64 #s(literal -1/6 binary64) eps))) eps (cos.f64 x)) eps))

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

Calls

3 calls:

32.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	eps
9.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes31.0ms (0.2%)

Memory

3.2MiB live, 39.2MiB allocated

Counts

30 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (.f64 (.f64 (.f64 eps x) x) #s(literal 1/12 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x (/.f64 x eps) x) (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (* eps (+ eps x)) (.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 x eps) (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps))) (.f64 eps eps))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 (.f64 (.f64 eps x) x) eps) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) x) x (.f64 (.f64 eps #s(literal 1/2 binary64)) eps)) (.f64 x x) (.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) #s(approx (+ (* -1/6 eps) (* -1/2 x)) (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps))

Outputs

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

Calls

3 calls:

13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	x
8.0ms	eps

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`eps`
98.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes30.0ms (0.2%)

Memory

-0.5MiB live, 37.2MiB allocated

Counts

27 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (.f64 (.f64 (.f64 eps x) x) #s(literal 1/12 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x (/.f64 x eps) x) (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (* eps (+ eps x)) (.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 x eps) (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps))) (.f64 eps eps))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 (.f64 (.f64 eps x) x) eps) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) x) x (.f64 (.f64 eps #s(literal 1/2 binary64)) eps)) (.f64 x x) (.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) #s(approx (+ (* -1/6 eps) (* -1/2 x)) (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (*.f64 #s(literal -1/6 binary64) eps)) eps (cos.f64 x)) eps))

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

Calls

3 calls:

14.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps
7.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes41.0ms (0.3%)

Memory

-23.9MiB live, 22.6MiB allocated

Counts

24 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (.f64 (.f64 (.f64 eps x) x) #s(literal 1/12 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x (/.f64 x eps) x) (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (* eps (+ eps x)) (.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 x eps) (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps))) (.f64 eps eps))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 (.f64 (.f64 eps x) x) eps) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) x) x (.f64 (.f64 eps #s(literal 1/2 binary64)) eps)) (.f64 x x) (.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))

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

Calls

3 calls:

27.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps
7.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes27.0ms (0.2%)

Memory

-9.5MiB live, 28.7MiB allocated

Counts

23 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (*.f64 eps x) x) #s(literal -1/2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) #s(approx ( eps (+ eps x)) (*.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) #s(approx (+ (* (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) x) (+ (* (* eps eps) -1/6) 1)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (+.f64 x eps) #s(literal -1/2 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (/ (* (neg (* eps eps)) (cos x)) (neg eps)) (fma.f64 (fma.f64 (.f64 (.f64 eps x) x) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps (+ eps x)) 1/12) -1/2) x) (* eps -1/2)) (.f64 (.f64 (.f64 eps x) x) #s(literal 1/12 binary64))) x (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 x (/.f64 x eps) x) (/.f64 #s(literal 1 binary64) eps)) eps) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 #s(approx (* eps (+ eps x)) (.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 #s(literal -1/2 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 (fma.f64 (fma.f64 (.f64 eps (+.f64 eps x)) #s(literal 1/12 binary64) #s(literal -1/2 binary64)) x (.f64 eps #s(literal -1/2 binary64))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (.f64 (neg.f64 (.f64 eps eps)) #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (+ (* -1/6 (* (cos x) eps)) (* (sin x) -1/2)) eps) (cos x)) (fma.f64 #s(approx (+ (* (+ (* (* eps eps) 1/12) -1/2) x) (* -1/2 eps)) (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 x eps) (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps))) (.f64 eps eps))) x (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 #s(approx (* (neg (* eps eps)) (cos x)) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 (.f64 (.f64 eps x) x) eps) (.f64 (.f64 eps eps) #s(literal -1/24 binary64))) x) x (.f64 (.f64 eps #s(literal 1/2 binary64)) eps)) (.f64 x x) (.f64 (neg.f64 eps) eps))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Outputs

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

Calls

3 calls:

12.0ms	x
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	eps

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory

19.4MiB live, 19.4MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`eps`
97.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory

15.2MiB live, 15.2MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.6%	1	`x`
97.6%	1	`eps`
97.6%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes22.0ms (0.2%)

Memory

-23.1MiB live, 14.6MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

16.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps
3.0ms	x

Results

Accuracy	Segments	Branch
97.6%	1	`x`
97.6%	1	`eps`
97.6%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.6%	1	`x`
97.6%	1	`eps`
97.6%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory

9.5MiB live, 9.5MiB allocated

Accuracy

Total -58.5b remaining (-2857.2%)

Threshold costs -58.5b (-2857.2%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify42.0ms (0.3%)

Memory

3.7MiB live, 41.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	367
1	144	367
2	146	367
3	147	367

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps) eps (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))

Outputs
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps) eps (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) (.f64 eps eps) #s(literal -1/48 binary64)) eps) eps) eps (*.f64 #s(literal 1/2 binary64) eps)))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 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)) #s(literal 2 binary64)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))))
(.f64 #s(approx (cos (/ (+ ( 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) (.f64 #s(approx (sin ( 1/2 (+ 0 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)) #s(literal 2 binary64)))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #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)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx (+ ( -1/6 (* (cos x) eps)) (* (sin x) -1/2)) (fma.f64 #s(literal -1/6 binary64) eps (*.f64 #s(literal -1/2 binary64) x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (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))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 eps x)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (+.f64 x eps) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps x) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 x eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps))

soundness1.5s (11.7%)

Memory

0.9MiB live, 789.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	386	3975
1	1177	3719
2	3278	3637
3	7926	3637
0	8160	3377
0	107	496
1	314	496
2	775	489
3	2829	489
4	6198	489
0	8141	458
0	78	546
0	117	540
1	474	528
2	4250	528
0	10641	513
0	6	16
0	10	16
1	53	16
2	380	16
3	4766	16
0	8210	16
0	478	6299
1	1449	5996
2	4208	5913
0	8794	5456

Stop Event

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

Compiler

Compiled 491 to 311 computations (36.7% saved)

preprocess153.0ms (1.2%)

Memory: -13.5MiB live, 230.8MiB allocated
Compiler: Compiled 482 to 222 computations (53.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	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	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	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%)

sample6.7s (53%)

explain100.0ms (0.8%)

preprocess35.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0%)

localize30.0ms (0.2%)

series5.0ms (0%)

simplify170.0ms (1.4%)

rewrite150.0ms (1.2%)

eval36.0ms (0.3%)

prune8.0ms (0.1%)

simplify233.0ms (1.8%)

localize156.0ms (1.2%)

series66.0ms (0.5%)

simplify236.0ms (1.9%)

rewrite197.0ms (1.6%)

eval148.0ms (1.2%)

prune86.0ms (0.7%)

simplify112.0ms (0.9%)

localize177.0ms (1.4%)

series49.0ms (0.4%)

simplify166.0ms (1.3%)

rewrite202.0ms (1.6%)

eval209.0ms (1.7%)

prune55.0ms (0.4%)

simplify156.0ms (1.2%)

localize268.0ms (2.1%)

series58.0ms (0.5%)

simplify231.0ms (1.8%)

rewrite210.0ms (1.7%)

eval155.0ms (1.2%)

prune44.0ms (0.4%)

regimes61.0ms (0.5%)

regimes31.0ms (0.2%)

regimes73.0ms (0.6%)

regimes54.0ms (0.4%)

regimes51.0ms (0.4%)

regimes31.0ms (0.2%)

regimes30.0ms (0.2%)

regimes41.0ms (0.3%)

regimes27.0ms (0.2%)

regimes13.0ms (0.1%)

regimes10.0ms (0.1%)

regimes22.0ms (0.2%)

regimes7.0ms (0.1%)

regimes5.0ms (0%)

simplify42.0ms (0.3%)

soundness1.5s (11.7%)

preprocess153.0ms (1.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	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